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 1st 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 3rd or 4th. 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).