Data Sufficiency Problems To Prepare For SBI PO Exam

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.

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.

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.

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.

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.

Score Well In SBI & IBPS, PO & Clerk Exams

Related pages

solving surdsnabard establishediob polist of international airportsibps bank bookssarva up grameen bankquadrilateral questionsgeometric progresionhow to solve arithmetic progressionsurds and indicespallavan grama bankpipe and cisterntmb savings accountmeaning of coding and decodingproblems in permutations and combinationslatest gk and current affairswho is the governor of rbi in indiasymbol of rbia geometric progressiontamilnad mercantile bank careersalligationibps exam for clerkdata sufficiency questions and answersbearer cheque and order cheque meansgramya bank recruitmentsbi clericalproblems on surds and indicescomputer questions for ibps clerk exammahila diwasformulas of profit and lossdifference between circumference and perimeterpractice syllogismspresent head of rbiibps preparation guidetamilnadu international airportgovernor of rbi in indianame of chennai sea portprobability sums with solutionsalligation problems and answerssbi bank exam papersvenn diagram reasoningpermutations and combinations solved problemsproblems on surds and indicessyllogism questions with possibilityhow many types of cheques in bankratio and proportion tutorialsbi bank clarksbi bank exam booksibps po preparationodisha gramya bank recruitmentgrameen vikas banktypes of cisternreasonings questions and answersibps booksquestion on permutation and combinationbank po aptitude questions and answersquestions on permutation and combinationgk question for bank examsurds problems and solutionsbook for bank examsbi exam preparation bookssyllogism test onlinefirst bank to launch atm in indiahard aptitude questions with solutionssbi bank exam paperslargest salt water lake in indiafirst bank to introduce atmcarrier in sbibank exam solved papershow to write bearer chequerbi establishmentreasoning questions for bank exams with answersidbi openingsallegation and mixture problemsindia's largest fresh water lakeibps exam datesbanking exams sample papersgovernor of rbi in indiacurrent affairs & gk