# Data Sufficiency - Previous Year CAT/MBA Questions

You can practice all previous year OMET questions from the topic Data Sufficiency. This will help you understand the type of questions asked in OMET. It would be best if you clear your concepts before you practice previous year OMET questions.

**XAT 2019 QADI | Data Sufficiency**

A bag contains marbles of three colours-red, blue and green. There are 8 blue marbles in the bag. There are two additional statement of facts available:

- If we pull out marbles from the bag at random, to guarantee that we have at least 3 green marbles, we need to extract 17 marbles.
- If we pull out marbles from the bag at random, to guarantee that we have at least 2 red marbles, we need to extract 19 marbles.

Which of the two statements above, alone or in combination shall be sufficient to answer the question "how many green marbles are there in the bag"?

- A.
Both statements taken together are suﬃcient to answer the question, but neither statement alone is suﬃcient.

- B.
Each statement alone is suﬃcient to answer the question.

- C.
Statements 1 and 2 together are not suﬃcient, and additional data is needed to answer the question.

- D.
Statement 2 alone is suﬃcient, but statement 1 alone is not suﬃcient to answer the question.

- E.
Statement 1 alone is suﬃcient, but statement 2 alone is not suﬃcient to answer the question.

Answer: Option D

**Explanation** :

We know that in all there are 8 blue marbles.

Let us first look at statement I.

As per statement I if we are to pull out 17 marbles from the bag, we will ensure that there are at least 3 greeen marbles. Now out of 17 marbles removed, 8 are blue .So from the 9 marbles that are removed, if at least 3 are green, it would mean maximum possible no of red marbles removed are 9-3 or 6.Which means that the red marbles in the bag are 6.However, this statement alone gives us no information about the no of green marbles. Hence statement I alone is not sufficient to answer the question.

Let us next look at statement II.

As per this statement, if we are to pull out 19 marbles from the bag, we would have at least 2 red marbles. Out of the 19 marbles removed, suppose 8 are blue. Now out of the remaining 11 marbles removed, if we have at least 2 red marbles, it would mean that the maximum possible no of green marbles removed is 9.This means that in all there are 9 green marbles in the bag .

Hence statement 2 alone is sufficient to answer the question.

Hence, option (d).

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**XAT 2019 QADI | Data Sufficiency**

We have two unknown positive integers m and n, whose product is less than 100.

There are two additional statement of facts available:

- mn is divisible by six consecutive integers { j, j + 1,...,j + 5 }
- m + n is a perfect square.

Which of the two statements above, alone or in combination shall be sufficient to determine the numbers m and n?

- A.
Statements 1 and 2 together are not suﬃcient, and additional data is needed to answer the question.

- B.
Both statements taken together are suﬃcient to answer the question, but neither statement alone is suﬃcient.

- C.
Each statement alone is suﬃcient to answer the question.

- D.
Statement 2 alone is suﬃcient, but statement 1 alone is not suﬃcient to answer the question.

- E.
Statement 1 alone is suﬃcient, but statement 2 alone is not suﬃcient to answer the question.

Answer: Option B

**Explanation** :

Looking at the initial statement , we know that mn < 100.

Looking at statement I ,we get to know that the product mn has to be a multiple of 10 since it is divisible by 6 consecutive integers .So the product can be either 10, 20, 30 ….90

Now of all these numbers only 60 is divisible by 6 consecutive numbers i.e. numbers 1 to 6.60 can be expressed as a product of 2 nos. in the following ways : 1 × 60, 2 × 30, 3 × 20, 4 × 15, 5 × 12, 6 ×10

So from statement I alone we cannot determine values of m and n. Looking at statement II alone determine values of m and n as the only information provided to us is that “m + n” is a perfect square. So we can have numerous possibilities for m and n [e.g (7, 9), (2, 7), (1, 3) etc ]

Combining both statements out of (1, 60), (2, 30), (3, 20), (4,15), (5, 12), (6, 10), the only pair of values such that “m+n” is a perfect square is (6, 10). Hence both statements are required to answer the question.

Hence, option (b).

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**XAT 2018 QADI | Data Sufficiency**

These statements provide data that may help answer the respective questions. Read the questions and the statements and determine if the data provided by the statements is sufficient or insufficient, on their own or together, to answer the questions. Accordingly, choose the appropriate option given below the questions.

A group of six friends noticed that the sum of their ages is the square of a prime number. What is the average age of the group?

**Statement I**: All members are between 50 and 85 years of age.

**Statement II**: The standard deviation of their ages is 4.6.

- A.
Statement I alone is sufficient to answer.

- B.
Statement II alone is sufficient to answer.

- C.
Either of the statement is sufficient to answer.

- D.
Both statements are required to answer.

- E.
Additional information is required.

Answer: Option A

**Explanation** :

**From statement I: **

Sum of their ages lies between (6 × 50) and (6 × 85), i.e., 300 and 510.

The only square of a prime number in this range is 192 = 381.

∴ The average of their ages = 381/6.

Hence, the question can be answered using statement I alone.

**From statement II:**

Standard Deviation = 4.6 = $\frac{\sqrt{\sum ({x}_{i}-\overline{x})}}{6}$

Since there are two unknowns here, the question cannot be answered using this statement alone.

Hence, option (a).

Workspace:

**XAT 2018 QADI | Data Sufficiency**

These statements provide data that may help answer the respective questions. Read the questions and the statements and determine if the data provided by the statements is sufficient or insufficient, on their own or together, to answer the questions. Accordingly, choose the appropriate option given below the questions.

Harry and Sunny have randomly picked 5 cards each from a pack of 10 cards, numbered from 1 to 10. Who has randomly picked the card with number 2 written on it?

**Statement I**: Sum of the numbers on the cards picked by Harry is 5 more than that of Sunny.

**Statement II**: One has exactly four even numbered cards while the other has exactly four odd numbered cards.

- A.
Statement I alone is sufficient to answer.

- B.
Statement II alone is sufficient to answer.

- C.
Either of the statement is sufficient to answer.

- D.
Both statements are required to answer.

- E.
Additional information is required.

Answer: Option D

**Explanation** :

**From statement I:**

The sum of all the 10 cards = 55.

The sum of the numbers picked by Harry is 30 and that picked by Sunny is 25.

A sum of 30 can be obtained if the cards picked are 2, 4, 6, 8 and 10.

A sum of 25 can be obtained if the cards picked are 2, 3, 4, 7 and 9.

∴ We cannot determine who picked card number 2.

**From statement II:**

We cannot ascertain who picked card number 2.

From statements I and II together:

Sum of 4 odd cards and 1 even card will always be even

∴ Harry should get 4 odd cards and 1 even card such that his sum is 30.

Case 1:

Harry picks – 1, 3, 10, 7, 9 (Sum is 30)

Sunny picks – 2, 4, 6, 8, 5 (Sum is 25)

In this case Sunny picks card 2.

Case 2:

Harry picks – 1, 8, 5, 7, 9 (Sum is 30)

Sunny picks – 2, 4, 6, 3, 10 (Sum is 25)

In this case also Sunny picks card 2.

Case 3:

Harry picks – 6, 3, 5, 7, 9 (Sum is 30)

Sunny picks – 2, 4, 1, 8, 10 (Sum is 25)

In this case also Sunny picks card 2.

There will be no other possibility.

∴ Both statements together are required to answer the question.

Hence, option (d).

Workspace:

**Answer the next 2 questions based on the following information:**

In an innings of a T20 cricket match (a team can bowl for 20 overs) 6 bowlers bowled from the fielding side, with a bowler allowed maximum of 4 overs. Only the three specialist bowlers bowled their full quota of 4 overs each, and the remaining 8 overs were shared among three non-specialist bowlers. The economy rates of four bowlers were 6, 6, 7 and 9 respectively. (Economy rate is the total number of runs conceded by a bowler divided by the number of overs bowled by that bowler). This however, does not include the data of the best bowler (lowest economy rate) and the worst bowler (highest economy rate). The number of overs bowled and the economy rate of any bowler are in integers.

**XAT 2017 QADI | Data Sufficiency**

Read the two statements below:

S1: The worst bowler did not bowl the minimum number of overs.

S2: The best bowler is a specialist bowler.

Which of the above statements or their combinations can help arrive at the minimum number of overs bowled by a non-specialist bowler?

- A.
S1 only

- B.
S2 only

- C.
Either S1 or S2

- D.
S1 and S2 in combination

- E.
The minimum number of overs can be determined without using S1 or S2

Answer: Option E

**Explanation** :

There are 3 specialist bowlers and 3 non- specialists bowlers.

The three specialist bowlers bowled 4 overs each and 3 non-specialist bowlers would have bowled 8 overs.

8 overs can be bowled by 3 non-specialist bowlers when they bowl 3, 3 and overs.

This is the only possibility since maximum overs a non-specialist can bowl is 3 overs.

So, the least number of overs bowled by a non-specialist bowler would be 2 only.

So, none of the S1 and S2 required to answer the question.

Hence, option (e).

Workspace:

**XAT 2017 QADI | Data Sufficiency**

Read the two statements below:

S1: The economy rates of the specialist bowlers are lower than that of the non-specialist bowlers.

S2: The cumulative runs conceded by the three non-specialist bowlers were 1 more than those conceded by the three specialist bowlers.

Which of the above statements or their combinations can help arrive at the economy rate of the worst bowler?

- A.
S1 only

- B.
S2 only

- C.
Either S1 or S2

- D.
S1 and S2 in combination

- E.
The economy rate can be calculated without using S1 or S2.

Answer: Option D

**Explanation** :

S1: The given economy rates of 4 bowlers are 6, 6, 7 and 9. So, the non-specialist bowlers would have 7, 9, x as their economy rates and specialist bowlers would have y, 6, 6 as their economy rates.

S2: The overs bowled by specialist bowlers would be 4, 4 and 4 each. The number of overs bowled by non-specialist bowlers would in any combination of 3, 3 and 2 each.

The runs given by specialist bowlers would be 6 × 4 + 6 × 4 + 4y = 48 + 4y …(1)

**Case 1**: For non-specialist bowlers, overs bowled are 3, 3, 2 and economy rate is 7, 9 and x respectively.

∴ The runs given by non-specialist bowlers = (7 × 3 + 9 × 3 + x × 2) = 48 + 2x ...(2)

According to the question: (2) – (1) = 1

∴ 2x – 4y = 1

Now, 2x – 4y cannot give an odd value.

**Case 2**: For non-specialist bowlers, overs bowled are 3, 3, 2 and economy rate is x, 7 and 9 respectively.

The runs given by non-specialist bowlers would be (9 × 2 + 7 × 3 + 3x) = 39 + 3x

According to the question: (2) – (1) = 1

∴ 39 + 3x = 48 + 4y + 1

This is satisfied for x =10 and y = 5

Thus, we need both the statements to get to worst economy rate of the bowler.

Hence, option (d).

Workspace:

**XAT 2016 QADI | Data Sufficiency**

Anita, Biplove, Cheryl, Danish, Emily and Feroze compared their marks among themselves. Anita scored the highest marks, Biplove scored more than Danish. Cheryl scored more than at least two others and Emily had not scored the lowest.

**Statement I**: Exactly two members scored less than Cheryl.

**Statement II**: Emily and Feroze scored the same marks.

Which of the following statements would be sufficient to identify the one with the lowest marks?

- A.
Statement I only.

- B.
Statement II only.

- C.
Both Statement I and Statement II are required together.

- D.
Neither Statement I nor Statement II is sufficient.

- E.
Either Statement I or Statement II is sufficient.

Answer: Option B

**Explanation** :

Anita scored the highest marks, hence Anita cannot have the lowest marks.

Biplove scored more than Danish, hence Biploye cannot have the lowest marks.

Cheryl scored more than at least two others, hence Cheryl cannot have the lowest marks.

Emily had not scored the lowest.

∴ Either Danish or Feroze will have the lowest marks.

From Statement I: Cheryl’s has the 4th highest marks

Here, we cannot uniquely identify the person with least marks with only this information.

From Statement II: Emily and Feroze scored same marks.

∵ Emily doesn’t have lowest marks, Feroze also cannot have the lowest marks.

∴ Only Danish can have the lowest marks.

⇒ Statement II is sufficient to identify the person with the lowest marks

Hence, option (b).

Workspace:

**XAT 2016 QADI | Data Sufficiency**

A person standing on the ground at point A saw an object at point B on the ground at a distance of 600 meters. The object started flying towards him at an angle of 30° with the ground. The person saw the object for the second time at point C flying at 30° angle with him. At point C, the object changed direction and continued flying upwards. The person saw the object for the third time when the object was directly above him. The object was flying at a constant speed of 10 kmph.

Find the angle at which the object was flying after the person saw it for the second time. You may use additional statement(s) if required.

Statement I: After changing direction the object took 3 more minutes than it had taken before.

Statement II: After changing direction the object travelled an additional 200√3 meters.

Which of the following is the correct option?

- A.
Statement I alone is sufficient to find the angle but statement II is not.

- B.
Statement II alone is sufficient to find the angle but statement I is not.

- C.
Statement I and Statement II are consistent with each other.

- D.
Statement I and Statement II are inconsistent with each other.

- E.
Neither Statement I nor Statement II is sufficient to find the angle.

Answer: Option D

**Explanation** :

From the given data,

m∠CAB = 30°; m∠CBA = 30° and AB = 600 m

∴ BC = AC = 200√3 m … [By sine rule]

Statement I: After changing the direction the object took 3 more minutes than it had taken before.

The object travels 200√3 m from B to C at 10 km/hr

Thus, in 3 minutes it can travel 500 m. Hence, the object travels a total of 500 + 200√3m from C.

Thus, we know the hypotenuse CD by which we can find out the angle.

Statement II: After changing directions, the object travels 200√3 m.

Since, the object travels the same distance as before, this can only happen if the object stays on the course as before without changing any direction.

Thus, we can clearly see that the two angles from the statements are inconsistent with each other.

Hence, option (d).

Workspace:

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