**Data Sufficiency Questions for IIFT PDF**

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**Question 1: **What is the cost price of the chair?

I. The chair and the table are sold at profits of 15% and 20% respectively.

II. If the cost price of the chair is increased by 10% and that of the table is increased by 20%, the profit reduces by Rs. 20.

a) The question can be answered with the help of one statement alone.

b) The question can be answered with the help of any one statement independently.

c) The question can be answered with the help of both statements together.

d) The question cannot be answered even with the help of both statements together.

**Question 2: **A person is walking from Mali to Pali, which lies to its north-east. What is the distance between Mali and Pali?I. When the person has covered $\frac{1}{3}$ the distance, he is 3 km east and 1 km north of Mali.

II. When the person has covered $\frac{2}{3}$ the distance, he is 6 km east and 2 km north of Mali.

a) The question can be answered with the help of one statement alone.

b) The question can be answered with the help of any one statement independently.

c) The question can be answered with the help of both statements together.

d) The question cannot be answered even with the help of both statements together.

**Question 3: **What is the number of type-2 widgets produced, if the total number of widgets produced is 20,000?

I. If the production of type-1 widgets increases by 10% and that of type-2 decreases by 6%, the total production remains the same.

II. The ratio in which type-1 and type-2 widgets are produced is 2 : 1.

a) if the question cannot be answered even with the help of both the statements taken together.

b) if the question can be answered by any one of the two statements.

c) if each statement alone is sufficient to answer the question, but not the other one (e.g. statement I alone is required to answer the question, but not statement II and vice versa.

d) if both statements I and II together are needed to answer the question.

**Question 4: **What will be the time for downloading software?

I. Transfer rate is 6 kilobytes per second.

II. The size of the software is 4.5 megabytes.

a) The question can be answered by one of the statements alone and not by the other.

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

c) The question can be answered by using both the statements together, but cannot be answered by using either statement alone.

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

**Instructions**

Each question is followed by two statements, I and II. Mark the answer

**Question 5: **How many different triangles can be formed?

I. There are 16 coplanar, straight lines.

II. No two lines are parallel.

a) if the question cannot be answered even with the help of both the statements taken together.

b) if the question can be answered by any one of the two statements.

c) if each statement alone is sufficient to answer the question, but not the other one (e.g. statement I alone is required to answer the question, but not statement II and vice versa.

d) if both statements I and II together are needed to answer the question.

**Question 6: **Nandini paid for an article using currency notes of denominations Re. 1, Rs. 2, Rs. 5, and Rs. 10 using at least one note of each denomination. The total number of five and ten rupee notes used was one more than the total number of one and two rupee notes used. What was the price of the article?

A. Nandini used a total of 13 currency notes.

B. The price of the article was a multiple of Rs. 10.

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

b) The question can be answered by using either of the statements alone.

c) The question can be answered by using both statements together but not by either statement alone.

d) The question cannot be answered on the basis of the two statements.

**Instructions**

Each question is followed by two statements, I and II. Mark the answer

**Question 7: **If α and β are the roots of the equation $(ax^2+bx+c=0)$, then what is the value of $(α^2 +β^2)$?

I.$α+β=\frac{-b}{a}$

II.$2αβ =\frac{c}{a}$

a) if the question cannot be answered even with the help of both the statements taken together.

b) if the question can be answered by any one of the two statements.

c) if each statement alone is sufficient to answer the question, but not the other one (e.g. statement I alone is required to answer the question, but not statement II and vice versa.

d) if both statements I and II together are needed to answer the question.

**Question 8: **In a class of 30 students, Rashmi secured the third rank among the girls, while her brother Kumar studying in the same class secured the sixth rank in the whole class. Between the two, who had a better overall rank?

A. Kumar was among the top 25% of the boys merit list in the class in which 60% were boys.

B. There were three boys among the top five rank holders, and three girls among the top ten rank holders.

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

b) The question can be answered by using either of the statements alone.

c) The question can be answered by using both statements together but not by either statement alone.

d) The question cannot be answered on the basis of the two statements.

**Question 9: **x, y, and z are three positive odd integers, Is x+z divisible by 4?

I. y – x = 2

II. z – y = 2

a) The question can be answered with the help of statement I alone,

b) The question can be answered with the help of statement II alone,

c) Both, statement I and statement II are needed to answer the question, and

d) The statement cannot be answered even with the help of both the statements.

**Question 10: **O is the centre of two concentric circles. AE is a chord of the outer circle and it intersects the inner circle at points B and D. C is a point on the chord in between B and D. What is the value of AC/CE?

A. BC/CD=1

B. A third circle intersects the inner circle at B and D and the point C is on the line joining the centres of the third circle and the inner circle.

a) the question can be answered by one of. the statements alone, but cannot be answered by using the other statement alone.

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

c) the question can be answered by using both the statements together, but cannot be answered by using either statement alone.

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

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**Answers & Solutions:**

**1) Answer (D)**

Let the cost price of the Chair be x and that of the table be y.

Using statement 1)

Hence we get the total selling price = 1.15x + 1.2y and profit = 0.15x + 0.2y

Using this alone we can’t find the cost price of the chair.

Using Statement 2)

Total cost price = 1.10 x + 1.2y

Using Statement 1 and 2 together,

We get profit in second case = 0.05x.

Reduction in profit = (0.15x + 0.2y) – 0.05x = 0.1x + 0.2y = 20

Hence we can’t deduce the value of x even after using both statements together.

**2) Answer (B)**

Considering first statement alone, we can calculate 1/3rd of the complete distance as $\sqrt{1^2 + 3^2}$ Hence, we can evaluate complete distance too.

Considering second statement alone, we can calculate 2/3rd of the complete distance as $\sqrt{2^2 + 6^2}$ Hence, we can evaluate complete distance too.

So answer will be B as complete distance can be calculated by using any of the statement alone.

**3) Answer (B)**

Considering 1st statement alone:

When total number of widgets is 20000

let’s say share of type-1 = x

and share of type-2 = y

So x+y = 20000

and 1.1x+0.94y = 20000

Hence we can find value of x and y by statement 1 alone.

Now considering second statement alone;

$x+y = 20000$

$\frac{x}{y} = \frac{2}{1}$

Hence with second statement also, we can find value of x and y

So answer will be B.

**4) Answer (C)**

We cannot answer the question using either of the statements alone. If we consider both the statements i.e. transfer rate is 6 kilobytes per second and the size of the software is 4.5*1024 kilobytes = 4608 kilobytes then download time = 4608 / 6 seconds. Hence, the question can be answered by using both the statements together, but cannot be answered by using either statement alone.

**5) Answer (A)**

Considering given statements, we can’t find an absolute number of triangles as lines in a plane can be concurrent also with several other possibilities.

So answer will be A.

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**6) Answer (D)**

Let the no. of 1,2,5,10 Rs notes be x,y,z,w.

According to given condition we have z+w=x+y+1 .

Now considering statement A

The possible values are 4+3=3+3+1 .

But in this case the data is not sufficient to find price of article as the both 5 and 10 rs can have any of the 4 or 3 notes.

Hence statement A is not sufficient.

Now considering statement B ,

The price of the article was a multiple of Rs. 10.

For this, more than 1 possibility of no. of notes of a particular value is there. Also 2 statements together can’t give the total price of the article.

**7) Answer (D)**

$(α^2 +β^2)$ can be reduced to $(α+β)^2 – 2(αβ)$

Now as we can see, we need both values of (α+β) and (αβ) to solve the equation.

Hence answer will be D.

**8) Answer (A)**

We know that Rashmi secured the third rank among the girls, while her brother Kumar studying in the same class secured the sixth rank in the whole class.

Considering statement A we have 18 B and 12 G and out of 18 boys kumar is among top 4 . But in this case we can’t get the relative posiiton of rashmi and kumar.

Consider statement B. We know that among top 5 , 3 are boys and 2 are girls .So rashmi is not among top5 and we know that Kumar’s rank is 6 . So Rashmi is definately below Kumar. Hence, the question can be answered by using one of the statements alone but not by using the other statement alone.

**9) Answer (C)**

If only first statement taken into consideration:

y-x = 2 where x, y and z are three odd integers.

Nothing absolute can be said about divisibility of x+z with 4.

Now if only second statement taken into consideration :

z-y=2 and nothing absolute can be said about divisibility of x+z with 4.

If we consider both statement simoultaneously then

we get x+z = 2y

Now as we know y is an odd integer , so 2y will never get a factor of 4.

Hence x+z is not divisible by 4.

As we find an absolute answer by using both statements Hence answer will be C)

**10) Answer (B)**

Using statement A we know that C is midpoint of both BD and AE . Also using statement B we know that C is midpoint of BD and AE. Hence , the question can be answered by using either statement alone.

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