Data Sufficiency(Exams > Cat > Di And Lr ) Questions and answers for exam Preparation

Exams > Cat > Di And Lr

DATA SUFFICIENCY MCQs

Total Questions : 71 | Page 6 of 8 pages

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

Discuss Question

Answer: Option B. -> B
:
B

From II we can find out the length of the tower

Thus option (b)

Question 52.

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.

Discuss Question

Answer: Option C. -> C
:
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).

Question 53.

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.

Discuss Question

Answer: Option A. -> A
:
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 54.

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.

Discuss Question

Answer: Option C. -> C
:
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 55.

Discuss Question

Answer: Option B. -> B
:
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 56.

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.

Discuss Question

Answer: Option A. -> A
:
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 57.

If x is a positive integer, find the remainder when x is divided by 6
A. When x-1 is divided by 6, the remainder is 1
B. When 3x is divided by 6, the remainder is 0

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
Each statement alone is sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Discuss Question

Answer: Option A. -> Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
:
A

Option (a)

Statement A alone is sufficient. When x-1 is divided by 6, the remainder is 1. therefore, when x is divided by 6; the remainder will be 2.

Statement B states that 3x is exactly divisible by 6. take 2 cases; say x=8 and in this case 3x= 24 is divisible by 6. but in another case, if x=16; then 3x= 48; which is divisible by 6; but 16 leaves a remainder of 4.

Hence B does not conclusively answer the question

Question 58.

What is the value of the positive integer n?
A. The product of the numbers a, and b, which are respectively three less and two less than n,is 0.
B. n!/2 =(n-2)!

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
Each statement alone is sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Discuss Question

Answer: Option B. -> Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
:
B

Option (b)

From A

(n - 3) (n - 2) = 0

n = 2 or 3

A alone is not sufficient

From B

Only for n = 2

n!/2 =(n-2)!

B alone is sufficient.

Question 59.

What is the perimeter of the triangle ABC? One of its side is 10√3 units.
A. BC is the hypotenuse of the right angle triangle ABC.
B. The sum of the areas of the semicircles described on the three sides of the triangle ABC is 100 π sq. units.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
Each statement alone is sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Discuss Question

Answer: Option D. -> BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
:
D

Option (d)

Given, sum of areas of semi-circles x, y and z is 100π

If BC = a cm, AC = b cm, AB = c cm.

Area of semi-circle x is π/2 x a²/4 cm2

Area of semi circle y is π/2 x c²/4 cm2

Area of semi circlezx is π/2 x b²/4 cm2

½ π/4 (a² + b² +c²) =100π

a2 + b² + c² = 800

from Statement 1:We know that in ABC is a right angle triangle.

a² = b² +c² = 2(b² +c²) = 800

b² +c² = 400

b² +c² = a² = 400 ;a = 20

b or c = 10√3 and the sides are 10, 10√3, 20

the perimeter = 30 + 10√3 cm

Question 60.

The cost price of an article is 100. Find the profit made by selling it.
A. Ten percent discount was given on the list price and the profit percentage made is 25 percentage points more than the discount percent.
B. List price is Rs.180 and profit percent is 1/5th of the mark up percentage.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
Each statement alone is sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Discuss Question

Answer: Option C. -> Each statement alone is sufficient
:
C

Option (C)

From A profit % is 35% (i.e. 10 +25) => profit = Rs.35

From B Markup% = 80%

profit % = 1/5 x 80 = 16%

profit = Rs.16

Either statement is sufficient