**Data Sufficiency Questions for RRB NTPC Set-2 PDF**

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**Question 1:Â **3 friends namely- Pam, Ram, and Sam have certain number of pen and pencil with them. The total number of pens and pencils with all of them together is 18. Each of them has at least one pen and pencil and the number of pen and the number of pencils with each of them is distinct. Moreover, each of them has more pencils than pen. Find the number of pen and the number of pencils with Ram.

A) The total number of pens is 6 while Ram has 3 pencils.

B) The number of pens with Pam is less than that with Ram and Shyam. But, Pam has more objects than Ram.

a)Â Choose A if the answer can be determined using either statement alone.

b)Â Choose B if the answer can be determined using only one statement alone.

c)Â Choose C if the answer can be determined using both the statements together.

d)Â Choose D if the answer cannot be determined using both the statements together.

**Question 2:Â **In this question two statements I and II are given. Study both the sentences and analyse which one is sufficient to answer the question.

Is x=y?

Statement I: $(x-23)^2 = (y-23)^2$

Statement II: $(x+y)(\frac{1}{x} + \frac{1}{y}) – 4 = 0$

a)Â The question can be answered by using one of the statements alone but not by the other statement alone.

b)Â The question can be answered by using either statement alone.

c)Â The question can be answered by using both the statements together.

d)Â The question cannot be answered even by using both the statements together.

**Question 3:Â **Amongst six distinct positive integers, 13 is the highest while 5 is the lowest. What is the average of the six numbers?

Statement 1: The sum of the six numbers is 11 more than the square of an integer.

Statement 2: Exactly half of the numbers are prime and the sum of the numbers is also prime.

a)Â Statement 1 alone is sufficient to answer the question

b)Â Statement 2 alone is sufficient to answer the question

c)Â Statement 1 and 2 together are sufficient to answer the question

d)Â Both the statements together are also not sufficient to answer the question

**Question 4:Â **Read the following information and choose the appropriate option.

What is Ramâ€™s present age?

Statement I: 5 years ago Ramâ€™s age was twice the age of Shyam. Shyamâ€™s age was a perfect square back then and even now his age is a perfect square.

Statement II: Ramâ€™s age is 5 times the age of Mohan whose current age is the largest single digit prime number.

a)Â The question can be answered by using one of the statements alone but not by the other statement alone.

b)Â The question can be answered by using either statement alone.

c)Â The question can be answered by using both the statements together.

d)Â The question cannot be answered even by using both the statements together.

**Question 5:Â **Is B taller than D?

**Statement 1:** A is taller than B who is shorter than C.

**Statement 2:** C is taller than D who is taller than A.

a)Â Statement 1 alone is sufficient to answer the question

b)Â Statement 2 alone is sufficient to answer the question

c)Â Either Statement alone is sufficient to answer the question

d)Â Both Statement 1 and Statement 2 together are sufficient to answer this question

e)Â Both Statement 1 and Statement 2 together are also not sufficient to answer this question

**Instructions**

Each of the questions below consists of a question and two statements numbered 1Â and 2Â given below it. You have to decide whether the data provided in the statements are sufficient to answer the question.

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**Question 6:Â **Two persons A and B are standing some distance apart and start moving towards each other. They meet after a time â€˜tâ€™ seconds. What was the distance between them before they started moving towards each other?

**Statement 1:** The speeds of A and B are â€˜v1â€™ and â€˜v2â€™ respectively.

**Statement 2:** The speeds of A and B are in the ratio 2:3.

a)Â If the data in statement I alone is sufficient to answer the question while the data in statement II alone is not.

b)Â If the data in statement II alone is sufficient to answer the question while the data in statement I alone is not.

c)Â If the data in both the statements together is sufficient to answer the question.

d)Â If the data in either statement alone is sufficient.

e)Â If the data even in both statements together is not sufficient to answer the question.

**Question 7:Â **Is x(y+2) an odd number, where x and y are distinct integers?

**Statement I**: x and y are prime numbers

**Statement II**: y>11

a)Â If the data in statement I alone is sufficient to answer the question while the data in statement II alone is not.

b)Â If the data in statement II alone is sufficient to answer the question while the data in statement I alone is not.

c)Â If the data in both the statements together is sufficient to answer the question.

d)Â If the data in either statement alone is sufficient.

e)Â If the data even in both statements together is not sufficient to answer the question.

**Question 8:Â **In the decimal representation of a, where 0 < a < 1, is the digit in tenths place a non-zero number?

**Statement I**: 16a is an integer

**Statement II**: 32a is an integer

a)Â If the data in statement I alone is sufficient to answer the question while the data in statement II alone is not.

b)Â If the data in statement II alone is sufficient to answer the question while the data in statement I alone is not.

c)Â If the data in both the statements together is sufficient to answer the question.

d)Â If the data in either statement alone is sufficient.

e)Â If the data even in both statements together is not sufficient to answer the question.

**Question 9:Â **In a school 40% of the students in 12th standard are in Commerce stream and the rest in Science stream. If 20% of the students in Science stream are females, what is the percentage of males in the commerce stream?

**Statement I**. The number of females in the Science stream is 36 less than the number of boys

**Statement II**. forty-percent of all students in 12th standard are females

a)Â if the data in statement I alone is sufficient to answer the question while the data in statement II alone is not.

b)Â if the data in statement II alone is sufficient to answer the question while the data in statement I alone is not.

c)Â if the data in both the statements together is sufficient to answer the question.

d)Â if the data in either statement alone is sufficient.

e)Â if the data even in both statements together is not sufficient to answer the question.

**Question 10:Â **Is the positive integer X divisible by 12?

**Statement I**. When X is divided by 16 the remainder is 4

**Statement II**. When X is divided by 18 the remainder is 6

a)Â if the data in statement I alone is sufficient to answer the question while the data in statement II alone is not.

b)Â if the data in statement II alone is sufficient to answer the question while the data in statement I alone is not.

c)Â if the data in both the statements together is sufficient to answer the question.

d)Â if the data in either statement alone is sufficient.

e)Â if the data even in both statements together is not sufficient to answer the question.

**Question 11:Â **6 friends A, B, C, D, E, F are standing in a straight line according to their heights. (The tallest person is standing at the first position and shortest is at 6th position). Who is the shortest among the six?I A is taller than B, who in turn is taller than C and E

II E is three places behind B and 1 place ahead of F

a)Â If only statement I is sufficient to answer the question.

b)Â If only statement II is sufficient to answer the question.

c)Â If either of the statement taken alone is sufficient.

d)Â If question cannot be answered using both the statements.

e)Â If both the statements are required to answer the question.

**Instructions**

Each of the questions below consists of a question and two statements numbered 1Â and 2Â given below it. You have to decide whether the data provided in the statements are sufficient to answer the question.

**Question 12:Â **N is 2 digit number such that it has an odd number of factors. What is the sum of the digits of N?

**Statement I.** The sum of the digits is not divisible by 3

**Statement II.** The sum of the digits is even

c)Â If the data in both the statements together is sufficient to answer the question.

d)Â If the data in either statement alone is sufficient.

e)Â If the data even in both statements together is not sufficient to answer the question.

**Question 13:Â **In a class of some students, 22 play harmonica, 30 play keyboard, and 28 play guitar. How many students play all the three instruments?

Statement I: The number of students who play exactly two instruments is 6

Statement II: The total number of students in the class is 150% more than the number of students who play guitar

a)Â The question can be answered using only statement I alone or only statement II alone.

b)Â The question can be answered using either statement alone.

c)Â The question can be answered only by using both statements together.

d)Â The question cannot be answered even by using both statements together.

**Question 14:Â **Is x = y?

Statement 1: x+3y+4z = 80

Statement 2: 3x+2y+5z = 100

a)Â Statement 1 alone is sufficient to answer the question while Statement 2 alone is not

b)Â Statement 2 alone is sufficient to answer the question while Statement 1 alone is not

c)Â Both the statements together are sufficient to answer the question

d)Â Both the statements together are also not sufficient to answer the question

**Question 15:Â **Two persons start running simultaneously around a circular track from the same point, at the same time and in the same direction. What is the ratio of speeds of the faster runner to that of the slower one?

I. The length of the track is 450m

II. When they met for the sixth time after starting the race, the slower person covered a distance of 3700m

a)Â The question can be answered by using statement I alone or using statement II alone

b)Â The question can be answered by using either statement alone.

c)Â The question can be answered only by using both statements together.

d)Â The question cannot be answered even by using both statements together.

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**Answers & Solutions:**

**1)Â AnswerÂ (B)**

Letâ€™s assume Pam has a pen and b pencils, Ram has c pen and d pencils, and Sam has e pen and f pencils.

So, a<b, c<d, and e<f

Also, a+b+c+d+e+f = 18

Now, letâ€™s assume A to be true.

So, a+c+e = 6. So, a/c/e = 1/2/3 as all of them have distinct number of pens and pencils.

Also, Ram has 3 pencils. So, the number of pen with him can be 1 or 2. So, answer cannot be determined from this alone.

Assume B alone:

a<c,e but a+b>c+d

We know that each of them has distinct pen and pencils.

Letâ€™s assume a,c,e are 1,2,3

So, b,d,f (min) can be 2,3,4. But this case is not possible as Pam doesnâ€™t have more objects than Ram.

Only case that can be is when a=1, c=2, and e=3 and b=5, d=3, and f=4

So, we can determine the number of pens and pencils with Ram using B alone. Thus, B is the correct answer.

**2)Â AnswerÂ (A)**

Statement I: $(x-23)^2 = (y-23)^2$

=> $x-23 = \pm (y-23)$

=> x=y or x+y = 46

Statement II: $(x+y)(\frac{1}{x} + \frac{1}{y}) – 4 = 0$

=> $\frac{(x+y)^2}{xy} = 4 $

=> $\frac{x^2 + y^2 + 2xy}{xy} = 4 $

=> $\frac{x^2 + y^2}{xy} = 2 $ or $x^2 + y^2 -2xy = 0$

=> $(x-y)^2 = 0$ or x=y

We can see that the question can be answered using statement 2 alone. Thus, A is the correct answer.

**3)Â AnswerÂ (A)**

The numbers must range from [5,13]

Since both 5 and 13 are included in the six numbers, the other 4 numbers must be among 6, 7, 8, 9, 10, 11 and 12.

Letâ€™s consider statement 1. So, the sum of the six numbers is 11 more than a perfect square. Min and Max sum of the six numbers can be 48 and 60. So the only perfect square that we should consider is 49. So, the sum of the six numbers should be 49+11 = 60

This is only possible when the six numbers are 5, 9, 10, 11, 12, 13. Since the sum of the numbers is known, the average can be calculated.

Statement 2: So, exactly 3 of the six numbers are prime and the sum of the numbers is also prime.

Now, 5 and 13 are both prime. So, the third number should be either 7 or 11.

Letâ€™s consider 7 as the third prime.

So, the sum should be 5+7+13 + (Sum of 3 composite numbers among 6, 8, 9, 10, and 12) or 25 + (Sum of 3 composite numbers among 6, 8, 9, 10, and 12) prime.

But, none of the combination yields a prime sum.

Letâ€™s assume 11 is the third prime.

So, the sum should be 5+11+13 + (Sum of 3 composite numbers among 6, 8, 9, 10, and 12) or 29 + (Sum of 3 composite numbers among 6, 8, 9, 10, and 12) prime.

So, there are 2 possible cases when sum is prime.

(i) When the numbers are (5+11+13+6+8+10) where the sum is 53, and

(ii) When the numbers are (5+11+13+8+10+12) where the sum is 59

We can see that the average will be different in both the cases. So, II is not sufficient.

Thus, A is the correct answer.

**4)Â AnswerÂ (B)**

From I, the only possible age of Shyam is 9 years (Since the difference between his present age and his age 5 years ago are perfect squares with a difference of 5)

Since we know Shyamâ€™s age we can easily find the Ramâ€™s age as well. 5 years ago Ram’s age was twice the age of Shyam. So Shyam’s age would have been 4. Thus, Ram’s age would have been 8. Thus his present age would be 13.

Thus I alone is sufficient to answer the question.

From II, we know that Moanâ€™s age is 7. Thus, Ramâ€™s age would be 35.

Hence even statement II alone is sufficient. Hence the correct answer is option B.

**5)Â AnswerÂ (D)**

From the statements we know that the decreasing order of heights is:

C>D>A and

A>B<C

Combining these statements we know that, D>A>B. So B is shorter than D.

**6)Â AnswerÂ (A)**

From statement 1 we know that their speeds are v1 and v2. So the distance will be (v1+v2)*t.

From the second statement we only know the ratio of the speeds and without the absolute values we cannot compute the distance between them.

**7)Â AnswerÂ (E)**

x(y+2)

I: x and y are prime.

So, if any of x and y is 2, x(y+2) is a even number. While, when both are odd x(y+2) is also odd.

II: y>11

This is clearly not sufficient as even y will yield even number and odd x and y will yield odd number.

Using I and II together:

So, x=2 then the number is even, and when x is odd prime number, the number is odd.

Thus, the question cannot be answered even by using both statements together.

**8)Â AnswerÂ (E)**

I: If 16a is an integer, a can be 1/2, 1/4, 1/8, 1/16 or 0.5, 0.25, 0.125, 0.0625

Thus, from this statement, we canâ€™t infer that the tenth decimal digit is non-zero.

II: If 32a is an integer, a can be 1/2, 1/4, 1/8, 1/16, 1/32 or 0.5, 0.25, 0.125, 0.0625, 0.03125

Thus, from this statement, we canâ€™t infer that the tenth decimal digit is non-zero.

If both statements are used, we can infer that â€˜aâ€™ is one among 0.5, 0.25, 0.125, 0.0625.

But, even then we canâ€™t conclude that the tenth decimal digit is non-zero since 0.0625 has 0 has tenth decimal digit.

Thus, the answer is E.

**9)Â AnswerÂ (B)**

Let the total number of students in 12th standard be x. Then total students in Commerce = .4x and students in Science = .6x

Number of females in the Science stream = .6x $\times$2 = .12x Thus, no. of males in the Science stream = .48x

From Statement I, .48x – .12x = 36

=> .36x = 36. Thus, x = 100. From this we cannot find the percentage of males in Commerce stream.

From statement II, Total girls in 12th = .4x

Thus, total girls in Commerce stream = .4x – .12x = .28x

Thus, total males in Commerce stream = Total students in Commerce – girls in Commerce = .4x – .28x = .12x

From this we can find the percent of male students in Commerce. Thus, B alone is enough to answer the given question.

**10)Â AnswerÂ (C)**

We have to find whether the given statements are enough to find whether X is divisible by 12 i.e. X is divisible by both 3 and 4.

From statement I, X is of the form 16m + 4. 16m + 4 is divisible by 4 but we cannot know whether X is divisible by 3 or not. Thus, statement I alone is not sufficient to answer the given question.

From statement II, X is of the form 18k + 6. 18k + 6 is divisible by 3 but we cannot know whether X is divisible by 4 or not. Thus, statement II alone is not sufficient sufficient to answer the given question.

If we combine both the statements we find that X is divisible by both 3 and 4. Thus, both statements together can answer if X is divisible by 12. Thus, C is the right choice.

**11)Â AnswerÂ (E)**

From statement I alone, we cannot determine the position of anyone.

From statement II alone, we can infer some structure, but still we can’t conclude who is the shortest.

But if combine both the statements, then from statement II, we can be sure that B is either at 1st position on at 2nd position. But from statement I, the possibility of B being at the first position can be ruled out. Hence B stands at 2nd position. So C is at fifth and F is at 6th.

Hence if we combine both the statements together, then we can answer the given question.

**12)Â AnswerÂ (B)**

We are given that N is a two digit number having odd number of factors.

So we can say that N is a perfect square.

2 digit perfect squares are 16, 25, 36, 49, 64, 81

The sum of the digits of these numbers is as follow

16 – 7

25 – 7

36 – 9

49 – 13

64 – 10

81 – 9

From statement I we can rule out 9 but we still have 4 possibilities left. Hence we cannot answer the question from statement I alone.

From statement II, we know that the sum of the digits is even. Thereâ€™s only one sum which is even. i.e 10 Hence we can answer the question using statement II alone.

**13)Â AnswerÂ (D)**

The number of students who donâ€™t play any instrument has not been mentioned in the question or in the two statements. Without it, the number of students who play all the three instruments cannot be found out. Thus, the answer is D.

**14)Â AnswerÂ (C)**

To find the relation between x and y we first have to eliminate z.

Multiplying the equation from Statement 1 by 5 we get,

5x+15y+20z = 400 —- (1)

Multiplying the equation from Statement 2 by 4 we get,

12x+8y+20z = 400 —- (2)

Subtracting equation (1) from (2) we get, x = y.

**15)Â AnswerÂ (C)**

Let a m/s be the speed of the faster person and b m/s be the speed of the slower person

In statement I, only the length of the track is given. We cannot find the ratio of their speeds from this information alone.

In statement II, the distance travelled by the slower person is given but not the distance of the faster person. Thus, again we cannot find the ratio of their speeds from this information alone.

If we combine both information we get, the length of track is 450m and distance travelled by the slower person after six meetings as 3700m.

When the two people meet for the first time, the faster one travels extra distance equal to the length of the track. Thus, the distance travelled by the faster persons after six meetings = 3700+ 450 x 6 = 6400m

Thus, in equal time the faster one and the slower one travels 6400m and 3700m respectively.

Thus, the ratio of their speeds = 6400/3700 = 64 : 37

Thus, the question can be answered if we combine both the statements together.

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