# Free Data Sufficiency - 03 Practice Test - CAT

### Question 1

Mark (a) if the question can be answered from statement I alone

Mark (b) if question can be answered from statement II alone

Mark (c) if question can be answered using both statements together but not by using either statement alone

Mark (d) if the question cannot be answered by using both the statements.

Which is the greatest amongst a, b and c?

a + c = 2b

b= a+ d , c= a + 2d where d is a real number

#### SOLUTION

Solution :D

From I we can only infer that a, and c are in A.P.

From II we can infer a, b and c are in A.P but we don’t know if d is positive or negative. Thus we cannot find out the greatest number.

Option (d)

### Question 2

Mark (a) if the question can be answered from statement I alone

Mark (b) if question can be answered from statement II alone

Mark (c) if question can be answered using both statements together but not by using either statement alone

Mark (d) if the question cannot be answered by using both the statements.

What is the relation between A and B?

I. D is A’s grandfather.

II. B is D’s son.

#### SOLUTION

Solution :D

Using I and II we can only infer that B is A’s grandfather’s son. Now B can b A’s uncle or A’s father thus exact relationship is not known.

Option d

### Question 3

Mark (a) if the question can be answered from statement I alone

Mark (b) if question can be answered from statement II alone

Mark (c) if question can be answered using both statements together but not by using either statement alone

Mark (d) if the question cannot be answered by using both the statements.

X and Y are two points between P and Q. Find the length XY?

I. PQ= 40cm.

II. PY=XQ= 10 cm

#### SOLUTION

Solution :C

From I and II we infer the following

P______10cm_______Y_____________X____10cm____Q

Thus we can find length XY

Note: Since the lengths of PY and XQ are known thus we will have to stick to the above inference only. The point cannot be in the order PXYQ

Option (c)

### Question 4

Mark (a) if the question can be answered from statement I alone

Mark (b) if question can be answered from statement II alone

Mark (c) if question can be answered using both statements together but not by using either statement alone

Mark (d) if the question cannot be answered by using both the statements.

What is the height of tower X.

I. The angle of elevation of tower from a point on the road is 30 degrees.

II. The angle of elevation of the tower from a man who is 10 m away from the tower is 60 degrees and the height of man is 2m

#### SOLUTION

Solution :B

From II we can find out the length of the tower

Thus option (b)

### Question 5

Mark (a) if the question can be answered from statement I alone

Mark (b) if question can be answered from statement II alone

Mark (c) if question can be answered using both statements together but not by using either statement alone

Mark (d) if the question cannot be answered by using both the statements.

People in a club either speak French or Russian or both. Find the number of people in a club who speak only French.

I. There are 300 people in the club and the number of people who speak both French and Russian is 196.

II. The number of people who speak only Russian is 58.

#### SOLUTION

Solution :C

Choice (c) To make a Venn diagram, we need both statements. Total = 300.

### Question 6

Mark (a) if the question can be answered from statement I alone

Mark (b) if question can be answered from statement II alone

Mark (c) if question can be answered using both statements together but not by using either statement alone

Mark (d) if the question cannot be answered by using both the statements.

A sum of Rs.38,500 was divided among Jagdish, Punit and Girish. Who received the minimum amount?I. Jagdish received 2/9 of what Punit and Girish together received.II. Punit received 3/11 of what Jagdish and Girish together received.

#### SOLUTION

Solution :C

Choice (c) From first statement we get only J’s share. Only by combining the statements we get the values of each student.

### Question 7

Mark (a) if the question can be answered from statement I alone

Mark (b) if question can be answered from statement II alone

Mark (c) if question can be answered using both statements together but not by using either statement alone

Mark (d) if the question cannot be answered by using both the statements.

Given, x + 2y + z = 8;2x + y + z = 7

What are the values of x, y, z?

I: x, y, z are positive integers.

II : x, y, z are distinct numbers.

#### SOLUTION

Solution :A

Subtracting an equation from the other, we get y - x = 1

The possible values of x, y, z are tabulated below.

x y z x+2y+z 2x+y+z

1 2 3 8 7

2 3 0 8 7

From statement 1, (x, y, z) = (1, 2, 3)

Statement 2 alone does not help because without statement 1, we can have infinite

solutions. The correct option is a.

### Question 8

Mark (a) if the question can be answered from statement I alone

Mark (b) if question can be answered from statement II alone

Mark (c) if question can be answered using both statements together but not by using either statement alone

Mark (d) if the question cannot be answered by using both the statements.

Is the four digit number ‘abcd’ a perfect square?

1. a = 2, b = 2, d = 6

2. b = 4, c = 8, d = 6

#### SOLUTION

Solution :B

Wherever the units digit of a perfect square is6, the tens place must be odd.

∴From statement 2 alone, we can say that thenumber is not a perfect square.

Hence the correct option is b.

### Question 9

Mark (a) if the question can be answered from statement I alone

Mark (b) if question can be answered from statement II alone

Mark (c) if question can be answered using both statements together but not by using either statement alone

Mark (d) if the question cannot be answered by using both the statements.

What is fourth term of a given A.P.?

1. The sum to 9 terms of the A.P is 180.

2. The difference between the first and the second terms of the A.P is 8.

#### SOLUTION

Solution :A

We know that middle term of an AP is the mean or average of that AP. So the fourth term will be the average of the first 9 terms of that AP. So fourth term = 180/9 = 20.

Statement 2 cannot give a unique answer. So the correct option is a.

### Question 10

Mark (a) if the question can be answered from statement I alone

Mark (b) if question can be answered from statement II alone

Mark (c) if question can be answered using both statements together but not by using either statement alone

Mark (d) if the question cannot be answered by using both the statements.

In a quiz there are 5 contestants A, B, C, D and E. We know that D has a rank higher than that of E and B has a rank higher than that of C. it is also known that the rank of C is lower than the median. Find the person who got the first rank.

1. A got the last rank.

2. B is not among top 2.

#### SOLUTION

Solution :C

From 1, we know that A is last, C is second last. So 1

^{st}rank can be occupied by B or D. So 1 alone cannot answer the question.From 2, we know that B is not among top 2 so B can be 3

^{rd}or 4^{th}. Still we have no clue about who has the first rank. So statement 2 alone can’t give the answer. But when we combine both, we know that D is rank 1 because B is not in top 2. So the correct option is (c).