Data Sufficiency Problems To Prepare For SBI PO Exam

Dear Reader,
Below are 4 problems on data sufficiency dealing with two digit numbers.

Directions to Solve :
Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is / are sufficient to answer the given question. Read the both 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 II 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 or in Statement II alone are sufficient to answer the question.
Give answer (D) if the data even in both Statements I and II together are not sufficient to answer the question.
Give answer (E) if the data in both Statements I and II together are necessary to answer the question.

Question 1

What is the two-digit number?

I. The difference between the two digits is 3.
II. The sum of the two digits is 4 more than their difference.

Answer : option E.

Solution :

Let the tens and unit digits be X and Y respectively.

Then,

From statement I, we have: X-Y = 3 ...(1)
From statement II, we have: (X+Y) = 3+4 = 7...(2)

Adding (1) and (2), we get 2X = 10 => X = 5

Putting X value in (1) or (2), we get: Y = 2

Required two digit number is 52.

Here the data in both Statements I and II together are necessary to find the answer.

Hence the answer is option E.

Question 2

What is the sum of the digits of a two-digit number?

I. The difference between the digits of that number is 1.

II. One-seventh of the number is 7 more than one-third of 21.

Answer : option E.

Solution :

Let the tens and unit digits be X and Y respectively.

Then the two digit number is (10X+Y)

From statement I, we have: X-Y = 1 ...(1)

From statement II, we have: (10X+Y)/7 = 7 + (21/3)
(10X+Y)/7 = 7 + 7
(10X+Y)/7 = 14
(10X+Y) = 98...(2)

Adding (1) and (2), we get 11X = 99 => X = 9
Then, Y = X-1 = 8.
Therefore the two digit number is 98.

Required sum = 9+8 = 15.

Here, the data in both Statements I and II together are necessary to find the answer.

Hence the answer is option E.

Question 3

What will be the ratio between the two digits in the two digit number?

I. The largest digit is 9.
II. The sum of the digits in the number is 5 times their difference.

Answer : option B.

Solution :

Let the tens and unit digits be X and Y respectively.

Statement I do not give the answer.

From statement II, we have:

(X+Y) = 5(X-Y)
(X+Y) = 5X-5Y
4X = 6Y
X/Y = 6/4 = 3/2

Therefore the required ratio = X/Y = X:Y = 3:2

Here, the data in Statement II alone are sufficient to find the answer, while the data in Statement I alone are not sufficient.

Hence the answer is option B.

Question 4

What is the two-digit number?

I. The product of two digits in the number is 32 and the ratio of their digits is 2:1
II. Sum of the two digits is 12 and their difference is 4.

Answer : option C.

Solution :

Let the tens and unit digits be X and Y respectively.

Then the two digit number is (10X+Y)

From statement I, we have:
Product = XY = 32
Ratio = X/Y = 2/1 = 2
X = 2Y

Then, product XY = (2Y)Y = 2(Y^2) = 32
(Y^2) = 16
Y = 4
And X = 2Y = 2x4 = 8.
Therefore the number is 84.

From statement II, we have

Sum = X+Y = 12
Difference = X-Y = 4

Adding above two, we get, 2X = 16 => X = 8.
Then, Y = 12 - 8 = 4

Therefore, required number = 84.

Here, the data either in Statement I or in Statement II alone are sufficient to answer the question.

Hence the answer is option C.


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