A rectangular floor that is 4 metres wide is to be completely covered with square tiles, each with the side of length 0.25 metre. What is the least number of such tiles required?
A. The length of the floor is three times the width.
B. The area of the floor is 48 square metres.
MAT 2004 Question Paper
Each item is followed by two statements A and B. Answer each question using the following Options :
Solution
Width of floor = 4 m and side of square tile = 0.25 m. Now, to find the number of tiles required we need to divide the area of floor by area of tile.
A) : Length = 12 m, thus area of floor = 48 sq. mt
Hence, this statement is sufficient.
B) : Area of floor = 48 sq. mt
Hence, this statement is also sufficient.
=> Ans - (B)
Each student in a class of 40 students voted for exactly one of the three candidates A, B or C for the post of class representative. Did candidate A receive the maximum votes from the 40 votes cast?
A. Candidate A received 11 of the votes
B. Candidate C received 14 of the votes
Solution
Total number of student in class = 40
A) : Candidate A received 11 of the votes
Since, A received less than half the number of votes, then A did not receive the maximum number of votes.
Thus, statement A alone is sufficient.
B) : Candidate C received 14 of the votes
Now, A could have received more than 20 votes or even less than 14, since it cannot be determined, hence this statement alone is not sufficient.
=> Ans - (A)
$$I_1, I_2 and I_3$$ are lines in a plane. Is $$I_1$$ perpendicular to $$I_3$$?
A. $$I_1$$ is perpendicular to $$I_2$$
B. $$I_2$$ is perpendicular to $$I_3$$
Solution
Clearly, each statement alone is insufficient, as there is information about only two lines in each statement.
By combining, both statements, we get that if $$I_1$$ is perpendicular to $$I_2$$ and $$I_2$$ is perpendicular to $$I_3$$ , then $$I_1$$ is parallel to $$I_3$$
Thus, the answer to the question is : No, $$I_1$$ is not perpendicular to $$I_3$$, which is feasible by combining both statements.
=> Ans - (C)
Was 70 the average grade on a class test?
A. On the test, half of the class had grades below 70 and half of the class had grades above 70.
B. The lowest grade on the test was 45 and the highest grade on the test was 95.
Solution
A) : Let us assume there are two students in the class, scores of each are 68 and 73 respectively. (Since, half scored less than 70 and half more than 70)
Now, average is not equal to 70, but if each scored 68 and 72, then the average will be 70.
Since, marks are not given, hence this statement alone is not sufficient.
B) : Similarly this statement alone is also not sufficient, as marks of rest of the students are not given.
Even by combining both statements, we wont be able to find the average.
=> Ans - (D)
If $$x$$ is an integer, then what is the value of $$x^2$$ ?
A. $$\left(\frac{1}{5}\right) < \left(\frac{1}{(x + 1)}\right) < \left(\frac{1}{2}\right)$$
B. $$(x - 3) (x- 4) = 0$$
Solution
A) : $$\left(\frac{1}{5}\right) < \left(\frac{1}{(x + 1)}\right) < \left(\frac{1}{2}\right)$$
=> $$2<(x+1)<5$$
=> $$1<x<4$$
Thus, possible values of $$x$$ are : 2, 3 and since there is not a unique value, hence this statement alone is insufficient.
B) : $$(x - 3) (x- 4) = 0$$
=> $$x=3,4$$
Similarly, this statement alone is also not sufficient. But by combining both statements, we get : $$x=3$$ and $$x^2=9$$
=> Ans - (C)
Refer to the given line graph and the pie charts to answer these questions:
How many hectares of FSI has been distributed between 1994-2002?
Solution
From the given line graph, we know that the distribution of FSI is done each year given from 1994 to 2001, but for the year value of FSI is not given, we will calculate for years from 1994 to 2001.
40+80+120+100+115+120+145+120 = 840
And, these values are given in '000 hectares.
Hence, FSI has been distributed between 1994-2001 = 8,40,000
Now, looking at the options, we can conclude that from 1994-2002, the total FSI distribution will be more than this.
Hence, only option D is possible.
All other options are less than 8,40,000.
How many years witnessed a decline in FNI and an increase in FSI?
During 1994-2002, the greatest proportion of FNI was put to commercial use in
Study the information given below to answer these questions:
Investing in real estate would be a profitable venture at this time. A survey in House magazine revealed that 85% of the magazine's readers are planning to buy a second home over the next few years. A study of the real estate industry, however, revealed that the current supply or homes could only provide for 65%of that demand each year.
Which of the following, if true, reveals a weakness in the evidence cited above?
Which of the following, if true, would undermine the validity of the investment advice in the paragraph above?
The following graph represents the Gross Receipts of three fast food restaurants from 2000-2002. Use it to answer these questions:
The 2000-2002 gross receipts for Mega Burger exceeded those of Pizza Pie by approximately
Solution
Gross receipts of mega burger = 2.5 + 2.5 + 3.4 = 8.4 million
Gross receipts of pizza pie = 1 + 2 + 3 = 6 million
=> Required difference $$\approx2$$ million
=> Ans - (B)
From 2001-2002, the percent increase in receipts for Pizza Pie exceeded the percent increase of Mega Burger by approximately
Solution
% increase in receipts of pizza pie from 2001-2002 = $$\frac{(3-2)}{2}\times100=50\%$$
% increase in receipts of mega burger from 2001-2002 = $$\frac{(3.4-2.5)}{2.5}\times100=36\%$$
=> Required difference $$\approx15\%$$
=> Ans - (D)
The 2002 decline in Crunchy Chicken receipts may be attributed to the
Solution
In 2002, there are increasing receipts of burgers and pizzas, but we cannot say for sure, why it declined for crunchy chicken.
=> Ans - (C)
The Following graphs represent Gross Receipts of all the major fast Food restaurants from 2001-2003. Use them to answer these questions:
The gross receipts for 2001 are approximately what percent of the gross receipts for all the three years?
Solution
Gross receipts for 2001 = Rs. 75,00,000
Gross receipt for all three years = Rs. (75,00,000+85,50,000+81,00,000) = Rs. 2,41,50,000
=> Required percentage = $$\frac{7500000}{24150000}\times100\approx30\%$$
=> Ans - (A)
Over all the three years, the average percentage of gross receipts for Crunchy Chop exceeds the average percentage of gross receipts for Pizza Pie by approximately
Solution
Gross receipts of Crunchy Chop over the years = $$(\frac{46.3}{100}\times75,00,000)+(\frac{40.60}{100}\times85,50,000)+(\frac{12.30}{100}\times81,00,000)$$
= $$34,72,500+34,71,300+9,96,300=79,40,100$$
Gross receipts of Pizza Pie over the years = $$(\frac{12.80}{100}\times75,00,000)+(\frac{24.60}{100}\times85,50,000)+(\frac{37}{100}\times81,00,000)$$
= $$9,60,000+21,03,300+29,97,000=60,60,300$$
=> Required % $$\approx\frac{(80,00,000-60,00,000)}{60,00,000}\times100$$
= $$\frac{100}{3}=33.3\approx30\%$$
=> Ans - (B)
The gross receipts earned by the other restaurants in 2002 amount to precisely
Solution
Total gross receipts for 2002 = Rs. 85,50,000
Gross receipts earned by the other restaurants in 2002 = $$\frac{5.3}{100}\times85,50,000$$
= Rs. 4,53,150
=> Ans - (D)
The data in the following table and graph pertains to the Fellow and Associate categories of professionals. Study the data and line graph given below to answer these Questions:
Number of branches in each region
I. Western Region — 14
II. Southern Region — 26
III. Eastern region — 3
IV. Central Region — 17
V. Northern Region — 7
The total number of associates is nearly ............ times the total number of Fellows of all the five regions.
Solution
Total number of associates of all the five regions = 79291
Total number of fellows of all the five regions = 16093
=> Required ratio = $$\frac{79291}{16093}\approx\frac{80000}{16000}=5$$
=> Ans - (B)
The category showing the total number of Fellows of all the regions as nearly one - ninth of the total Associates of all the regions is
Solution
We need the ratio of Associates : Fellows = 9 : 1
(A) : Full time = $$\frac{61286}{12985}\approx4.5$$
(B) : Part time = $$\frac{6218}{1762}\approx3.5$$
(C) : Not in practice = $$\frac{11787}{1346}\approx9$$
=> Ans - (C)
The regions having the number of branches in the ratio 1 : 2 are
Solution
Clearly, number of branches in northern region = 7
and number of branches in western region = 14
=> Required ratio = $$\frac{7}{14}=1:2$$
Thus, northern and western region have branches in the ratio = 1:2
=> Ans - (D)
The average number of Fellows per branch of the Eastern region is approximately
Solution
Number of fellows of eastern region (III) = 2345
Number of branches = 3
=> Required average = $$\frac{2345}{3}=781.67\approx780$$
=> Ans - (B)
The average growth of membership per year is
Solution
Average growth of membership per year = (membership in last year - membership in first year)/difference in years
= $$\frac{(49324-29505)}{5}\approx\frac{19820}{5}=3964$$
=> Ans - (B)
Each of these questions consists of two quantities, one in Column A and the other in Column B. Compare the two quantities and mark your answer as
Quantities 1 : The number of posts needed for a fence 144 m long when posts are placed 1.2 m apart.
Quantities 2 : 12 posts.
Solution
Quantity 1 : Number of posts needed = $$\frac{144}{1.2}=120$$ posts
Quantity 2 : 12 posts
=> Quantity 1 is greater.
=> Ans - (A)
Quantities 1 : $$3\left(\frac{1}{2}\right)\%$$
Quantities 2 : $$3\left(\frac{35}{1000}\right)$$
Solution
Quantity 1 : $$3\left(\frac{1}{2}\right)\%$$
= $$\frac{7}{2}\times\frac{1}{100}=0.035$$
Quantity 2 : $$3\left(\frac{35}{1000}\right)$$
= $$0.105$$
=> Quantity 2 is greater.
=> Ans - (B)
Quantities 1 : Distance covered by a motorist going at 50 km per hour from 10:55 p.m. to 11:25 p.m. the same evening is
Quantities 2 : 25 km
Solution
Quantity 1 : Distance covered in half hour travelling at 50 km/hr
= $$\frac{1}{2}\times50=25$$ km
Quantity 2 : $$25$$ km
Thus, both are equal.
=> Ans - (C)
Quantities 1 : $$\left(\frac{x}{4}\right)\%$$ of 400
Quantities 2 : $$x$$
Solution
Quantity 1 : $$\left(\frac{x}{4}\right)\%$$ of 400
= $$\frac{x}{400}\times400=x$$
Quantity 2 : $$x$$
Thus, both are equal.
=> Ans - (C)
Quantities 1 : The average of $$\surd81, 60\%, 1\left(\frac{1}{2}\right)$$
Quantities 2: 3
Solution
Quantity 1 : Average = $$\frac{9+0.6+1.5}{3}$$
= $$\frac{11.1}{3}=3.7$$
Quantity 2 : 3
=> Quantity 1 is greater.
=> Ans - (A)
In each of these questions, there is a statement with two assumptions numbered I and II. Consider the statement and the assumptions to decide which assumption is/are implicit in the statement. Give your answer as
Of all the newspapers published in Bangalore, readership of TTI is the highest in the metropolis.
I. TTI is not popular in mofussil areas.
II. TTI has the popular feature of political cartoons in it.
If any time, you have financial difficulties, come to me, I will help you out.
I. You have financial difficulties.
II. promise to provide you financial help.
Given below are two statements followed by two conclusions numbered I and II. Assume the statements to be true even if they show variance from your own experience. Decide which conclusion logically follows from the two statements. Give your answer as
Some nurses are nuns.
Maya is a nun.
I. Some nuns are nurses.
II. Some nurses are not nuns.
Solution
The venn diagram for above statements is :
Conclusions : I. Some nuns are nurses = true
II. Some nurses are not nuns = may or may not be true (depending on first).
Thus, either conclusion I or II follows.
=> Ans - (C)
All apples are oranges.
Some oranges are papayas.
I. Some apples are papayas.
II. Some papayas are apples.
Solution
The venn diagram for above statements is :
Conclusions :I. Some apples are papayas = false
II. Some papayas are apples. = false
Thus, neither conclusion follows.
=> Ans - (D)
In each of these questions, there is given a statement followed by two courses of action numbered I and II. A course of action is an administrative step or decision to be taken for improvement, follow up or further action regarding the problem on the basis of the information in the statement. Assume everything in the statement to be true and decide which course of action follows logically from the given statement. Give your answer as
In spite of the principal's repeated warnings, a child was caught exploding crackers secretly in the school.
I. All crackers should be taken away from the child and he should be threatened never to do it again.
II. The child should be severely punished for his wrong act.
Solution
Since the act has been repeated despite various warnings, so course I would only be another warning and would not help. Severe punishment to set example for him and others is inevitable. Thus, course II shall follow.
=> Ans - (B)
Most children in India are unable to get an education as they get involved in earning a livelihood during their childhood itself.
I. Education should be made compulsoryfor all children upto the age of 14.
II. Employment of children under the age of 14 years should be banned.
The Asian Development Bank has approved a $285 million loan to finance a project to construct coal ports by Madras port and Paradip porttrusts.
I. India should use financial assistance from other international financial organisations to develop such ports in other places.
II. India should not seek assistance from foreign agencies.
Solution
Such kind of products should be encouraged because they form important assets and will bring lot of profit in the country. So, India should use financial assistance.
Thus only action I follows.
=> Ans - (A)
In answering these questions, you have to use the revenue data for the three companies A, B and C provided in the graph:
Which quarter has the highest average revenue?
Solution
Quarter which has the highest revenue will also have the highest average revenue. Revenue of Quarter :
First = 4+5+10 = 19
Second = 6+6+10 = 22
Third = 8+5+12 = 25
Fourth = 10+6+11 = 27 [MAX]
=> Ans - (D)
What is the total revenue for all the companies in all the quarters?
Solution
Total revenue for all the companies in all the quarters
= $$(4+5+10)+(6+6+10)+(8+5+12)+(10+6+11)=93$$
=> Ans - (D)
In each of these question, you are given two statements. To answer these questions, you can use oneor both the statements. Give your answer as
How many hours will it take for all the students and teachers together to put up a tent?
A. There are 4 teachers and 7 students.
B. All the teachers working together can put up the tent in 5 hours while all the students working together can do so in 3 hours.
Solution
Statement A alone is insufficient, as there is no time given and statement B alone is sufficient, as the number of teachers and students are missing.
All the teachers can complete 1/5 of work in 1 hour and all students can complete 1/3 of work in 1 hour. Therefore in 1 hr they can complete 8/15 of work in 1 hour and total work will be completed in 15/8 hours.
$$\therefore$$ Statement B alone is sufficient.
=> Ans - (B)
What is the remainder when the square of N is divided by 5?
A. When N is divided by 5, the remainder is 3.
B. N is an even integer.
Solution
A : When N is divided by 5, the remainder is 3.
=> $$N=5k+3$$, where $$k$$ is an whole number.
Let $$k=0$$, => $$N=3$$
Thus, when $$N^2=9$$ is divided by 5, remainder = 4
=> Statement A alone is sufficient.
Clearly, second statement is insufficient, as there can be multiple solutions.
=> Ans - (A)
What is the value of the 2-digit number ab?
A. The difference between its digits is 4.
B. The sum of its digits is 4.
Solution
Let the digits of the number be $$x$$ and $$y$$
Clearly, each statement alone is not sufficient as there can be many possibilities. By combining the above statements, we get :
=> $$x+y=4$$ and $$x-y=4$$
By solving above equations, we get : $$x=4$$ and $$y=0$$, thus number = 40
$$\therefore$$ Both statements together are sufficient.
=> Ans - (C)
a, b and c are the three digits of a number abc. abc is a multiple of 3. Find (a + b + C).
A. a = 3, b = 4.
B. C is an odd number.
Solution
If $$abc$$ is a multiple of 3, then $$(a+b+c)$$ will also be multiple of 3.
(A) : $$a=3$$ and $$b=4$$
=> $$3+4+c=3k$$, where $$k$$ is a natural number.
=> Possible values of $$c=2,5,8$$
Thus, statement A alone is not sufficient.
(B) : If C is odd, there can be multiple values of the number, thus statement B alone is insufficient.
By combining above statements together, we get the number as 345
$$\therefore$$ Both statements together are sufficient.
=> Ans - (C)
N is an integer between 1 and 93. What is the value of N?
A. N is both the square and the cube of an integer.
B. The square root of N is divisible by 8.
Solution
(A) : Perfect squares between 1 and 93 = 1,4,9,16,25,36,49,64,81
Perfect cubes between 1 and 93 = 1,8,27,64
=> Possible values of N = 1, 64
Thus, first statement alone is not sufficient.
(B) : Number of square roots between 1 and 93 = 1,2,3,4,5,6,7,8
Now, since it is divisible by 8, only one possible value of N exist, => $$N=64$$
$$\therefore$$ Statement B alone is sufficient.
=> Ans - (B)
Refer the Following information to answer these questions:
Six items — U, V, W, X, Y and Z are being separated into 3 Groups — Group 1, Group 2 and Group3, according to the following conditions:
(i) The number of items in Group 1 is less than or equal to the number of items in Group 2.
(ii) The number of items in Group2 is less than or equal to the number of items in Group 3.
(iii) Vand W cannot be in the same group.
(iv) X can be in Group 3 onlyif Y is in Group 3.
Which one of the following is an acceptable grouping of the six items?
If Group 1 contains only the item Y, then which of the following must be true?
If W and Y are in the same group and V is in Group 3, then which of the following must be false?
If Group 2 contains only one item, which is neither W nor V, then which of the following must be true?
in each of these questions, a statement is given, followed by two conclusions. Give your answer as
Statement: This world is neither good nor evil; each man manufactures a world for himself.
Conclusions:
I. Some people find this world quite good.
II. Some people find this world quite bad.
Statement: Domestic demand has been increasing faster than the production of indigenous crude oil.
Conclusions:
I. Crude oil must be imported.
II. Domestic demand must be reduced.
Statement: Parents are prepared to pay any price for an elite education to their children.
Conclusions:
I. All parents these days are very well off.
II. Parents have an obsessive passion for a perfect development of their children through good schooling.
Statement: From the next academia year, students will have the option of dropping Mathematics and Science for their school living.
Conclusions:
I. Students who are weak in Science and Mathematics will be admitted.
II. Earlier, the students did not have the choice of continuing their education without these subjects.
Read the following statements to answer these questions.
(i) A,B,C, D, E and F form a group of friends from a club.
(ii) There are two house wives, one lecturer, one architect, one accountant and one lawyer in the group.
(iii) There are 2 married couples in the group.
(iv) The lawyer is married to D who is a housewife.
(v) No lady in the group is either an accountantor architect.
(vi) C, the accountant, is married to F, the lecturer.
(vii) Ais married to D, and E is not a housewife.
Which of the following is a married couple?
What is E's profession?
How many members of the group are males?
How is B related to C?
Which of the statements (i) to (vii) is superfluous to find answers to the questions above?
Study the information given below to answer these questions:
A, B, C, D are all related. A is the daughter of B. B is the son of C. C is the father of D.
Which of the following statements is true?
Which of the following is necessarily false?
Study the information given below to answer these questions:
Anna, Bhai, Nana, Dada, Appa and Bal are brothers. They are having their dinner seated at a round table. Appa is next to Nana who is 3 seats from Dada. Annais seated 2 seats away from Bal.
Which is necessarily true?
If Bal does not want to be with Bhai, then
Which of the following is necessarily true?
Find the missing link in the sequences given in each of these questions:
2, 3, 8, 63, ?
1, 4, 9, 25, ?
Solution
This is a sequence of squares of natural numbers and the numbers are having a difference in AP. Hence 1,2,3,5,7... Hence the next number is 49.
ACD, EGI, JLM, ?
$$\frac{4}{9}, \frac{9}{20}, ( ? ), \frac{39}{86}$$
Solution
As we can clearly observe in the numerator, the numerator of the previous term is multiplied by 2 and 1 is added. So numerator will be 9(2)+1=19
Similarly, denominator of the previous term is multiplied by 2 and then 2 is added. So 20(2)+2=42
Hence the fraction will be 19/42
Q1F, S2E, U6D, W21C, ?
2Z5, 7Y7, 14X9, 23W11, 34V13, ?
Given below are pairs of events 'A' and 'B". You haveto read both the events ‘A' and "B' to decide their nature of relationship. You have to assumethat the information given in ‘A’ and "B"is true and you will not assume anything beyond the given information in deciding your answer. Give your answer as
Event A: The national selectors have decided to retain the same 14 players for the third and final test series against New Zealand.
Event B: India has won the second test against New Zealand.
Solution
As we can clearly see, that New Zealand selection committee won the series hence players have been retained. So A is the effect and B is the immediate and principal cause
Event A : Since Rani's own child had died at birth, she was desperate for another.
Event B : Rani had quietly kidnapped the child, less than two days old, and shipped it out of the hospital.
Solution
As we can clearly see, that Rani had kidnapped the child because she was desperate for another child. Hence B is the effect and A is the principal cause.
For the following questions answer them individually
Renu is elder than Anita. Rocky is younger than Anita. Sohan is elder than Renu. Who is the eldest in the group?
Solution
From the first two statements we get Rocky<Anita<Renu. From the third statement we get, Sohan is elder than Renu. Hence Sohan is the eldest in the group
Among the six cities — P, Q, R, S, T and U — P is not a hill station; Q and T are historical places; S is not an industrial city; P and S are not historical cities; P and Q are not similar kinds of cities. Which of two cities are historical places?
Mr. Brijesh : A public sector company 'ABC' was privatised 3 years ago. It has increased profitability since then. This is a clear indication that industries will fare better in the private sector than in the public sector.
Mr. Sinha : That's wrong. Closer perusal of ABC's balance sheets shows that it has been profitable since the appointment of a professional managing director 3 years ago, while it was still in the public sector.
Which best describes the weakness in Mr. Brijesh's judgement which Mr. Sinha is using?
Informed people generally assimilate information from several divergent sources before coming to an opinion. However, most popular news organisations view foreign affairs solely through the eyes of our State Department. In reporting the political crisis in foreign country B, the news organisations must endeavour to find out alternative sources of information.
Which of the following inferences can be drawn from the argument above?
How many squares are there in the given figure?
A light bulb company produces 2000 light bulbs per week. The manager wants to ensure that standards of quality remain constant from week to week. The manager therefore claims that out of 2000 light bulbs produced per week, 500 light bulbs are rejected. Of the following, the best criticism of the manager's plan is that the plan assumes that
Animesh walked 30 metres towards West, turned to his right and walked 20 metres. He then turnedto his left and walked 10 metres, then turnedto his left and walked 40 metres. He turned to his left and walked 5 metres. He again turned to his left and continued walking. In which direction is Animesh walking now?
A greater number of fresh vegetables is sold in Kanpur than in Lucknow. Therefore, the people in Kanpur have better nutritional habits than those in Lucknow. Each of the following, if true, weakens the conclusions above, except
Traffic safety experts predict that the installation of newly designed seat belts in all cars in India would reduce the average number offatalities per traffic accident by 30%. In order to save lives, the Department of Transport (DOT) is considering requiring automobile manufacturers to install belts of this design in all cars produced after 2005.
Which of the following, if true, represents the strongest challenge to the DOT's proposal?
A decade after a logging operation in India began cutting downtrees in a territory that served as a sanctuary for Bengal tigers, the incidence of tigers attacking humans in nearby villages has increased by 300%. Since the logging operation has reduced the number of acres of woodland per tiger on an average from 16 acres to approximately 12 acres, the scientists have theorised that tigers must need a minimum number of acres of woodland in order to remain content.
Which of the following statements, if true, would most strengthen the scientists’ hypothes is ?
In a certain code language, if A is written as C, B as D, C as E and so on up to Z, then how will PECULIAR be written in that code?
Solution
Each letter is being replaced by a letter that is two places ahead.
P + 2 = R
E + 2 = G
C + 2 = E
U + 2 = W
L + 2 = N
I + 2 = K
A + 2 = C
R + 2 = T
$$\therefore\ $$PECULIAR will be coded as RGEWNKCT in the code language.
Hence, the correct answer is Option C
A company recently registered a big jump in clothing sales after hiring a copywriter and a graphic artist to give its clothing catalogue a magazine-like format designed to appeal to a more upscale clientele. The company is now planning to launch a house wares catalogue using the same concept. The company's plan assumes that
If TV is called Radio’, 'Radio is called Aeroplane’, ‘Aeroplane is called Helicopter’, ‘Helicopter is called Bus’, 'Bus is called Bike’, "Bike is called Water’, "Water is called Frog’, ‘Frog is called Tomato’, ‘Tomato is called Furniture’ and ‘Furniture is called Cigarette’, then what is Tomato sauce made up of?
Solution
We know that tomato sauce is made up of tomato
Since tomato is called furniture, Tomato sauce is made up of furniture.
Hence B is the answer
The Election Commission has revised upwards the ceiling of total expenditure on all counts for Lok Sabha candidates to Rs. x lakh.
Which of the following, if true, will make the ceiling an effective measure for a free and fair election?
Read the following passages carefully to answer the questions.
Passage I :
One of the basic principles of people management for most of the 20th century was to narrow an individual's task down to a small, heavily monitored, transparently cost-effective unit of work. This was particularly the case in many areas of manufacturing, where it was felt to be a necessary route to greater competitiveness. It left the individual with little chance to show any initiative. Today, that tenet is being turned largely on its head. Much more is expected from employees; their value to a company's well-being is increasingly acknowledged, even if not necessarily properly recognised. This transition has been accompanied by the emergence of ‘human resource management’,a term not universally
acknowledged as representing much more than ‘personnel management’, but one which does signify a broader ambit than in the past. Just how much broader is discussed here, along with the widely differing attitudes of trade unions to human resource management and the issues that management must confront. Also examined are the issues that have been preoccupying human resource managers themselves. An example is the rapid emergence of new technology, which puts pressures on workers that cannot always be easily resolved. It is on the nature of good management practice that nothing, in isolation, provides the answer to every prayer. As John Grapper relates, British Airways, which lays claim to being the world’s favourite airline, has embraced human resource management to what is generally considered to be good effect. It sees its employees as frontline troops in the competitive battle with other airlines. Its overall success is acknowledged; witness its ability to produce profits while rivals notch up huge losses. Grapper traces the pressure to re-think heavily monitored, narrowly defined work patterns as having come from Japan,
where the team approach, with decisions made by the consensus, is acknowledged to be a potent competitive weapon. Much of the shift is due to the fact that traditionally structured principles are incompatible with rapid technological change. This is especially so in service industries, where labour accounts for a large majority of total costs, and where employees can beat the forefront of enhancing standards of service. The mixed attitudes of unions to HRM emerge against a background of distrust. Inevitably, if responsibility is pushed further down the organisation, with established lines of authority being eroded, the union's traditional role is called into question. This suspicion is exemplified by a national officer of the Transport and General Workers’ Union, who also accuses employers of often having as their real motivation, a desire to weaken collective strength. An academic's view is that HRM sits uncomfortably with industrial relations, since among other things, managers will endeavour to bypass unions achieve their ends. But not all unions are opposed to HRM, one particularly perceptive view being that it is inevitably an acknowledgement by management that workers should be more involved in decision making. A rider to this is that it brings managers under greater pressure to deliver and opens them to accusations of merely playing lip-service to the concept if they prove unhappy about being challenged. A further view is that HRM in the United Kingdom is a pale shadow of the regimesthat exist in Continental Europe, since the ‘power’ offered to workers is rather illusory and allows little scope for feedback from the workers to the upper echelons of management. This argument could well be supported by the attitudes which are reported in Christopher Lorenz's article about whether or not a value can be put on human resources and if, indeed, management really wishes to do so. Lorenz points to the growing numberof chief executives who are at least paying attention to concepts which enhance the status of employees. But the question is whether this has any more substances than is revealed by the perfunctory acknowledgement in so many company annual reports of how valuable employees are to the organisation. One of the inevitable outcomes of ‘empowerment’ of employeesis that they will make mistakes and that they should be left (for helped) to learn by them. Yet this prospect help make some management's draw back from delegating real power of decision further down the line and thus from taking HRM to its proper conclusion. In a world of rapid technological advance, human resources play a crucial role—but not just in ensuring that the latest piece of technology performs. They are also a barometer of what is achievable and whatis not, as Michael Dixon illustrates. What is particularly clear is that employees' reactions to new technology must be read carefully if they are not to be misinterpreted. For, however impressive any technology might be, some of its technical possibilities may have to be sacrificed in order to match what employees are happy—or can be persuaded—to work with. Even in companies where HRM becomes very much the chief executive's remit, much of the responsibility for ensuring that employees’ views are understood by managementstill falls to the human resource manager. Many managersstill feel vulnerable in the organisational hierarchy. However, Simon Holberton suggests that while they Know whattheir role should be, many human resource managers find themselves insufficiently informed by their companies to design programmes to meet manager's demands. Significantly, training is at the top of the list of their priorities. And while the economic climate has changed considerably for the worse with budgets slashed or put on hold, training is still widely perceived to be one of the most pressing requirements if a wide swathe of companies is not to be left unprepared to take advantage of an economic upturn.
The author would agree with which of the following ?
The success of British Airways can be attributed to
One of the salient features of the Japanese work patternis that
The trade unions oppose human resource management policies because
Why do some managements not allow seeping down of responsibility?
Read the following passages carefully to answer these questions given at the end of each passage:
Passage II :
Definitions of ‘culture’ are contested. In anthropological usage, the word refers to a system of shared meanings through which collective existence becomes possible. However, aS many recent critiques of this position point out, this sense of culture gives no place to the idea of judgement, and hence to the relations of power by which the dominance of ideas and tastesis established. As Said says about Matthew Arnold's view of culture:
"What is at stake in society is not merely the cultivation of individuals, or the development of a class of finely tuned sensibilities, or the renaissance of interests in the classics, but rather the assertively achieved and won hegemonyof an identifiable set of ideas, which Arnold honorifically colls, culture, over all other ideas in society.”
The implications of Arnold's view of culture are profound; they lead us towards a position in which culture must be seen in terms of that which it eliminates as much as that which it establishes. Said argues that when culture is consecrated by the state, it becomes a system of discriminations and evaluations through which a series of exclusions can be legislated from above. By the enactment of such legislation, the state comes to be the primary giver of values. Anarchy, disorder, irrationality, inferiority, bad taste and immorality are, in this way, defined and then located outside culture and civilisation by the state and its institutions. This exclusion of alterity is an important device by which the hegemony of the state is established; either certain ‘others’ are defined as being outside culture, as are ‘mad' people; or they are domesticated, as with penal servitude—Foucault’s monumental studies on the asylum and the prison demonstrate this.
It is this context which we must understand in order to fully appreciate the challenge posed by the community to the hegemony of the state, especially to the notion that the state is the sole giver of values. At the same time, the dangeris that we may in the process he tempted to valourise the community as somehow representing a more organic mode, and therefore a more authentic method of organising culture. Many scholars feel that culture is more organically related to the traditions of groups, whereastraditions are falsely invented by the hands of state. The issues are by no meansas simple, for culture and tradition are not instituted in society once and forever, but are subject to the constant change and flux which are an essential feature of every society. Indeed, the very attempt to freeze and fix cultural traditions may be inimical to their survival. Finally, in the contests between state, communities and collectivities of different kinds on one hand and the individual on the other, we can see the double life of culture: its potential to give radical recognition to the humanity of its subjects as well as its potential to keep the individual within such tightly defined bounds that the capacity to experiment with selfhood—which is also a mark of
humanity—may be jeopardised.
So, we arrive at this double definition of culture. By this | mean that the word ‘culture’ refers to both a system of shared meanings which defines the individual's collective life, as well as a system for the formulation of judgements which are used to exclude alterities, and which thus keep the individual strictly within the bounds defined by the society. It is in view of this that the question of cultural rights seems to me to be placed squarely with in the question of passions rather than interests. It is time now to define passion. After the classical work of Hirschman on political passions, if was usual to think of passions as obstructions in the path of reason. Passions had to be overcome for enlightened interest to emerge. This view of passions is extremely limited. Indeed, certain kinds of revelations, including the recognition of oneself as human, become possible only through passion. If the self is constituted only through the Other—so that desire, cognition, memory
and imagination become possible through the play of passion—then the revelatory role of passion must be acknowledgednot only in the life of the individual but also in the life of the collective. Passion then mustplaya role in politics.
As we hove seen, the demandfor cultural rights at this historical momentis in a context, where cultural symbols have been appropriated by the state, which tries to establish a monopoly over ethical pronouncements. The state is thus experienced as a threat by smaller units, who feel that their ways of life are penetrated, if not engulfed, by this larger unit. The situation is quite the opposite of the relation between the part and the whole in hierarchical systems, a relation seen as the characteristics mark of traditional politics in South Asia. In a hierarchical system, differences between constitutional units were essential for the ‘whole’ to be constituted.
In other words, small units came to be defined by being bearer of special marks in a hierarchical entity. And although by definition they could not be equal in such a system, the very logic of hierarchy assured that they could not be simply engulfed into the higher totality. This was both a source of their oppression as well as a guarantee of their acceptance (though not a radical acceptance) of their place in the world, My argument is not an appeal for a return to hierarchy as a principle of organisation. Rather, it is an effort to locate the special nature of the threat which smaller groups feel.
Culture refers to the
Culture is established through
Solution
This is based on the passage where it explains that culture, especially as defined by Matthew Arnold, refers to a set of dominant ideas that are asserted and spread over other ideas in society.
Which of the following is true?
Achieving selfhood involves
The role of the stole is to
For the following verbal analogies pick the pair that exhibits the most similar relationship to the given analogy:
Autumn; Wither
Augur; Future
Solution
The given analogy is:
Augur: Future => An augur is someone who predicts or foretells the future.
A) Knight: Medieval → A knight is associated with the medieval period but does not predict it.
B) Poet: Century → A poet belongs to a century but does not predict it.
C) Vanguard: Pack → A vanguard leads a group (pack), but this is about leadership, not prediction.
D) Historian: Past → A historian studies and analyzes the past, just as an augur study signs to predict the future. (Correct)
Stately; Demeanour
Rash; Stoic
Solution
Rash means acting without thinking, whereas Stoic refers to someone who remains calm and unemotional. These words are opposites in nature.
A) "Articulate" means well-spoken, and an "Orator" is a public speaker. These words are related but not opposites.
B) "Dubious" means doubtful or suspicious, while "Scoundrel" means a dishonest person. They are not contrasting like "Rash" and "Stoic".
C) "Dolorous" means full of sorrow or grief. "Spouse" refers to a husband or wife. There is no direct opposition between the two.
D) An Agnostic doubts religious beliefs, while a Cleric is a spiritual leader. These two are contrasting, like "Rash" and "Stoic".
Hence, Option D is the correct answer.
From the alternatives provided, choose the one that best fills the blank:
They lament and express their despair ............. the way Gandhi has been forgotten in his own land.
Solution
"Over" is used to indicate what the lament or despair is about.
Hence, the correct sentence is :
They lament and express their despair over the way Gandhi has been forgotten in his own land.
The government ........... on this issue.
After having sought my help, .............
I have known her .......... the end of the World War II.
The landlady .......... since morning.
In each of these questions, you are given a sentence. A part of the sentence is underlined. This is followed by four ways of phrasing the underlined part. Choice (1) repeats the original; the other three are different. Select the version that best rephrases the underlined part:
Many employers now believe that the advancement in technology has improved the, environment for the workers who can now work up to 18 hours a day and still does not feel physically tired.
It is difficult to diagnose malaria because its first symptoms are similar to any viral fever.
To create a new game means expending lot of sweat, and calls for all the members of the development team to play its role with aplomb throughout the long - drawn - out procedure before the game sees the light of the day.
The state has at least twenty colleges of whom only six are officially recognised.
The all-pervasiveness of the Internet has led to a joke, that a few bored homosapiens left to themselves in a single room with a couple of computers for some days, would eventually produce something that would either make Shakespeare jealous or plain wild.
Each of the sentences against these questions has two blanks, each blank indicating that something has been omitted. Choosethe set of words for each blank that best fits the meating of the sentence as a whole:
The term ‘rare earths’ is in fact a , .............. for paradoxically, the rare-earth elements are in actuality ............., being presentin low concentration in virtually all the minerals.
Solution
The sentence talks about the term "rare earths" and how it's not quite accurate because these elements are actually quite common, not rare.
"Misnomer" means a wrong or inaccurate name, which fits perfectly because "rare earths" is not the right term. "Ubiquitous" means something that is found everywhere, which fits because these elements are present in many minerals, just in small amounts.
So, the correct choice is Misnomer — ubiquitous, meaning the term is wrong because these elements are actually found everywhere.
According to the $$12^{th}$$ century cosmologies, the natural philosopher must strive to .......... a state of detached objectivity in order to free his capacity for constructing useful hypothesis from the ................. of unquestioned assumptions and accepted opinions about nature.
The columnist was very gentle when he mentioned his friends but was bitter and ever ........... when he discussed people who ............ him.
She conducted the interrogation not only with dispatch but with .........., being a person who is ......... in manner yet subtle in discrimination.
In these questions, find out the part of the sentence that has an error. Choose 'D' if there is no error.
They cook meals, lay the table and wash up (A)/ clean the house (B)/ and mend the clothes (C)
He seemed distracted (A)/ thinking less about what he was doing tonight (B)/than what he would be doing on the morrow (C).
For an educated man of the time, virtualy the only way to gain power and prestige (A)/ was studying the Confucian classics (B)/and work his way up the ladder (C)/as a scholar-official.
For several reasons (A)/social psychologists have been studying (B)/ the effects competition (C)/ on performance and productivity.
Each of these questions consists of a word, given in CAPITALS, followed by four words. Choosethe word that is most nearly the same in meaning to the word givenin CAPITALS. Since some of the questions require you to distinguish the fine shades of meaning, be sure to consider all the choices before deciding which oneis the best:
DESULTORY
SACCHARINE
Solution
"Saccharine" means excessively sweet, either in taste or in an overly sentimental way. "Syrupy" is the closest synonym, as it also means something overly sweet or sentimental.
TENACIOUS
CONJURER
Each of these questions consists of a word, followed by four words. Choose the word that is most nearly opposite in meaning to the word given in question:
RADICAL
FLAMBOYANT
TANTALISING
Solution
"Tantalizing" means tempting, teasing, or arousing desire without fulfillment.
Now, let’s analyze the options:
A) Toiling → Means working hard; not opposite to "tantalizing."
B) Seance → A spiritual meeting; unrelated.
C) Repulsive → Means disgusting, unattractive, or revolting, which is the opposite of something that is tempting or enticing.
D) Seamy → Means unpleasant or sordid, but not exactly opposite to "tantalizing."
Thus, the best antonym is "Repulsive."
INEFFABLE
For the following questions answer them individually
The average of 10 numbers is 40.2. Later it is found that two numbers have been wrongly added. The first is 18 greater than the actual number and the second number added is 13 instead of 31. Find the correct average.
Solution
To rectify the mistake, we need to do the operation on the total = $$(-18)+(-13+31)=0$$
$$\because$$ By adding zero, there will be no change in the sum of the numbers, thus the average will remain same = 40.2
=> Ans - (A)
In a class of 50 students, 23 speak English, 15 speak Hindi and 18 speak Punjabi. 3 speak only English and Hindi, 6 speak only Hindi and Punjabi and 6 speak only English and Punjabi. If 9 can speak only English, then how many students speak all the three languages?
Solution
The total students who speak English are = 23
According to the venn diagram = $$9+3+6+x=23$$
=> $$x=23-18=5$$
$$\therefore$$ 5 students speak all the three languages.
=> Ans - (D)
Two spinning machines A and B can together produce 3,00,000 metres of cloth in 10 hours. If machine B alone can produce the same amount of cloth in 15 hours, then how much cloth can machine A produce alone in 10 hours?
Solution
Effciency of machine A alone = $$\frac{1}{10}-\frac{1}{15}$$
= $$\frac{3-2}{30}=\frac{1}{30}$$
Thus, machine A alone produce 3,00,000 metres of cloth in 30 hours
$$\therefore$$ In 10 hours, machine A alone can produce = $$\frac{300000}{30}\times10=1,00,000$$ metres
=> Ans - (B)
37.85% and 92% alcoholic solutions are mixed to get 35 litres of an 89% alcoholic solution. How many litres of each solution are there in the new mixture?
Solution
Let $$x$$ and $$(35-x)$$ litres of each solution be mixed.
=> $$37.85\%$$ of $$x+$$ $$92\%$$ of $$(35-x)=89\%$$ of $$35$$
=> $$37.85x+92(35-x)=89\times35$$
=> $$37.85x-92x=(89\times35)-(92\times35)$$
=> $$54.15x=35\times3=105$$
=> $$x=\frac{105}{54.15}\approx1.94$$
$$\therefore$$ 1.94 litres of the first and 33.06 litres of the second
=> Ans - (A)
A train leaves Station X at 5 a.m. and reaches Station Y at 9 a.m. Another train leaves Station Y at 7 a.m. and reaches Station X at 10.30 a.m. At what time do the two trains cross each other?
Solution
Time taken by first train = 4 hours and time taken by second train = 3.5 hours
Since, distance travelled for both is same, ratio of time = $$8:7$$
=> Ratio of speeds of both trains (speed is inversely proportional to time) = $$7:8$$ respectively.
Let speed of first train be $$7x$$ km/hr and speed of second train be $$8x$$ km/hr and thus total distance between two stations = $$28x$$ km
Thus, distance travelled by first train in first two hours (till second train starts) = $$14x$$ km
=> Remaining distance between the trains at 7 am = $$14x$$ km and relative speed coming in opposite directions = $$7x+8x=15x$$ km/hr
Time taken for them to meet each other = $$\frac{14x}{15x}=\frac{14}{15}\times60=56$$ minutes
$$\therefore$$ The two trains will meet at 7:56 am
=> Ans - (B)
What is the value of M and N respectively if M39048458N is divisible by 8 and 11, where M and are single digit integers ?
Solution
Expression : M39048458N
For above number to be divided by 8, the last three digits, i.e. $$58N$$ must be divided by 8, => $$N=4$$
Now, for the number $$M390484584$$ to be divided by 11, difference between sum of even digits and sum of odd digits must be divided by 11.
=> Sum of even digits = $$(3+5+8+0+4)=20$$
=> Sum of odd digits = $$(8+4+4+9+M)=(25+M)$$
required difference = $$(25+M)-20=11$$
=> $$M=6$$
$$\therefore$$ $$(M,N)=(6,4)$$
=> Ans - (C)
Peter got 30% of the maximum marks in an examination and failed by 10 marks. However, Paul who took the some examination got 40% of the total marks and got 15 marks more than the passing marks. What were the passing marks in the examination?
Solution
Let maximum marks in the examination be $$100x$$ and passing marks be $$y$$
Peter got 30% of the maximum marks, => $$30x+10=y$$ ----------(i)
Similarly, for Paul = $$40x-15=y$$ -------(ii)
Subtracting equation (i) from (ii), => $$10x=25$$
=> $$x=2.5$$
Substituting it in equation (ii), we get : Passing marks = $$y=85$$
=> Ans - (D)
The marked price of a certain commodity is 30% higher than its cost price. A discount of 20% on the marked price makes the selling price Rs. 208. What is the net profit as a percent of cost price?
Solution
Let cost price of article be Rs. $$100x$$
=> Marked price = Rs. $$130x$$
After 20% discount, selling price = $$\frac{80}{100}\times130x=208$$
=> $$4\times26x=208$$
=> $$x=2$$ ---------(i)
Thus, cost price of article = Rs. 200
$$\therefore$$ Net profit as percent of cost price = $$\frac{(SP-CP)}{CP}\times100$$
= $$\frac{(208-200)}{200}\times100=4\%$$
=> Ans - (B)
The perimeter of a rectangular field is 52 m. If the length of the field is 2 m more than thrice the breadth, then what is the breadth of the field?
Solution
Let the breadth of the field be $$x$$ m and length = $$(3x+2)$$ m
=> Perimeter of rectangular field = $$2[(x)+(3x+2)]=52$$
=> $$4x+2=26$$
=> $$4x=26-2=24$$
=> $$x=\frac{24}{4}=6$$ m
=> Ans - (D)
In a class-room, there are 6 students. We need to divide them into 3 pairs for the purpose of assigning homework. In how many ways can we make such pairs?
Solution
To select first pair, we need to choose 2 students out of 6, this can be done in $$C^6_2$$ ways
Similarly, for the next 2 pairs = $$C^4_2$$ and $$C^2_2$$ ways
Now, to eliminate repetition, required number of ways = $$\frac{C^6_2\times C^4_2\times C^2_2}{3!}$$
= $$\frac{15\times6\times1}{6}=15$$
=> Ans - (C)
Train A travelling at 60km/hr leaves Mumbai for Delhi at 6 p.m. Train B travelling at 90 km/hr also leaves Mumbai for Delhi at 9 p.m. Train C leaves Delhi for Mumbai at 9 p.m. If all the three trains meet at the some time between Mumbai and Delhi, then what is the speed of Train C if the distance between Delhi and Mumbai is 1260 km?
Solution
Distance travelled by train A in 3 hours (till 9 p.m.) travelling at 60 km/hr = $$60\times3=180$$ km
Relative speed of Train A and B travelling in same direction = $$90-60=30$$ km/hr
Now, time when train A and train B will meet (Train C will also meet at this point, given) = $$\frac{180}{30}=6$$ hours
Thus, they will meet at 3 a.m. at a distance of $$(90\times6)=540$$ km from Mumbai = $$1260-540=720$$ km from Delhi.
$$\therefore$$ Speed of train C = $$\frac{720}{6}=120$$ km/hr
=> Ans - (C)
A boat, while going down-stream in a river covered a distance of 50 miles at an average speed of 60 miles per hour. While returning, because of the water resistance, it took one hour fifteen minutes to cover the same distance. What was the average speed during the whole journey?
Solution
Time taken by boat to go downstream = $$\frac{50}{60}=\frac{5}{6}$$ hours
Time taken for upstream distance = $$1+\frac{1}{4}=\frac{5}{4}$$ hours
Total time = $$\frac{5}{6}+\frac{5}{4}=\frac{25}{12}$$ hours and total distance covered = $$50+50=100$$ miles
$$\therefore$$ Average speed = total distance/total time
= $$\frac{100}{\frac{25}{12}}=48$$ mph
=> Ans - (B)
What is the third term in a sequence of numbers that leave remainders of 1, 2 and 3 when divided by 2, 3 and 4 respectively?
Solution
L.C.M. (2,3,4) = 12
Number of the form that leave remainders of 1, 2 and 3 when divided by 2, 3 and 4 respectively = $$12x-1$$
$$\because (2-1)=(3-2)=(4-3)=1$$, where $$x$$ is a natural number
Thus, the third number = $$12(3)-1=35$$
=> Ans - (D)
In a special racing event, the person who enclosed the maximum area would be the winner and would get Rs 100 for every square meter of area covered by him/her. Johnson, who successfully completed the race and was the eventual winner, enclosed the area shown in figure below. What is the prize money won? (Note: The arc from C to D makes a complete semi-circle).
AB = 3 m, BC = 10 m, CD = BE = 2 m
Solution
Total area of figure = ar(semi circle) + ar(rectangle BCDE) + ar(triangle ABE)
= $$\frac{\pi}{2} (r)^2 + (BC\times CD)+(\frac{1}{2}\times AB\times BE)$$
= $$1.57 \times(1)^2 + (10\times 2)+(\frac{1}{2}\times 3\times 2)$$
= $$1.57 + 20+3=24.57$$ $$m^2$$
$$\therefore$$ Total amount won $$100\times24.57=Rs.$$ $$2457$$
=> Ans - (B)
If $$2^{2x - 1} + 4^x = 3^{x - \frac{1}{2}} + 3^{x + \frac{1}{2}}$$, then x equals
Solution
Expression : $$2^{2x - 1} + 4^x = 3^{x - \frac{1}{2}} + 3^{x + \frac{1}{2}}$$
=> $$\frac{2^{2x}}{2} + 2^{2x} = \frac{3^x}{\sqrt3} + (3^x \times \sqrt3)$$
=> $$2^{2x}(\frac{1}{2}+1) = 3^x(\frac{1}{\sqrt3}+\sqrt3)$$
=> $$2^{2x}\times\frac{3}{2} = 3^x\times\frac{4}{\sqrt3}$$
=> $$2^{2x-1}\times3^1 = 3^{x-\frac{1}{2}}\times2^2$$
Now, comparing powers of (any one of) 2 or 3, we get : $$x=\frac{3}{2}$$
=> Ans - (D)
A and B can finish a job in 10 days while B and C can do it in 18 days. A started the job, worked for 5 days, then B worked for 10 days and the remaining job was finished by C in 15 days. In how many days could C alone have finished the whole job?
Solution
Let total work to be done{ L.C.M. (10,18)} = 90 units
Let efficiency of A, B and C be $$x,y,z$$ respectively.
A and B can finish a job in 10 days, => $$x+y=\frac{90}{10}=9$$ --------------(i)
Similarly, $$y+z=5$$ --------------(ii)
Adding equations (i) and (ii), => $$x+2y+z=14$$ ----------(iii)
According to ques, A worked for 5 days, B for 10 days and C for 15 days
=> $$5x+10y+15z=90$$
=> $$x+2y+3z=18$$ ---------(iv)
Subtracting equation (iii) from (iv), we get : $$2z=4$$
=> $$z=2$$
$$\therefore$$ Time taken by C alone to finish the work = $$\frac{90}{2}=45$$ days
=> Ans - (C)
If $$8^x 2^y = 512 and 3^{3 x + 2 y} = (3^2)^{(3 * 2)}$$ then what is the value of $$x$$ and $$y$$ ?
Solution
Given : $$8^x 2^y = 512$$
=> $$2^{3x}\times 2^y = (2)^9$$
=> $$2^{3x+y}= (2)^9$$
=> $$3x+y=9$$ -----------------(i)
Also, $$3^{3 x + 2 y} = (3^2)^{(3 * 2)}$$
=> $$3^{3x+2y}= (3)^{12}$$
=> $$3x+2y=12$$ -----------------(i)
Solving equations (i) and (ii), we get : $$x=2$$ and $$y=3$$
=> Ans - (B)
In his wardrobe, Timothy has 3 trousers. One of them is black, the second blue, and the third brown. In his wardrobe, he also has 4 shirts. One of them is black and the other 3 are white. He opens his wardrobe in the dark and picks out one shirt-trouser pair, without examining the colour. What is the likelihood that neither the shirt nor the trouser is black?
Solution
Probability that trouser is not black = $$1-\frac{1}{3}=\frac{2}{3}$$
Probability that shirt is not black = $$1-\frac{1}{4}=\frac{3}{4}$$
$$\therefore$$ Required probability = $$\frac{2}{3}\times\frac{3}{4} =\frac{1}{2}$$
=> Ans - (D)
In a factory, producing parts for an automobile, the parts manufactured on the shop floor are required to go through three quality checks, each conducted after a specific part of the processing on the raw material is completed. Only parts that are not rejected at one stage are put through the subsequent stages of production and testing. If average rejection rates at these three testing machines during a month are 10%, 5% and 2% respectively, then what is the effective rejection rate for the whole plant?
Solution
Successive rejection rate are 10%, 5% and 2% respectively.
Effective rejection rate after first two tests = $$10+5-(\frac{10\times5}{100})$$
= $$15-0.5=14.5\%$$
Similarly, effective rejection rate after third test = $$14.5+2-(\frac{14.5\times2}{100})$$
= $$16.5-0.29=16.21\%$$
=> Ans - (D)
A country follows a progressive taxation system under which the income tax rate applicable varies for different slabs of income. Total tax is computed by calculating the tax for each slab and adding them up. The rates applicable are as follows:
If my annual income is Rs. 1,70,000, then what is the tax payable by me?
Solution
Total tax payable on Rs. 1,70,000
= $$(50,000\times0\%)+(10,000\times10\%)+(90,000\times20\%)+(20,000\times30\%)$$
= $$0+1,000+18,000+6,000$$
= $$Rs.$$ $$25,000$$
=> Ans - (D)
The length of a rectangular plot is increased by 25%. To keep its area unchanged, the width of the plot should be
Solution
Let length of rectangular plot be 4 m and width be 10 m
=> Area = $$lb=40$$ $$m^2$$
After length is increased by 25%, new length = $$5$$ m
=> New width if area is same = $$\frac{40}{5}=8$$ m
$$\therefore$$ Reduction in width = $$\frac{(10-8)}{10}\times100=20\%$$
=> Ans - (D)
A man invests Rs. 5000 for 3 years, at 5% p.a. compound interest reckoned yearly. Income tax at the rate of 20%on the interest earned is deducted at the end of each year. Find the amount at the end of the third year.
Solution
Rate of interest = 5% and income tax rate on interest = 20%
=> 80% of interest is added for next year principal
Now effective rate of interest = 80% of 5% = $$4\%$$ Principal sum = Rs. 5000 and time = 3 years
$$\therefore$$ Amount under compound interest = $$P(1+\frac{r}{100})^t$$
= $$5000\times(1+\frac{4}{100})^3$$
= $$5000\times\frac{26}{25}\times\frac{26}{25}\times\frac{26}{25}$$
= $$17576\times\frac{8}{25}=Rs.$$ $$5624.32$$
=> Ans - (A)
A sum of Rs 36.90 is made up of 180 coins which are either 10 paise coins or 25 paise coins. Determine the number of each type of coins.
Solution
Let number of 10 paise coins be $$x$$ and number of 25 paise coins be $$(180-x)$$
According to ques,
=> $$\frac{1}{10}\times(x)+\frac{1}{4}\times(180-x)=36.90$$
=> $$\frac{x}{10}-\frac{x}{4}+45=36.90$$
=> $$\frac{3x}{20}=8.10$$
=> $$x=8.10\times\frac{20}{3}=54$$
$$\therefore$$ Number of 10 paise coins = 54 and number of 25 paise coins = 126
=> Ans - (B)
A man has 1044 candles. After burning, he can make a new candle from 9 stubs left behind. Find the maximum number of candles that can be made.
Solution
1 candle is made from 9 stubs, => 116 candles will be made from 1044 stubs
From 116 candles, 12 candles can be made with 8 stubs left.
Now total stubs left = $$12+8=20$$, out of which two candles can be made with two stubs left.
Thus, Maximum number of candles that can be made = $$(116+12+2)=130$$
(or) Number of candles made = $$(\frac{1044}{9^1})+(\frac{1044}{9^2})+(\frac{1044}{9^3})\approx130$$
=> Ans - (C)
Badri has 9 pairs of dark blue socks and 9 pairs of black socks. He keeps them all in the same bag. If he picks out three socks at random, then whatis the probability that he will get a matching pair ?
Solution
Since, there are only two types of socks in the bag. So, if Badri pick up 3 socks then certainly two of them are of same type. Thus this is a certain event.
=> Required probability = 1
=> Ans - (C)
A class photograph has to be taken. The front row consists of 6 girls who are sitting. 20 boys are standing behind. The two corner positions are reserved for the 2 tallest boys. In how many ways can the students be arranged?
Solution
The two boys in corner can be arranged in = $$2!$$ ways
Now, the remaining boys can be arranged in = $$18!$$ ways
There are 6 girls who can be arranged in = $$6!$$ ways
$$\therefore$$ Total number of ways in which all the students can be arranged
= $$2!\times18!\times6!$$
= $$18!\times1440$$
=> Ans - (A)
The LCM of two numbersis 280 and their ratio is 7 : 8. The two numbers are
Solution
Let the two numbers be $$7x$$ and $$8x$$
Now, L.C.M. $$(7x,8x)=7\times8\times x$$
According to ques,
=> $$56x=280$$
=> $$x=\frac{280}{56}=5$$
$$\therefore$$ The two numbers are : 35, 40
=> Ans - (C)
A certain number of people were supposed to complete a work in 24 days. The work, however, took 32 days, since 9 people were absent throughout. How many people were supposed to be working originally?
Solution
Using $$M_1D_1=M_2D_2$$
Let $$x$$ people were supposed to work initially.
=> $$x\times24=(x-9)\times32$$
=> $$3x=4(x-9)$$
=> $$3x=4x-36$$
=> $$x=36$$
=> Ans - (C)
In the given diagram, two circles pass through each other's center. If the radius of each circle is 2, then what is the perimeter of the region marked B?
Solution
Two circles with centres A and A' and having radius = 2 cm
$$\angle$$ BAC = $$120^\circ$$ [since ABA' forms a equilateral triangle] and length of an arc = $$\frac{\theta}{360^\circ}\times2\pi r$$
Perimeter of shaded portion = $$2\times($$ length of arc BC$$)$$
= $$2\times(\frac{120^\circ}{360^\circ}\times2\pi r)$$
= $$2\times(\frac{1}{3}\times2\pi\times2)$$
= $$2\times\frac{4\pi}{3}=\frac{8\pi}{3}$$
=> Ans - (A)
Cloth Makers Inc. has p spindles, each of which can produce q metres of cloth on an average in r minutes. If the spindles are made to run with no interruption, then how many hours will it take for 20,000 meters of cloth to be produced?
Solution
Time taken to make $$(pq)$$ metres of cloth = $$r$$ min
=> Time taken to make 20,000 m of cloth = $$\frac{r}{pq}\times20,000$$ minutes
$$\therefore$$ Required time (in hour) = $$20,000\times\frac{r}{60(pq)}$$
=> Ans - (D)
If Dennis is $$\frac{1}{3^{rd}}$$ the age of his father Keith now, and was $$\frac{1}{4^{th}}$$ the age of his father 5 years ago, then how old will his father Keith be 5 years from now?
Solution
Let Keith's present age be $$3x$$ years and Dennis's present age be $$x$$ years
=> According to ques,
=> $$(3x-5)=4\times(x-5)$$
=> $$3x-5=4x-20$$
=> $$x=15$$
$$\therefore$$ Keith's age after 5 years = $$3(15)+5=50$$ years
=> Ans - (D)
A mail-sorting clerk is given 4 envelopes addressed to different people and 4 letters. She has to carefully put the letters in the correct envelopes and then mail them. However, she carelessly puts any letter in any envelope, making sure that each envelope has precisely one of those 4 letters. What is the likelihood that all the letters are in the correct envelope?
The ages of the two persons differ by 20 years. If 5 years ago, the older one be 5 times as old as the younger one, then their present ages, in years, are
Solution
Let present ages of the two persons be $$x$$ and $$(x-20)$$ years
According to ques,
=> $$(x-5)=5\times(x-20-5)$$
=> $$x-5=5x-125$$
=> $$4x=120$$
=> $$x=\frac{120}{4}=30$$
$$\therefore$$ Their present ages = 30, 10 years
=> Ans - (B)
A person has deposited Rs. 13,200 in a bank which pays 14% interest. He withdraws the money and invests in Rs. 100 stock at Rs. 110 which pays a dividend of 15%. How much does he gain or lose?
Solution
Principal sum = Rs. 13,200 and rate of interest = 14%
=> Interest earned = $$\frac{14}{100}\times13200=Rs.$$ $$1848$$
Thus, number of shares purchased = $$\frac{13200}{110}=120$$
=> Income from stock = (15% of Rs. 100) x 120
= $$15\times120=Rs.$$ $$1800$$
$$\therefore$$ Loss = $$1848-1800=Rs.$$ $$48$$
=> Ans - (A)
If a% of x is equal to b% of y, then c% of y is what % of x?
Solution
Given : a% of x is equal to b% of y
=> $$ax=by$$
=> $$y=\frac{ax}{b}$$
Multiplying both sides with $$(\frac{c}{100})$$
=> $$\frac{c}{100}\times y=(\frac{c}{100})\times(\frac{ax}{b})$$
=> $$c\%$$ of $$y=\frac{x}{100}\times\frac{ac}{b}$$
$$\therefore$$ $$c\%$$ of $$y$$ is $$(\frac{ac}{b})\%$$ of $$x$$
=> Ans - (B)
The number of boys is more than the number of girls by 12% of the total strength of the class. The ratio of the number of boys to that of the girls is
Solution
Let total strength of class = 100
Let number of boys be $$x$$ and number of girls be $$(100-x)$$
According to ques,
=> $$x-(100-x)=\frac{12}{100}\times100$$
=> $$2x-100=12$$
=> $$x=\frac{112}{2}=56$$
Thus, boys = 56 and girls = 44
$$\therefore$$ Required ratio = $$\frac{56}{44}=14:11$$
=> Ans - (B)
Ten points are marked on a straight line and eleven points are marked on another straight line. How many triangles can be constructed with vertices from among the above points?
Solution
A triangle can be formed by taking any two points of a straight line and third point on the second straight line
=> Number of ways = $$(C_2^{10}\times11)+(C_2^{11}\times10)$$
= $$495+550=1045$$
=> Ans - (C)
The sum of two numbers is 462 and their highest common factor is 22. What is the maximum number of pairs that satisfy these conditions?
Solution
Let numbers be $$22x$$ and $$22y$$, where $$x$$ and $$y$$ are co-prime numbers.
=> $$22x+22y=462$$
=> $$(x+y)=\frac{462}{22}=21$$
Now, number of possible values of $$(x,y)=(1,20) (2,19) (4,17) (5,16) (8,13) (10,11)$$
$$\therefore$$ There are 6 such pairs.
=> Ans - (D)
In a class, 40% of the boys is same as 1/2 of the girls and there are 20 girls. Total number of students in the class is
Solution
Number of girls = 20
Now, 40% of boys = 10
=> $$100\%$$ boys $$\equiv10\times\frac{100}{40}=25$$
$$\therefore$$ Total students = $$20+25=45$$
=> Ans - (B)
A man bets on number 16 on a roulette wheel 14 times and loses each time. On the $$15^{th}$$ spin, he does a quick calculation and finds out that the number 12 had appeared twice in the 14 spans and is therefore unable to decide whether to bet on 16 or 12 in the $$15^{th}$$ spin. Which will give him the best chance and what are the odds of winning on the bet that he takes? (Roulette has numbers 1 to 36).
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