CAT 2003 Question Paper (Leaked)

The success rate of moving from written test to interview stage for males in 2003 can be given by 637/60133 and for females in the same year can be given by 399/40763 . We can see that the rate of males is clearly more that that of females. hence statement A is false. 

Now the success rate of moving from written test to interview stage for females in 2002 was 138/15389 and for females in the year 2003 was 399/40763.So the  rate in 2002 is less than that in 2003. . Hence both statements are false.

In 2002, the number of females selected for the course as a proportion of the number of females who bought application forms was 48/19236 and for males was 171/61205. So rate for males was higher than that of female. Hence option A is false.

In 2002, among those called for interview, the success rate for females was 48/138 and for males 171/684. So the rate was higher for females .Both are false.  Hence option D.

The percentage of absentees in the written test among females in 2002 was 3847/19236 and in 2003 was 4529/45292. Thus  percentage of absentees decreased from 02 to 03. Hence statement A is true.

The percentage of absentees in the written test among males in 2003 is 3065/63298 which is clearly less than that of female in 2003. Hence statement b is false . Hence option A.

The rate of growth is the slope of the line. In the second and third months, there is an increase in the slope of the line. After the third month, there is a fall in the slope of the line i.e., the rate of growth is declining. Therefore, option b) is the correct answer.

The rate of growth is the slope of the line.

From the graphs, we can see that the slope of the line is maximum for Geeta (red line) in the first two months. So, option a) is the correct answer.

The rate of growth is the slope of the line. During the third month, Geeta has a negative slope whereas all the others have a positive slope. So, the rate of growth of Geeta is the least. Option a) is the correct answer.

Seeta's growth percentage = (57-50)/50 * 100% = 14%

Geeta's growth percentage = (61-49)/49 * 100% = 24.5%

Ram's growth percentage = (61-52)/52 * 100% = 17.30%

Shyam's growth percentage = (61 - 53.5)/53.5 * 100% = 14.01%

So, Seeta's growth percentage is the least.

The number of people with age less than 40 are at least:

In no of children 0 category => 1 male and 1 female

In no of children 1 category => 1 male and 1 female

In no of children 2 category => 1 male and 1 female

In no of children 3 category => 2 male and 1 female

There are atleast 9 people who have age less than 40.

9 people out of 30 people => 30%

There are atmost 23 people with age greater than 35 . Hence (23/30)*100 = 76.67 . So option C. 

There are atleast 4  respondents that fall into the 35 to 40 years age group (both inclusive) . So 400/30 = 13.333 % . Hence , the percentage of respondents that fall into the 35 to 40 years age group (both inclusive) is at least 13.333%. 

It is clear from the table that for products category the percentage of spam mail is increasing from sep02 to June 03 . But the rate at which it is growing is decreasing. Hence option c . 

In dec 2002 , 19 % of all spam mails were from health category and In jun 2003 , 18 % of all spam mails were from health category. Now since the total spam mails received in dec 02 were greater than that in jun 03 . Number of spam mails in health cateory in dec 02 will be greater than that in jun 03. 

Since we don't know by how much more total spam mails were received in Sep 02 as compared to mar 03 we can't compare  the number of spam emails in financial category received in September 2002 as  to that in March 2003. Hence option D. 

Only one security issued in 17 July 2002 was undersuscribed.

The security issued in June 2003 had lower maturity in 2nd round but no. of bids were more . Hence option C. 

For the security issued in 4th June 2003 , the value of non-competitive bids accepted in the first round islesas than that in the second round Hence option D is not true. 

There are in total 7 companies - 3 steels , 2 cement , 2 textile  for which the profit is more than 10% of the turnover. 

There are 2 steel companies with turnover of more than 2000 and having profit less than 300. 

There are 3 steel and 2  cement companies with a turnover more than 1000 and profit exceeding 10% of turnover. hence there are 5 choices for the investor. 

 From table it is clear that for University of California - Berkeley annual tuition fee does not exceed $23,000 and median starting salary is at least $70,000. Hence option D.

There are only 2 colleges - New York university and stanford university which are uniformly better (higher median starting salary AND lower tuition fee) than Dartmouth College. 

We can clearly make out from the given table that there are 8  schools in the list which have single digit rankings on at least 3 of the 4 parameters. 

Number of children of age 9 years or less are 48 and those whose height does not exceed 135 cm are 45 . 45 is lesser, hence answer is 45. 

There are 40 children of age more than 10 years and 25 children that are taller than 150 cm. Considering 25 which is less than 40 . Also there are 9 children whose weight is more than 48 kg. Hence there are 25-9 = 16 children whose weight will bw less than 48 kg and all other requirement. 

Number of children older than 6 years but not exceeding 12 years are 55 and number older than 12 years are 23 . Also children weighing more than 38 kgs are 67. Out of these 67 , 23 will have age more than 12 . Hence we have 67 - 23 = 44 childrens will the given requirement. Hence option C.

From the table we can see that , profitability in A , B ,C , D (4914)/(24568) , (4075)/(25468) , (4750)/(23752) , (3946)/(15782) . So clearly  D has the highest profitability. 

If A acquires firm B , the total sales of 2 firms is 50036 . now the percent market share can be given by 50036*100/89576 which is equal to around 55% . Hence option A. 

We are given that there are two housewives, one professor, one engineer, one lawyer and one accountant among A, B, C, D, E and F.

The other information given is that only two married couples are in the group.

We are given that the lawyer is married to D, and D is a housewife.

We are also given that no woman in the group is either an engineer or an accountant.

C is an accountant, has to be male, and is married to F, who is a professor, who has to be female. 

Putting this information in the table, we get,

We are also given that A is married to the housewife. We know that there are only two married couples in the group, and C and F are already one couple in that group. We also know that D is a housewife and married to a lawyer, so this has to be the second couple, and A has to be the lawyer.

This leaves us with B and E, as well as housewife and engineer professions. Given that E is not a housewife, E has to be the Engineer and B has to be the housewife. Since the engineer cannot be a woman, E has to be a man, and B has to be a woman. 

Putting all the information in the table, we get,

From the table, we can see that A and D are a married couple.

Hence, the correct answer is option D.

We are given that there are two housewives, one professor, one engineer, one lawyer and one accountant among A, B, C, D, E and F.

The other information given is that only two married couples are in the group.

We are given that the lawyer is married to D, and D is a housewife.

We are also given that no woman in the group is either an engineer or an accountant.

C is an accountant, has to be male, and is married to F, who is a professor, who has to be female. 

Putting this information in the table, we get,

We are also given that A is married to the housewife. We know that there are only two married couples in the group, and C and F are already one couple in that group. We also know that D is a housewife and married to a lawyer, so this has to be the second couple, and A has to be the lawyer.

This leaves us with B and E, as well as housewife and engineer professions. Given that E is not a housewife, E has to be the Engineer and B has to be the housewife. Since the engineer cannot be a woman, E has to be a man, and B has to be a woman. 

Putting all the information in the table, we get,

We can see that E is an engineer.

Hence, the correct answer is option A.

We are given that there are two housewives, one professor, one engineer, one lawyer and one accountant among A, B, C, D, E and F.

The other information given is that only two married couples are in the group.

We are given that the lawyer is married to D, and D is a housewife.

We are also given that no woman in the group is either an engineer or an accountant.

C is an accountant, has to be male, and is married to F, who is a professor, who has to be female. 

Putting this information in the table, we get,

We are also given that A is married to the housewife. We know that there are only two married couples in the group, and C and F are already one couple in that group. We also know that D is a housewife and married to a lawyer, so this has to be the second couple, and A has to be the lawyer.

This leaves us with B and E, as well as housewife and engineer professions. Given that E is not a housewife, E has to be the Engineer and B has to be the housewife. Since the engineer cannot be a woman, E has to be a man, and B has to be a woman. 

Putting all the information in the table, we get,

We can see that A, C and E are the three males in the group. 

Hence, the correct answer is option B.

Since C wants either home or finance or none so options A and D are eliminated.
Since F does not want any portfolio if D gets one, Option C is eliminated.

B says that if D gets power or telecom then he must get the other one.Option D clearly violates that.

AVOCADO paint can be manufactured by adding orange and pink in equal quantity. 0.5 ltr of orange would cost 11 and the cheapest way to make pink would be by mixing white and red , so the cost for 0.5 ltr of pink comes out to be 8.75 . SO total cost becomes 11+8.75 = 19.75 Rs. which is the cheapest.

WASHEDORANGE can be made by mixing orange and white , orange can be made by mixing equal quantities red and yellow which would be 1/2 of white quantity. Thus RED, YELLOW, and WHITE in the ratio 1:1:2 are needed.

Cream would be undoubtedly the most profitable as maximum amount of white paint is used in it and white is the cheapest out of all other paints. Hence option B.

We are given that A and G sit to the extreme right on the dias, but the order is not mentioned. So, seats 6 and 7 must be A and G in some order.

B sits in the middle of the presentation, occupying seat number 4.

C and D have to be seated as far as possible, and seats 4, 6 and 7 are already occupied. So, C and D must be placed in seats 1 and 5 in some order.

The seats left are 2 and 3, and E and F have to be placed in those seats in some order.

Putting all the information in the table, we get,

We can see that A, C, D or G can be placed in the corner. But F cannot be seated at either end.

Hence, the correct answer is option C.

We are given that A and G sit to the extreme right on the dias, but the order is not mentioned. So, seats 6 and 7 must be A and G in some order.

B sits in the middle of the presentation, occupying seat number 4.

C and D have to be seated as far as possible, and seats 4, 6 and 7 are already occupied. So, C and D must be placed in seats 1 and 5 in some order.

The seats left are 2 and 3, and E and F have to be placed in those seats in some order.

Putting all the information in the table, we get,

We can clearly see that E and A cannot be seated together.

Hence, the correct answer is option D.

We are given that A and G sit to the extreme right on the dias, but the order is not mentioned. So, seats 6 and 7 must be A and G in some order.

B sits in the middle of the presentation, occupying seat number 4.

C and D have to be seated as far as possible, and seats 4, 6 and 7 are already occupied. So, C and D must be placed in seats 1 and 5 in some order.

The seats left are 2 and 3, and E and F have to be placed in those seats in some order.

Putting all the information in the table, we get,

All the combinations mentioned in options A, B and D are possible from the above configuration. However, the combination mentioned in option C is not possible as E and G cannot be seated on either side of B.

Hence, the correct answer is option C.

Let a,d,j,g be the shots put by ashish,dhanraj,ganesh and jugraj respectively. According to given conditions we have ,
g=a-8;

d+r=37;

j=d+8;

a=5+d;

a+g=40 .

Solving we have a=24, d=19 and j=27.so d+j=45 

From the given statements, we can infer that the amounts spent by the women are Rs.2234, Rs.1193, Rs.1340, and Rs.2517. Also, we know that one of the 5 women spent Rs.1378 more than Chellamma. Also, we know that each woman spent at least Rs.1000.

The person who spent Rs.2234 cannot be the person who spent Rs.1378 more than Chellamma. Also, we know that Chellamma spent the least among the five women.

Case 1:
Chellamma spent Rs.1193.
=> One of the 5 women spent 1193+1378 = Rs.2571.

We know that Shahnaz spent the most. Therefore, Shahnaz should have spent Rs.2571.

Archana didn't spend Rs.2517. Also, Helen spent more than Dhenuka.
Therefore, Helen should have spent Rs.2517.

Dhenuka didn't spend Rs.1340.
Therefore, Dhenuka should have spent Rs. 2234 and Archana should have spent Rs.1340.

However, it has been given that the woman who spent Rs. 2234 arrived before the lady who spent Rs. 1193. According to the given order, Archana arrived before Dhenuka. Therefore, we can eliminate this case. 

Case 2:

Rs.2517 is the highest amount spent. Shahnaz spent Rs.2517.
=> Amount spent by Chellamma = 2517 - 1378 = Rs.1139

Dhenuka didn't spend Rs.1340. Helen spent more than Dhenuka. Therefore, Dhenuka should have spent Rs.1193. 

Now, we know that the woman who spent Rs. 2234 arrived before the lady who spent Rs. 1193. Helen did not arrive before Dhenuka but Archana did. Therefore, Archana should have spent Rs.2234 and Helen should have spent Rs.1340.

According to given conditions amount spent by everyone is,

Hence, option B is the right answer. 

From the given statements, we can infer that the amounts spent by the women are Rs.2234, Rs.1193, Rs.1340, and Rs.2517. Also, we know that one of the 5 women spent Rs.1378 more than Chellamma. Also, we know that each woman spent at least Rs.1000.

The person who spent Rs.2234 cannot be the person who spent Rs.1378 more than Chellamma. Also, we know that Chellamma spent the least among the five women.

Case 1:
Chellamma spent Rs.1193.
=> One of the 5 women spent 1193+1378 = Rs.2571.

We know that Shahnaz spent the most. Therefore, Shahnaz should have spent Rs.2571.

Archana didn't spend Rs.2517. Also, Helen spent more than Dhenuka.
Therefore, Helen should have spent Rs.2517.

Dhenuka didn't spend Rs.1340.
Therefore, Dhenuka should have spent Rs. 2234 and Archana should have spent Rs.1340.

However, it has been given that the woman who spent Rs. 2234 arrived before the lady who spent Rs. 1193. According to the given order, Archana arrived before Dhenuka. Therefore, we can eliminate this case. 

Case 2:

Rs.2517 is the highest amount spent. Shahnaz spent Rs.2517.
=> Amount spent by Chellamma = 2517 - 1378 = Rs.1139

Dhenuka didn't spend Rs.1340. Helen spent more than Dhenuka. Therefore, Dhenuka should have spent Rs.1193. 

Now, we know that the woman who spent Rs. 2234 arrived before the lady who spent Rs. 1193. Helen did not arrive before Dhenuka but Archana did. Therefore, Archana should have spent Rs.2234 and Helen should have spent Rs.1340.

According to given conditions amount spent by everyone is,

Hence, option A is the right answer.

From the given statements, we can infer that the amounts spent by the women are Rs.2234, Rs.1193, Rs.1340, and Rs.2517. Also, we know that one of the 5 women spent Rs.1378 more than Chellamma. Also, we know that each woman spent at least Rs.1000.

The person who spent Rs.2234 cannot be the person who spent Rs.1378 more than Chellamma. Also, we know that Chellamma spent the least among the five women.

Case 1:
Chellamma spent Rs.1193.
=> One of the 5 women spent 1193+1378 = Rs.2571.

We know that Shahnaz spent the most. Therefore, Shahnaz should have spent Rs.2571.

Archana didn't spend Rs.2517. Also, Helen spent more than Dhenuka.
Therefore, Helen should have spent Rs.2517.

Dhenuka didn't spend Rs.1340.
Therefore, Dhenuka should have spent Rs. 2234 and Archana should have spent Rs.1340.

However, it has been given that the woman who spent Rs. 2234 arrived before the lady who spent Rs. 1193. According to the given order, Archana arrived before Dhenuka. Therefore, we can eliminate this case. 

Case 2:

Rs.2517 is the highest amount spent. Shahnaz spent Rs.2517.
=> Amount spent by Chellamma = 2517 - 1378 = Rs.1139

Dhenuka didn't spend Rs.1340. Helen spent more than Dhenuka. Therefore, Dhenuka should have spent Rs.1193. 

Now, we know that the woman who spent Rs. 2234 arrived before the lady who spent Rs. 1193. Helen did not arrive before Dhenuka but Archana did. Therefore, Archana should have spent Rs.2234 and Helen should have spent Rs.1340.

According to given conditions amount spent by everyone is,

Hence, option C is the right answer. 

Considering (i), Ignesh has to eat 6 vadas, since 6 is the only multiple of 3.

Also, using the same information, we can say that a person consumes 2 vadas and 4 idlis.

Using (vii), Bimal eats 2 more idlis than Ignesh.

Possibilities:

Bimal - 8, Ignesh - 6

Bimal - 6, Ignesh - 4

But Ignesh cannot have 4 idlis because the person who eats 4 idlis eats 2 vadas.

Hence we take Bimal - 8 and Ignesh - 6.

Also, we get that Bimal eats 6 - 2 = 4 vadas.

So far, we get the following information.

Using (vi), there is a person who eats twice as many idlis as Mukesh. The only pair satisfying is 8, 4.

So, Mukesh eats 4 idlis. Plus the person who eats 4 idlis eats 2 vadas. Hence, we get

Daljit also eats Vada as per info (v), so we get the following 

(iv) gives us the information that the one who eats 1idli does not have vada.

Considering the persons who had chutney and those who didn't, 3 persons do not have chutney. Bimal is one of them(the one eating 4 vadas).

Mukesh is the second one to not take chutney(last hint). Also, Sandip does not take chutney. Hence, we get this information as well.

Option A, stating that Daljit eats 5 idlis, is right.

Considering (i), Ignesh has to eat 6 vadas, since 6 is the only multiple of 3.

Also, using the same information, we can say that a person consumes 2 vadas and 4 idlis.

Using (vii), Bimal eats 2 more idlis than Ignesh.

Possibilities:

Bimal - 8, Ignesh - 6

Bimal - 6, Ignesh - 4

But Ignesh cannot have 4 idlis because the person who eats 4 idlis eats 2 vadas.

Hence we take Bimal - 8 and Ignesh - 6.

Also, we get that Bimal eats 6 - 2 = 4 vadas.

So far, we get the following information.

Using (vi), there is a person who eats twice as many idlis as Mukesh. The only pair satisfying is 8, 4.

So, Mukesh eats 4 idlis. Plus the person who eats 4 idlis eats 2 vadas. Hence, we get

Daljit also eats Vada as per info (v), so we get the following 

(iv) gives us the information that the one who eats 1idli does not have vada.

Considering the persons who had chutney and those who didn't, 3 persons do not have chutney. Bimal is one of them(the one eating 4 vadas).

Mukesh is the second one to not take chutney(last hint). Also, Sandip does not take chutney. Hence, we get this information as well.

Hence, Ignesh eats 6 Vadas.

Considering (i), Ignesh has to eat 6 vadas, since 6 is the only multiple of 3.

Also, using the same information, we can say that a person consumes 2 vadas and 4 idlis.

Using (vii), Bimal eats 2 more idlis than Ignesh.

Possibilities:

Bimal - 8, Ignesh - 6

Bimal - 6, Ignesh - 4

But Ignesh cannot have 4 idlis because the person who eats 4 idlis eats 2 vadas.

Hence we take Bimal - 8 and Ignesh - 6.

Also, we get that Bimal eats 6 - 2 = 4 vadas.

So far, we get the following information.

Using (vi), there is a person who eats twice as many idlis as Mukesh. The only pair satisfying is 8, 4.

So, Mukesh eats 4 idlis. Plus the person who eats 4 idlis eats 2 vadas. Hence, we get

Daljit also eats Vada as per info (v), so we get the following 

(iv) gives us the information that the one who eats 1idli does not have vada.

Considering the persons who had chutney and those who didn't, 3 persons do not have chutney. Bimal is one of them(the one eating 4 vadas).

Mukesh is the second one to not take chutney(last hint). Also, Sandip does not take chutney. Hence, we get this information as well.

Hence, Ignesh eating 6 vadas and 6 idlis eat Chutney.

Total to be paid = 1248 Baht

Each has to pay 1248/3 = 416 Baht

R paid 92 Baht

M paid 184+27 = 211 Baht

So, R owes S 416 - 92 = 324 Baht

Total to be paid = 1248 Baht

Each has to pay 1248/3 = 416 Baht

R paid 92 Baht

M paid 184+27 = 211 Baht

So, R owes S 416 - 92 = 324 Baht

M owes S 416-211 Baht = 205 Baht = 5 US Dollars

Let the radius of outer circle be 2R and the centre of both the circles be O.

Triangle $$ON_2E_1$$and all the other 3 similar triangles form a right angle at the centre. 

Let the radius of the inner ring road be R

The radius of outer will be 2R as the circumference of the outer ring road is double that of the inner ring road. 

So, in triangle $$ON_2E_1$$ using Pythagoras theorem the value of chords come out to be $$\sqrt5$$ * R so the total length of the chords 4 * $$\sqrt5$$ * R and circumference is equal to 2 *Pi*2R. The ratio gives option C.

Statement B is redundant. We already know that M has 5 siblings from the question. From statement A alone, we know that F has 2 brothers and M has 2 brothers and 3 sisters.

Considering statement A. The game ended normally.  Here we know that last 2 results were heads and the person receives 100 Rs. and since there was overall loss of 50 Rs we can calculate no. of matches which ended in tails or non consecutive heads . hence , statement a is sufficient to answer.
Considering statement B. The total number of tails obtained in the game was 138. So we know person lost here rs.138 and we can add any no. of single heads in between those tails such that the overall loss will be 50Rs. Hence this statement is also sufficient to answer.

Considering statements a we can deduce that she got letter S in her 21st purchase in previous 20 puchase she had either A, O or P . Hence statement a is not enough to answer. If we consider statement b we will know that out of 20 purchases 18 are vowel so 2 purchases contained letter P . So both statements are necessary to answer the question.

Let the distance be x. Time taken by A is T, so time taken by B is T+60 and time taken by C is T+90.
From statement A, we know that the ratio of speeds of A and C is x:(x-375) = x/T : x/(T+90)
We have only 1 equation and 2 unknows. We need the second statement to find the values. So, the question can be answered by using both the statements together.

$$2^x - x - 1 = 0$$ for this equation only 0 and 1 i.e 2 non-negative solutions are possible. Or we can plot the graph of $$2^x$$ and x+1 and determine the number of points of intersection and hence the solutin.

Graph of logx goes on increasing in 1st quadrant and graph of 1/x goes no decreasing with both intersecting only once

Surface area of sphere A (of radius a) is $$4\pi*a^2$$
Surface area of sphere B (of radius b) is $$4\pi*b^2$$
=> $$4\pi*a^2$$/$$4\pi*b^2$$ = 1/4 => a:b = 1:2
Their volumes would be in the ratio 1:8
Therefore, k = 7/8 * 100% = 87.5%

Substitute value of p,q,r in the options only option A satisfies .

5(x+2y-3z)-2(2x+6y-11z)-(x-2y+7z) = 5x+10y-15z-4x-12y+22z-x+2y-7z  = 0

The sum of the 3rd and 15th terms is a+2d+a+14d = 2a+16d
The sum of the 6th, 11th and 13th terms is a+5d+a+10d+a+12d = 3a+27d
Since the two are equal, 2a+16d = 3a+27d => a+11d = 0
So, the 12th term is 0
 

Let the number of questions answered correctly be x and the number of questions answered wrongly be y.

So, number of questions left unattempted = (50-x-y)

So, x - y/3 - (50-x-y)/6 = 32

=> 6x - 2y - 50 + x + y = 192 => 7x - y = 242 => y = 7x - 242

If x = 35, y = 3

If x = 36, y = 10

So, min. value of y is 3.

The number of wrongly answered questions cannot be less than 3.

From the options a, c and d all can possibly occur. Hence option b. Besides, if all people have different number of acquaintances, then first person will have 26 acquaintance, second person will have 25 acquaintance, third person will have 24 and so on till 27 th person will have 0 acquaintance. 0 acquaintance is practically not possible.

Smallest possible value would be at 5-x = x+2 i.e. x= 1.5 as shown

 Substituting we get smallest value as 3.5. 

f(x) = |x - 2| + |2.5 - x| + |3.6 - x|

For x belonging to (-infinity to 2), f(x) = 2-x + 2.5-x + 3.6-x = 8.1-3x

This attains the minimum value at x=2. Value = 2.1

For x belonging to (2 to 2.5), f(x) = x-2 + 2.5-x + 3.6-x = 4.1-x

Attains the minimum value at x = 2.5. Value = 1.6

For x belonging to (2.5 to 3.6), f(x) = x-2 + x-2.5 + 3.6-x = x-0.9

Attains the minimum at x=2.5, value = 1.6

For x > 3.6, f(x) = x-2+x-2.5+x-3.6 = 3x - 8.1

Attains the minimum at x= 3.6, value = 2.7

So, min value of the function is 1.6 at x=2.5

Between 100 and 200 both included there are 51 even nos. There are 7 even nos which are divisible by 7 and 6 nos which are divisible by 9 and 1 no divisible by both. hence in total 51 - (7+6-1) = 39 

There is one more method through which we can find the answer. Since we have to find even numbers, consider the numbers which are divisible by 14, 18 and 126 between 100 and 200. These are 7, 6 and 1 respectively.

Since  in all three cases the last digit is 1, the number should give remainder 1 when divided individually by 2,3,5 . So the no. may be 31 or 91 . Now 31 in base 2,3 and 5 give first digit as 1 in all the 3 cases while 91 gives exactly two out of the three cases the leading digit as 1. Hence option D.

Let A , B and f,s be the distance traveled and speed of the fastest and the slowest person respectively. Also f=2s so in the given time A=2B. Since the ration of the speeds is 2:1, they will meet at 2-1 points = 1 pont.

Both meet each other for first time at starting point . let b travel distance equal to 1 circumference i.e. 1000m so A=2000m . Both meet after 5 min so speed of slowest is 1000/5=200m/min . So speed of the fastest is 400m/min. So time taken by A to complete race 4000/400 = 10 min

If b = 4, then the answer to the question is no. If b = 32, then the answer is yes. So, using statement A alone, we cannot answer the question.
Using statement B alone, we can conclude that $$a^{44} < b^{11}$$

Using statement A, sum of roots = 0 and product of roots = 0, so b = c = 0.
Using statement B, sum of roots = x - 1/2 = -b/4 and product of roots = c/4 = b/4 = -x/2
So, we can calculate the values of b and c using either statement alone

Let the radius be r. Using statement B alone, r, r-5 and 2.5 form a right-angled triangle. So, we can answer the question using statement B alone.

Consider the first statement:
When the common ratio is less than 1 we can apply the formula of sum of infinite terms.
So, LHS = $$1/(a^2 - 1)$$
RHS = $$a/(a^2 - 1)$$
If a<1 then LHS<RHS

If a = 1,then LHS = RHS

So, we cannot answer the question using statement 1 alone

Using statement 2 alone, we know that a = 1/2. So, RHS > LHS
Hence, option a)

From statement 1 alone, we can infer that the triangle ABC is an equilateral triangle with side = 2 cm
Similarly, from statement 2 alone, we can infer that the triangle ABC is an equilateral of side 2 cm
So, the question can be answered using either statement alone

By the end of the year 2002, Shepard bought 4 times and sold 4 times. He is left with the initial number of goats that he had in 1998. If the percentage of goats bought is equal to or lesser than the percentage of goats sold, then there would be a net decrease in the total number of goats. For the number of goats to remain the same, p has to be greater than q, because p% is being calculated in a lesser number and q% is being calculated on a greater number. Hence, p > q.

Let the total number of sides be x.

Sum of internal angles in a polygon = (x-2)*180 where x is the number of sides.

It is given that the polygon has 25 convex sides, then the number of concave sides = x-25

(25*90)+(x-25)*270 = (x-2)180

x = 46

Number concave corners = x-25 = 46-25 = 21

1, 2, 3, 4,....n such that the sum is greater than 288
If n = 24, n(n+1)/2 = 12*25 = 300
So, n = 24, i.e. the 24th letter in the alphabet is the letter at position 288 in the series
​So, answer = x

Let $$\alpha $$ be equal to k.

=> f(x) = $$x^2-(k-2)x-(k+1) = 0$$

p and q are the roots

=> p+q = k-2 and pq = -1-k

We know that $$(p+q)^2 = p^2 + q^2 + 2pq$$

=> $$ (k-2)^2 = p^2 + q^2 + 2(-1-k)$$

=> $$p^2 + q^2 = k^2 + 4 - 4k + 2 + 2k$$

=> $$p^2 + q^2 = k^2 - 2k + 6$$

This is in the form of a quadratic equation.

The coefficient of $$k^2$$ is positive. Therefore this equation has a minimum value.

We know that the minimum value occurs at x = $$\frac{-b}{2a}$$

Here a = 1, b = -2 and c = 6

=> Minimum value occurs at k = $$\frac{2}{2}$$ = 1

If we substitute k = 1 in $$k^2-2k+6$$, we get 1 -2 + 6 = 5.

Hence 5 is the minimum value that $$p^2+q^2$$ can attain.

Let R ,r be radius of big and small circles respectively. We know that R=2r.

And since area = 12 ;

$$R^2 = \frac{12}{\pi}$$.
$$r^2$$ = $$\frac{3}{\pi}$$

By pythagoras theorem in the small triangle with side 'x' we have x = $$\sqrt{\ 3}r$$.

Angle OAB = $$\tan\ \theta\ \ =\ \ \frac{\ r}{\sqrt{\ 3}r}\ =\ 30$$
Hence Angle CAB = 60.

So area = $$\ \frac{\ 1}{2}\ \times\ 2\sqrt{\ 3}r\times\ 2\sqrt{\ 3}r\times\ \sin\ 60$$.
On substituting the value of sin 60 and $$r^2$$, we get

Area = $$9\sqrt3/\pi$$.

Taking lowest possible positive value of m i.e. 1 . Such that a+b+c+d=5 , so atleast one of them must be grater than 1 ,

take a=b=c=1 and d=2

we get $$a^2 + b^2 + c^2 + d^2 = 7$$ which is equal to $$4m^2+2m+1$$ for other values it is greater than $$4m^2+2m+1$$ . so option B

Let R be radius of big circle and r be radius of circle with centre S. Radius of 2 semicircles is R/2.

 From Right angled triangle OPS, using pythagoras theorem we get

$$(r+0.5R)^2 = (0.5R)^2 + (R-r)^2$$ . We get R=3r .

Now the area of big semicircle that cannot be grazed is Area of big S.C - area of 2 semicircle - area of small circle = $$\pi*R^2$$/2 - 2*$$\pi*(0.5R)^2$$/2-$$\pi*r^2$$ = $$\pi*R^2$$/2 - 2*$$\pi*(0.5R)^2$$/2-$$\pi*(R/3)^2$$= $$\pi*R^2$$/2 - $$\pi*(R)^2$$/4-$$\pi*(R)^2$$/9 = 5*$$\pi*R^2$$/36.  this is about 28 % of the area $$\pi*R^2$$/2 . Hence option B.

When the hexagon is divided into number of similar triangle AOF we get 12 such triangles . Hence required ratio of area is 1/12.
Alternate Approach :

Let us take side of the hexagon as a
Now We get AF = a
Now As OF || ED
Angle OFE +Angle E = 180
We know Angle E =120
So angle OFE=60 degrees.
Now therefore Angle AFO=120-60=60 degrees
Now in triangle AFO
Cos60=$$\frac{OF}{AF}$$
$$\frac{1}{2}=\frac{OF}{AF}$$
We get OF = $$\frac{a}{2}$$
Now therefore area of triangle AOF =$$\frac{1}{2}\times\ AF\times\ OF\times\ \sin60$$
So we get $$\frac{1}{2}\times\ a\times\ \frac{a}{2}\times\ \frac{\sqrt{\ 3}}{2}$$
=$$\frac{\sqrt{\ 3}}{8}a^2$$     (1)
Now area of hexagon = $$6\times\ \frac{\sqrt{\ 3}}{4}a^2$$      (2)
Dividing (1) and (2) we get ratio as $$\frac{1}{12}$$
Hence option A is the correct answer.

 x, y and z in the hundred's, ten's and unit's place. So y should start from 2

If y=2 , possible values of x=1 and z = 0,1 .So 2 cases 120,121.

Also if y=3 , possible values of x=1,2 and z=0,1,2.

Here 6 three digit nos. possible .

Similarly for next cases would be 3*4=12,4*5=20,5*6=30,.....,8*9=72 . Adding all we get 240 cases. 

Consider the triangle APB.  $$\angle$$P = 60 and AP = BP => APB is an equilateral triangle.

Hence AP = $$b$$    ...(1)

$$\text{AC}^2 = \text{AB}^2 + \text{BC}^2$$

$$\text{AC}^2 = b^2 + b^2$$  =>  $$\text{AC} = \sqrt{2}\times b$$  =>  $$\text{AO} = \dfrac{\text{AC}}{2} = \dfrac{b}{\sqrt{2}}$$

$$\text{AP}^2 = \text{AO}^2 + \text{OP}^2$$

$$b^2 = \dfrac{b^2}{2} + h^2$$    ...From (1)

$$2h^2 = b^2$$

Hence, option B is the correct answer.

Let BD = x .Semi-perimeter of triangle ABC = 12. Now by herons formula area of ABC is 24. Also Area = 0.5*x*10 . We get x = 24/5 .  AP = 6/5  and CQ = 16/5 . Hence the required ratio is 3:8. 

Let BQ = z , QD = y , PQ = x.

From similar triangles PQD and ABD we have

(y/x) = (z+y)/3 .

Also from  similar triangles PQB and CBD we have

(z/x) = z+y .

Solving we get z = 3*y.

Now required ratio is (z+y)/z.

We get eual to 4/3 which is equal to 1:0.75. 

For the given problem ,

$$\sum {n(n+1)/2} = 8436 $$ which is 

$$\sum {n^2/2} + \sum{n/2} = 8436 $$ which is equal to

n*(n+1)(2n+1)/12 + n*(n+1)/4 = 8436 , solving we get n=36.

Solving the equation might be lengthy. you can substitute the values in the options to arrive at the answer. 

Let the numbers be $$a_1,a_2....a_n.$$

Since the numbers are positive,

$$AM\geq GM$$

$$\frac{a_1+a_2+a_3....+a_n}{n}\geq (a_1*a_2....*a_n)^{1/n}$$

$$a_1+a_2+a_3....+a_n \geq n$$

$$2 log (2^x - 5) = log 2 + log (2^x - 7/2)$$
Let $$2^x = t$$
=> $$(t-5)^2 = 2(t-7/2)$$
=> $$t^2 + 25 - 10t = 2t - 7$$
=> $$t^2 - 12t + 32 = 0$$
=> t = 8, 4
Therefore, x = 2 or 3, but $$2^x$$ > 5, so x = 3

Since Angle BOC = Angle BCO = y.

Angle OBC = 180-2y .

Hence Angle ABO =  z = 2y = Angle OAB.

Now since x is exterior angle of triangle AOC .

We have x = z + y = 3y.

Hence option A. 

As seen in the fig. we have a right angled triangle with sides  r ,r-10 , r-20.

Using pythagoras we have $$r^2 = (r-10)^2 + (r-20)^2$$.

Solving the equation, we get r = 10 or 50.

But 10 is not possible , so r = 50.

Hence radius is 50.

We know $$w = vz /u$$ so taking max value of u and min value of v and z to get min value of w which is -4.

Similarly taking min value of u and max value of v and z to get max value of w which is 4

Take v = 1, z = -2 and u = -0.5, we get w = 4

Take v = -1, z = -2 and  u = -0.5, we get w = -4

If there is only 1 green ball, it can be done in 6 ways
If there are 2 green balls, it can be done in 5 ways.
.
.
.
If there are 6 green balls, it can be done in 1 way.
So, the total number of possibilities is 6*7/2 = 21

Equate the 2 equations we get value of x = 1 and -1 . Also we notice that there is intersection at x=0 . hence D

Let there only be 2 questions.

Thus there are $$2^{2-1}$$ = 2 students who have done 1 or more questions wrongly, 2$$^{2-2}$$ = 1 students who have done all 2 questions wrongly .

Thus total number of wrong answers = 2 + 1 = 3= $$2^n - 1$$.

Now let there be 3 questions. Then j = 1,2,3

Number of students answering 1 or more questions incorrectly = 4

Number of students answering 2 or more questions incorrectly = 2

Number of students answering 3 or more questions incorrectly = 1

Total number of incorrect answers = 1(3)+(2-1)*2+(4-2)*1 = 7 = $$2^3-1$$

According to the question , the total number of wrong answers = 4095 = $$2^{12} - 1$$.

Hence Option A.

For the given expression value of x,y,z are distinct positive integers . So the value of expression will always be greater than value when all the 3 variables are equal . substitute x=y=z we get minimum value of 6 .

$$(x^2(y+z) + y^2(x+z) + z^2(x+y))/xyz$$ = x/z + x/y + y/z + y/x + z/y + z/x

Applying AM greater than or equal to GM, we get minimum sum = 6

Take any 12 points.

The maximum number of edges which can be drawn through these 12 points are $$^{12}C_2$$ = 66

The minimum number of edges which can be drawn through these 12 points are 12-1 = 11 as the resulting figure need not be closed. It might be open.

positive integers n in the range $$12 \leq n \leq 40$$ such that the product (n -1)*(n - 2)*…*3*2*1 is not divisible by n, implies that n should be a prime no. So there are 7 prime nos. in given range. Hence option B.

No. of terms in series T , 3+(n-1)*8 = 467 i.e. n=59.

Now S will have atleast have of 59 terms i.e 29 .

Also the sum of 29th term and 30th term is less than 470.

Hence, maximum possible elements in S is 30. 

Let a,d,j,g be the shots put by Ashish, Dhanraj, Ganesh and Jugraj respectively.

According to given conditions we have ,
g = a-8; d + r = 37; j = d + 8; a = 5 + d; a + g = 40

Solving these equations, we have a = 24, d = 19 and j = 27 and r = 18. Hence option A is the correct answer.

We know that the total time taken is 1.5 hrs. Calculating the individual time taken and the adding and then equating to 1.5.

Let R be the radius of the outer-ring road.

$$\frac{\pi*R}{2*30*\pi} + \frac{\sqrt{5}*R}{2*15*\sqrt{5}}$$ = 1.5 solving we get R=30.

Let the radii of 2 circles be R and r respectively such that R=2*r. Triangle $$ON_2E_1$$ and all the other 3 similar triangles form a right angle at the centre. So, using Pythagoras theorem, the value of chords comes out to be $$\sqrt{\ 5}\times\ \dfrac{R}{2}$$ . Hence, the total distance travelled is $$\sqrt{\ 5}\times\ \dfrac{R}{2}$$ + $$0.5\ \times\ R\ \times\ \pi\ $$. The total time required can be calculated by distance/speed, which comes out to be 3.5 * R. Among options, only 105 is an integral multiple of 3.5.

The tone which author uses while asking “what French winemaker will ever admit that? is not at all harsh , so option a) is out . Also the author doesn't criticize while asking the question ,so Option c ) is clearly not the answer. We don't find any author professing any feelings which he doesn't have , hence the tone is not hypocritical. Option b ,suits the best i.e. his tone is satirical. 

Refer to the part of the passage which says  ' ...not because they think their wine isn’t as good as the best from California ...and they aren’t about the change...probably no other way if France is to avoid simply becoming a specialty source of old-fashioned wines for oldfashioned connoisseurs. ' .

From this, we can see that the author feels that the French should adopt the labeling strategy of the English-speaking countries to avoid becoming a producer of merely old-fashioned wines.

Option a) is the correct answer.

Consider the following part of the passage ' .. Consumer effectively recognize them as brand names, and have acquired a basic lexicon of wine .... with those Brazilian upstarts. In the wine heartlands of France, they are scared to death of that trend.. '. So, above all, French winemakers fear the knowledge or education that the consumers have derived from wine labels from the English speaking countries. Option b) is the correct answer.

Dr. Renaud findings suggest that fat-derived cholesterol can be dispersed by the tannins in wine. So, a survey that validates this finding would provide the most support. The survey in option d) is precisely one such survey. Option d) is the correct answer.

Consumers' appreciation of better quality wines is something that does not come because of the labeling or branding. So, this appreciation cannot be attributed to the labeling strategy followed by wine producers in English speaking countries.

Option c) is the correct answer.

Consider the following lines from the passage: "But he was overruled by Indian hands who said India would resist payment and paralyse the war effort". From this, we can understand the reason why the British didn't tax India to finance its war efforts. It was afraid that if India refused to pay, Britain's war efforts would be jeopardized. Option c) is the correct answer.

Refer to the 5th paragraph. It says "Though crushed, it reminded the British vividly that they were a tiny ethnic group who could not rule a gigantic subcontinent without the support of the important locals". From this, we can understand that the main lesson that the British learnt from the Sepoy Mutiny of 1857 was that they were a small ethnic group. Option c) is the correct answer.

If the returns from conquest decreased and the costs increased, it wouldn't make sense to continue empire-building in India. So, the sentence in option b) is not a reason for the emergence of the 'white man's burden' as a new rationale for empire-building in India.

White man's burden refers to the claim made by the British that the natives of the conquered countries were in need of the 'good' provided by them. This was a justification for their conquests. Option a) captures this idea succinctly.

Throughout the passage, the author talks about the various financial reasons for conquest and explains how the British were forced to grant independence when their returns from India diminished after the war. The main idea of the passage is to illustrate how the erosion of the financial basis of an empire supports the granting of independence to an empire's constituents. Option d) is the correct answer.

By the line "Even if the research promoted by them ................... in both developing and developed countries", we can say that not only MNCs but also governments are involved in the research development. 

So, MNCs are not the only group actors that are involved in genetically modified food research.

Hence, option C is the answer.

According to the passage, European nations are anti GM. So, among the given options we must select those countries that are present in Europe.

USA is not in Europe => option A is wrong.

India is not in Europe => option B is wrong.

Australia is not in Europe => option D is wrong.

Both Germany and France are in Europe => option C is the answer.

Refer to the last lines of the passage:"However, some weeds through genetically-modified pollen contamination may acquire resistance to a variety of weed-killers. The only way to destroy these weeds is through the use of ever-stronger herbicides which are poisonous and linger on in the environment." This line indicates the point made in 2 that once the weeds acquire resistance to weak herbicides, we have to apply stronger ones to eradicate them.

Refer to the lines made in the paragraph:"Even if the research promoted by them does focus on the high-value food items, much of biotechnology research is also funded by governments in both developing and developed countries. Indeed, the protato is a by-product of this type of research. If the protato passes the field trials, there is no reason to believe that it cannot be marketed in the global potato market. And this type of success story can be repeated with other basic food items." Here the author wants to illustrate that biotechnology resarch helps to address the concerns of the developing countries. For this illustration, the author gives the exmaple of potatoes.

Refer to the following lines in the passage:"It is quite likely that the GM controversy will soon hit the headlines in India since a spokesperson of the Indian Central government has recently announced that the government may use the protato in its midday meal programme for schools as early as next year. Why should “scientific progress”, with huge potential benefits to the poor and malnourished, be so controversial?" Here the author wants to highlight that the scientific progress which has a huge impact on large number of people is likely to be covered by the media.

Refer to the last lines of the second paragraph:"These large gatherings will be only what we make of them if not anything better, they can be as good places to collect new friends from as the slavemarkets of Istanbul were for beautiful slaves or New Market for race horses."

Here "They" refers to the large gatherings of casual acquaintances as illustrated in these lines.

The passage starts with the author's perception of social life. In the whole passage the author criticises the fact that we do not possess any social life. The author also gives his opinions of social life and then moves on to lament our little social life we have left. Option b and d are not clearly the main subject of the author. Option a is inappropriate as the author do not highlight our real social life but rather complaints of the social life.

The author's conception of social life is mentioned in the fourth paragraph where he says wonder and interest. Hence B is the correct answer.

The author is trying to say that people are not able to recognize the passionate attitude.

So, the word "discriminate" in this context means "recognize".

The author has not mentioned that crowd in poor Calcutta can turn violent => option A is wrong.

B negates the statements said by the author in the passage.

C is too generalized to be the answer for this question.

Hence, option D is the answer.

Options B and D negate the information given in the passage => B and D are incorrect.

C is stated in the passage but does not answer the question. 

Option A is the correct answer.

In the second line after the line mentioned in the question, the author says that "the feeling was general that all the physical processes of nature would prove to be unfolding themselves according to the rigourous mathematic laws".

Option C is the answer.

The author says that "The next advance was due to Newton, the greatest scientist of all time if account be taken of his joint contributions to mathematics and physics."

Joint contributions is metaphorically said as married in option B. Hence, option B is the answer.

The author says that Einstein's principle is merely an extension of classical Newtonian principle.

Option D agrees with this saying that new knowledge about natural phenomena builds on existing knowledge.

Hence, option D is the answer.

The author says that "Its SIGNIFICANCE lay in its assertion that absolute Galilean motion or absolute velocity must ever escape all experimental detection."

Here, "it" refers to Einstein's principle.

The meaning of the sentence is that it is not always possible to experiment.

Option C gives a similar meaning. Hence, C is the answer.

The four lines "Better if it last for years ............ not expecting Ithaka to make you rich" gives us the central theme of the poem.

It says that the journey is more important than the goal.

This meaning is conveyed in option B.

Hence, option B is the answer.

Option A gives the big picture of why the poet recommends a long journey.

The remaining options are short-sighted and the poet was not much concerned about them.

The whole poem was about the goal and the journey to reach the goal.

If we see the lines "Better if it lasts for years ............. not expecting Ithaka to make your rich", we can see that the poet is comparing Ithaka to life's distant goal.

Option D is the answer.

The poet is trying to say that one who pursues the journey to one's goal must not be afraid of hindrances in that journey.

Option C is similar to our conclusion.

Hence, option C is the answer.

The poet says that Ithaka is the reason for one's journey.

So, he is trying to be encouraging.

Among the given options, only exhorting fits the be correct answer.

Option a and d are gramatically incorrect as "The running of large business" is singular and hence should be followed by "consists." Option c doesn't make any sense as it is contextually incorrect. Option b is the most appropriate.

Option a is incorrect as the usage of "feeling disdainful" is incorrect. Option d is also incorrect due to the usage of "felt disdain." Option b is having a tense error as there is a present form used in the sentence. 

Option d is incorrect as "to fatalism" is incorrect, option b is incorrect as the usage of "falling back" is incorrect. Option c is incorrect as "falling back on fatalism" is singular and hence the correct usage should be "explanation" rather than "explanations."

The correct usage would be "The creativity is regarded not only as" 
Or in order to infer the correct usage we would break the sentence into 2 parts "Creativity in any field is regarded as valuable in itself and also regarded as a service to the nation".
 

In this sentence, the ideal situation is satisfactory. "Reflection" should precede action and thought should facilitate behaviour.

A is the best opening sentence. It introduces the author's trip to Princeton University.
This is followed by D, which talks about how the author prepared for his trip by gathering the email ids of a few Princeton students.
B then follows and describes what happened when the author emailed the students of Princeton.
The situation is then explained in sentence C and followed by sentence E.

The best opening sentence is C. It gives an introduction to the paragraph saying that Peoplesoft offered to by J.D.Edwards.
This is followed by A, which talks about how Oracle wanted to buy Peoplesoft just 4 days later.
Statement B then follows, by introducing Peoplesoft's boss Craig Conway and quoting his statements.
D follows B as it continues the statements of Mr.Craig.
E is the concluding sentence.

C opens the paragraph brilliantly. E follows C and explains why the phrase "war on terror" is a misnomer. B continues the explanation started in E. D then follows, and gives another reason why the phrase doesn't hold water. A concludes the paragraph aptly.

BD is a link. This is because B talks about "the unpleasant human animal" that the author has met and D says that such types are fortunately rare. Similarly, AC is a link. A says that the author is intolerant of human shortcomings, but that he has been lucky in meeting mostly charming people. C explains why this might be the case. E is the best opening sentence. The order of sentences is, therefore, EACBD.

C is the best opening sentence. It says that the Qwerty keyboard was designed for solving a specific problem. E follows and talks about what that problem is. This is followed by A which talks about how the Qwerty design solved this problem. It also talks about the shortcoming of the Qwerty design. This is followed by B which talks about a different design which tried to solve the same problem.
The last sentence is D, which says the second design was never widely adopted even though, with the advent of electrical typewriters and PCs, the original problem of the typrewriters ceased to be a problem anymore.

Option 1 is correct as "bundle of joy" refers to the baby. Option 2 is correct as bundle refers to "a collection of benefits" wrapped together. Option 3 is correct as "made a bundle" means "earning a lot of money." Option 4 is incorrect usage.

Option a is incorrect as the correct usage would be "He is distinctive about what is right and what is wrong"

Option a is incorrect as the correct usage would be "Everyone appreciated the headmaster's efforts." "Implication" is the incorrect usage here.

The correct usage would be "Ranchi will play host"

The correct usage would be "Farmers of all sorts"

Option c is incorrect as we never dispose subsidaries. The usage of dispose is flawed. Option d is incorrect as "formally ratified defeat" is incorrect usage. Option a is incorrect as "acquire" is an incorrect usage because no purchasers are required while acquiring. Option b correctly fits the sentence.

The detection to maladjustment to college culture becomes complicated when we develop friendships outside the college. Hence option c is correct.

The answer to the first blank is "different". There are always different regions in a country. On the other hand views can be "discrete" or "distinct." Hence option a is the most appropriate option.

The second part of the sentence says that the expert professionals will end up with no jobs. Hence replace is the correct word for the second blank and the answer is option A. "Resent" is the correct answer for the first blank.

In order to complement the phrase "in doing the work well" the second blank must have a positive word hence eliminating options B and C. "Seeking" is a wrong usage in this sentence. Author of this sentence is trying to say that the performance is not improved by withholding the rewards. Hence the answer is option D.