**Instructions: **In each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and

Give answer

(A) If the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question

(B) If the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question

(C) If the data either in statement I alone or in statement II alone are sufficient to answer the question

(D) If the data given in both statements I and II together are not sufficient to answer the question and

(E) If the data in both statements I and II together are necessary to answer the question.

**Question 1: **What is the area of the circle?

I.perimeter of the circle is 88 cms

II.diameter of the circle is 28 cms

a) If the data in statement I alone are sufficient to answer the question, while the data in statement

b) If the data in statement II alone are sufficient to answer the question, while the data in statement

c) If the data either in statement I alone or in statement II alone are sufficient to answer the question

d) If the data given in both statements I and II together are not sufficient to answer the question and

e) If the data in both statements I and II together are necessary to answer the question.

**Question 2: **What is the rate of interest?

I.simple interest obtained on the sum of 25000 in 2 years is 250 less than the interest obtained from compound interest during the same time

II.simple interest obtained in 10 years is equal to the original sum

a) If the data in statement I alone are sufficient to answer the question, while the data in statement

b) If the data in statement II alone are sufficient to answer the question, while the data in statement

c) If the data either in statement I alone or in statement II alone are sufficient to answer the question

d) If the data given in both statements I and II together are not sufficient to answer the question and

e) If the data in both statements I and II together are necessary to answer the question.

**Question 3: **what is the number of plants planted in columns and rows in the field?

Number of columns is 4 more than rows

In each column, the number of trees are even

a) If the data in statement I alone are sufficient to answer the question, while the data in statement

b) If the data in statement II alone are sufficient to answer the question, while the data in statement

c) f the data either in statement I alone or in statement II alone are sufficient to answer the question

d) If the data given in both statements I and II together are not sufficient to answer the question and

e) f the data in both statements I and II together are necessary to answer the question.

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**Question 4: **What is the area of right angle triangle ?

I.Height of right-angled triangle is ¾ th of its base

II.Length of the diagonal of the right angle triangle is 5 meters

c) If the data either in statement I alone or in statement II alone are sufficient to answer the question

e) If the data in both statements I and II together are necessary to answer the question.

**Question 5: **What is the present age of the father?

I.Present age of the father five times of the present age of his son

II.5 years ago age of the father is 15 times of the age of his son

e) If the data in both statements I and II together are necessary to answer the question.

**Instructions**

Each of the questions given below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements is sufficient to answer the question. Read both the statements. Give answer

**Question 6: **What is the annual salary of Mr. X.

I. The ratio of monthly salaries of X and Y is 9 : 7.

II. The monthly salary of X is more than that of Y by Rs. 16000.

a) if the data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.

b) if the data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.

c) if the data in statement I alone or in statement II alone is sufficient to answer the question.

d) if the data in both the statements I and II is not sufficient to answer the question.

e) if the data in both the statements I and II together is necessary to answer the question.

**Question 7: **What is the cost price of article ?

I. A man earns a profit of 20% on selling the article.

II. The selling price of article is Rs. 5016.

a) if the data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.

b) if the data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.

c) if the data in statement I alone or in statement II alone is sufficient to answer the question.

d) if the data in both the statements I and II is not sufficient to answer the question.

e) if the data in both the statements I and II together is necessary to answer the question.

**Question 8: **What will be the total cost of fencing a rectangular plot ?

I. The area of plot is 1134 sq. metre. The length of plot is 15 metre more than its breadth.

II. The cost of fencing is Rs. 180 per metre.

a) if the data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.

b) if the data in statement II alone is suf cient to answer the question, while the

data in statement I alone is not suf cient to answer the question.

Give answer

c) if the data in statement I alone or in statement II alone is sufficient to answer the question.

d) if the data in both the statements I and II is not sufficient to answer the question.

e) if the data in both the statements I and II together is necessary to answer the question.

**Question 9: **How many marks did Subodh obtain in Physics ?

I. The average marks of Subodh in History, Geography and Chemistry are 75.

II. His average marks in History, Geography and Physics are 78.

b) if the data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.

c) if the data in statement I alone or in statement II alone is sufficient to answer the question.

d) if the data in both the statements I and II is not sufficient to answer the question.

e) if the data in both the statements I and II together is necessary to answer the question.

**Question 10: **What is the population of the city A?

I. The ratio of the population of males and females in city A is 27 : 23 and the difference between their population is 100000.

II. The population of city A is 80% of that of city B. The difference of population of city A and city B is 312500.

c) if the data in statement I alone or in statement II alone is sufficient to answer the question.

d) if the data in both the statements I and II is not sufficient to answer the question.

e) if the data in both the statements I and II together is necessary to answer the question.

**Instructions**

<p “=””>Each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read the question and both the statements and –

Give answer a: if the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.

Give answer b: if the data in statement H alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.

Give answer c: if the data either in statement I alone or in statement II alone are sufficient to answer the question.

Give answer d: if the data even in both the statements I and H together are not sufficient to answer the question.

Give answer e: if the data in both the statements I and II together are necessary to answer the question.

**Question 11: **Train ‘A’ running at a certain speed crosses another train ‘B’ running at a certain speed in the opposite direction in 12 seconds. What is the length of train ‘B’ ?

I. The length of both the trains together is 450 metres.

II. Train ‘A’ is slower than train ‘B’.

a) if the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.

b) if the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.

c) if the data either in statement I alone or in statement II alone are sufficient to answer the question.

d) if the data even in both the statements I and II together are not sufficient to answer the question.

e) if the data in both the statements I and II together are necessary to answer the question.

**Question 12: **Area of a rectangle is equal to the area of a right angled triangle. What is the length of the rectangle ?

I. The base of the triangle is 40 cms.

II. The height of the triangle is 50 cms.

a) if the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.

b) if the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.

c) if the data either in statement I alone or in statement II alone are sufficient to answer the question.

d) if the data even in both the statements I and II together are not sufficient to answer the question.

e) if the data in both the statements I and II together are necessary to answer the question.

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**Question 13: **What was the total compound interest on a sum after three years

I. The interest after one year was Rs. 100/- and the sum was Rs. 1,000/-

II. The difference between simple and compound interest on a sum of Rs. 1,000/- at the end of two years was Rs. 10/-.

a) if the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.

b) if the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.

c) if the data either in statement I alone or in statement II alone are sufficient to answer the question.

d) if the data even in both the statements I and II together are not sufficient to answer the question.

e) if the data in both the statements I and II together are necessary to answer the question.

**Question 14: **What is the two digit number where the digit at the unit place is smaller ?

I. The difference between the two digits is 5.

II. The sum of the two digits is 7.

e) if the data in both the statements I and II together are necessary to answer the question.

**Question 15: **What is the speed of the boat in still water ?

I. It takes 2 hours to cover distance between A and B downstreams.

II. It takes 4 hours to cover distance between A and B upstreams.

e) if the data in both the statements I and II together are necessary to answer the question.

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**Answers & Solutions:**

**1) Answer (C)**

Let radius of the circle = $r$ cm

I : Perimeter = $2 \pi r = 88$

=> $2 \times \frac{22}{7} \times r = 88$

=> $r = 88 \times \frac{7}{44} = 14$ cm

$\therefore$ Area = $\pi r^2 = \frac{22}{7} \times (14)^2$

= $22 \times 2 \times 14 = 616 cm^2$

Thus, statement I alone is sufficient.

II : Diameter = 28 cm

=> Radius, $r = \frac{28}{2} = 14$ cm

$\therefore$ Area = $\pi r^2 = \frac{22}{7} \times (14)^2$

= $22 \times 2 \times 14 = 616 cm^2$

Thus, statement II alone is sufficient.

**Thus, either statement alone is sufficient.**

**2) Answer (C)**

Let rate of interest = $R \%$

I : P = Rs. 25,000 and time period = 2 years

=> $S.I. = \frac{P \times R \times T}{100}$

= $\frac{25000 \times R \times 2}{100} = 500 R$

Interest obtained from compound interest = $P [(1 + \frac{R}{100})^T – 1]$

=> $(500R + 250) = 25000 [(1 + \frac{R}{100})^2 – 1]$

=> $250 (2R + 1) = 25000 [(1 + \frac{R}{100})^2 – 1]$

=> $2R + 1 = 100 (1 + \frac{R^2}{100^2} + \frac{2 R}{100} – 1)$

=> $2R + 1 = \frac{R^2}{100} + 2R$

=> $R^2 = 100 \times 1 = 100$

=> $R = \sqrt{100} = 10 \%$

Thus, statement I alone is sufficient.

II : Let original sum = simple interest = $Rs. P$ and time period = 10 years

=> $S.I. = \frac{P \times R \times T}{100}$

=> $P = \frac{P \times R \times 10}{100}$

=> $R = \frac{100}{10} = 10 \%$

Thus, statement II alone is also sufficient.

**Thus, either statement alone is sufficient.**

**3) Answer (D)**

To find the number of plants planted, we need to find the number of columns and rows and then multiply them.

Let number of columns = $c$ and number of rows = $r$

(I) : Number of columns is 4 more than rows

=> $c – r = 4$

But, we do not know the exact value. So, statement I alone is not sufficient.

(II) : In each column ,number of trees are even, => number of rows are even in number

Again, we do not know the exact value. So, statement II alone is not sufficient.

Combining above statements, we still do not know the exact number of columns and rows. So, statement I and II together are not sufficient.

=> Ans – (D)

**4) Answer (E)**

I : Let base of the triangle = $4x$ m

=> Height of triangle = $\frac{3}{4} \times 4x = 3x$ m

There is no other info, so I alone is insufficient.

Similarly, II alone is also insufficient.

Combining both statements, and using pythagoras theorem, we get :

=> $(3x)^2 + (4x)^2 = (5^2)$

=> $9x^2 + 16x^2 = 25$

=> $x^2 = \frac{25}{25} = 1$

=> $x = \sqrt{1} = 1$

=> Base = 4 m and height = 3 m

$\therefore$ Area of triangle = $\frac{1}{2} \times 3 \times 4 = 6 m^2$

**Thus, both statements together are sufficient.**

**5) Answer (E)**

I : Let present age of son = $x$ years

=> Present age of father = $5x$ years.

There is no other information, so statement I is not sufficient.

Similarly, II alone is not sufficient.

Combining both statements, we get :

=> $(5x – 5) = 15 (x – 5)$

=> $5x – 5 = 15x – 75$

=> $15x – 5x = 75 – 5$

=> $10x = 70$ => $x = \frac{70}{10} = 7$

$\therefore$ father’s age = $5 \times 7 = 35$ years.

**Thus, both statements together are sufficient.**

**6) Answer (E)**

Statement I : Let monthly salary of X = Rs. $9x$ and Y = Rs. $7x$

Statement II : $X – Y = 16,000$

Combining above statements, we get :

=> $9x – 7x = 16,000$

=> $x = \frac{16,000}{2} = 8,000$

$\therefore$ X’s annual salary = $12 \times 9x = 108x$

= $108 \times 8,000$ = Rs. $8,64,000$

Thus, both statements together are required to answer the question.

**7) Answer (E)**

Clearly, both statements are required.

Let cost price = Rs. $100x$

Selling price after profit of 20% = $\frac{120}{100} \times 100x$

= Rs. $120x$

From statement II : Selling price = Rs. 5,016

=> $120x = 5016$

=> $x = \frac{5016}{120} = 41.8$

$\therefore$ Cost price = $100 \times 41.8$

= Rs. $4,180$

Thus, both statements together are required to answer the question.

**8) Answer (E)**

We need both dimensions and cost of fencing to answer the question. Thus, we require both statements.

Let breadth of the plot = $x$ m

=> Length = $(x + 15)$ m

=> Area of plot = $x (x + 15) = 1134$

=> $x^2 + 15x – 1134 = 0$

=> $x^2 + 42x – 27x – 1134 = 0$

=> $x (x + 42) – 27 (x + 42) = 0$

=> $(x + 42) (x – 27) = 0$

=> $x = 27 , -42$

As length of the plot cannot be negative => Breadth = $x = 27$ m

=> Length = $27 + 15 = 42$ m

Perimeter = $2 (42 + 27) = 2 \times 69$

= $138$ m

$\therefore$ Cost of fencing = $138 \times 180$

= Rs. $24,840$

Thus, Both statements together are required to answer the question.

**9) Answer (D)**

Statement I : Sum of marks in History, Geography and Chemistry

= $3 \times 75 = 225$

We cannot find physics marks from statement I alone

Statement II : Sum of marks in History, Geography and Physics

= $3 \times 78 = 234$

Again, from this statement alone, we cannot find physics marks.

Combining above statements, if we subtract equation(1) from (2), we get :

=> Physics – chemistry = 234 – 225 = 9

Again, we cannot find Physics marks even after combining both statements.

**10) Answer (C)**

Statement I : Lat males in city A = $27x$ and females in city A = $23x$

=> $27x – 23x = 1,00,000$

=> $x = \frac{1,00,000}{4} = 25,000$

$\therefore$ Total population of city A = $27x + 23x = 50x$

= $50 \times 25,000 = 12,50,000$

=> Statement I alone is sufficient.

Statement II : Let population of city B = $100x$

=> Population of city A = $\frac{80}{100} \times 100x = 80x$

=> $100x – 80x = 3,12,500$

=> $x = \frac{3,12,500}{20} = 15,625$

$\therefore$ Population of city A = $80 \times 15,625 = 12,50,000$

=> Statement II alone is sufficient.

$\therefore$ Either statement alone is sufficient.

**11) Answer (D)**

Clearly, no relation between the speeds of both train is given.

Thus, we cannot find the length of train B.

Thus, even both statements together are insufficient.

**12) Answer (D)**

Let length of rectangle = $l$ and breadth = $b$

From I & II : Base = 40 cm and height = 50 cm

=> Area of triangle = $\frac{1}{2} \times 40 \times 50$

= $20 \times 50 = 1000 cm^2$

Also, area of rectangle = area of triangle

=> Area of rectangle = $l \times b = 1000 cm^2$

But, there is no relation between length and breadth, so we cannot find length of rectangle.

**Thus, even both statements together are insufficient.**

**13) Answer (C)**

C.I. = $P [(1 + \frac{R}{100})^T – 1]$

I : Interest = 100 and sum = 1000 and time = 1 year

=> $100 = 1000 [(1 + \frac{R}{100})^1 – 1]$

=> $\frac{100}{1000} = [(1 + \frac{R}{100}) – 1]$

=> $\frac{R}{100} = \frac{1}{10}$

=> $R = \frac{100}{10} = 10 \%$

$\therefore$ C.I. after 3 years = $1000 [(1 + \frac{10}{100})^3 – 1]$

= $1000 [(\frac{11}{10})^3 – 1]$

= $1000 [\frac{1331}{1000} – 1] = 1000 \times \frac{331}{1000}$

= $331$

Thus, I alone is sufficient.

II : Sum = 1000 , rate = $R \%$

S.I. after 2 years = $\frac{P \times R \times T}{100}$

= $\frac{1000 \times R \times 2}{100} = 20R$

C.I. after 1st year = $\frac{R}{100} \times 1000 = 10R$

C.I. after 2nd year = $10R + \frac{R}{100} \times 10R = 10R + \frac{R^2}{10}$

=> Required difference = 10

=> $(10R + 10R + \frac{R^2}{10}) – (20R) = 10$

=> $\frac{R^2}{10} = 10$

=> $R^2 = 10 \times 10 = 100$

=> $R = \sqrt{100} = 10 \%$

$\therefore$ C.I. after 3 years = $1000 [(1 + \frac{10}{100})^3 – 1]$

= $1000 [(\frac{11}{10})^3 – 1]$

= $1000 [\frac{1331}{1000} – 1] = 1000 \times \frac{331}{1000}$

= $331$

Thus, II alone is sufficient.

**Thus, either statement alone is sufficient.**

**14) Answer (E)**

2 digit numbers where digit at unit place is smaller :

I : Difference between the two digits is 5

=> 2 digit numbers can be = 61 , 72 , 83 , 94

II : Sum of the two digits is 7

=> 2 digit numbers can be = 70 , 61 , 52 , 43

I & II : Clearly, the common number from the above two sets = 61

**Thus, I & II together are sufficient.**

**15) Answer (D)**

Clearly, we have to use both equations.

Let distance between A and B = $d$ km

Let speed of boat in still water = $x$ kmph

and speed of current = $y$ kmph

Using, $time = \frac{distance}{speed}$

=> $\frac{d}{x + y} = 2$ ———Eqn(1)

and $\frac{d}{x – y} = 4$ ———Eqn(2)

Dividing equation (2) by (1)

=> $\frac{x + y}{x – y} = \frac{4}{2}$

=> $x + y = 2x – 2y$

=> $2x – x = y + 2y$

=> $x = 3y$

=> $\frac{x}{y} = \frac{3}{1}$

$\therefore$ Ratio between speed of boat and current is known and not the exact value.

**Thus, even both statements together are insufficient.**

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