# Practice Questions -Data Sufficiency -3

## Practice Questions -Data Sufficiency -3

**Directions (1-5) Each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read the question and both the statements and ****Give answer.**

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

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

(c) If the data either in statement I alone or in statement H alone are sufficient to answer the question.

(d) If the data even in both the statements I and II together are not sufficient to answer the question.

(e) If the data in both the statements I and II together are necessary to answer the question.

1) Train ‘A’ running at a certain speed crosses another train ‘B’ running at a certain speed in the opposite direction in 12 seconds. What is the length of train ‘B’?

I. The length of both the trains together is 450 metres.

II. Train ‘A’ is slower than train ‘B’.

2) Area of a rectangle is equal to the area of a right angled triangle. What is the length of the rectangle?

I. The base of the triangle is 40 cm.

II. The height of the triangle is 50 cm.

3) What was the total compound interest on a sum after three years?

I. The interest after one year was 100/ – and the sum was 1,000/-.

II. The difference between simple and compound interest on a sum of 1,000/- at the end of two years was 10/ – .

4) What is the two digit number where the digit at the unit place is smaller?

I. The difference between the two digits is 5.

II. The sum of the two digits is 7.

5) What is the speed of the boat in still water?

I. It takes 2 hours to cover distance between A and B down-stream.

II. It takes 4 hours to cover distance between A and B up-stream.

**Directions (6-10) Each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read the question and both the 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.

(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.

(c) If the data either in statement I alone or in statement II alone are sufficient to answer the question.

(d) If the data in both the statements I and II together are not sufficient to answer the question.

(e) If the data in both the statements I and II together are necessary to answer the question.

6) What is the annual income of Mr. Krishnamurthy from April 2001 to March 2002?

I. The annual income of Mr. Krishnamurthy is 70% more than that of his boss.

II. In April 2001 the income of Krishnamurthy was 12000 and his income increases by 10% per month.

7) What is the area of circular field?

I. The circumference of the field is x metres.

II. The diameter of the field is v metres.

8) What is the speed of boat in stir water?

I. The boat covers a distance of 35 kms in 5 hours in down-stream.

II. The boat takes 7 hours to cover the same distance in up-stream.

9) How many students are there in the class?

I. The ratio between the number of boys and girls is 5 : 6 respectively.

II. The difference between the numbers of boys and girls is 7.

10) What is the amount of earned profit?

I. On selling the article for f 1740, 20% profit is earned.

II. The cost price of the article is 1400.

**Answer:**

1. (d) 2. (d) 3. (c) 4. (e) 5. (d) 6. (b) 7. (c) 8. (e) 9. (e) 10. (a)

**Explanations**

1) (d)

Time taken in crossing each other

Total length of trains = Relative speed

The information given in both statements is not sufficient as length of train A and individual speed of each train is required.

2) (d)

Area of rectangle = Area of tri-angle. From the information given in both the statements, we can find area of triangle or area of rectangle. For finding length, breadth is required, which is not known.

3) (c)

From the statement I,

r=(100×100)/1000=10%

Thus we have,

P = Rs. 1000, r = 10%,

t = 3years

Hence, C.I. can be determined

From the statement II

S.I=(1000×r×2)/100=20r

C.I=1000 [(1+(r/100))]

C.I-S.I

1000 [(200r+(r^{2}/10000))]-20r

2000r + r^{2 }-200r = 100

R=10

Hence, C.I. can be determined

4) (e)

Let the unit’s digit be x and ten’s digit be y and x < y.

Number = 10y + x

From statement I,

y – x = 5 ——- (i)

From statement II,

y + x = 7 —— (ii)

From (i) and (ii), x, y can be calculated and two digit number can be found.

5) (d)

Let the distance between A and B be z km.

Again, let speed of boat in still water be x kmph and that of stream be y kmph.

Rate downstream

= (x + y) kmph

Rate upstream = (x – y) kmph

From statement I,

z/(x+y)=2

From statement II

z/(x-y)=4

Data inadequate

6) (b)

From statement I,

If the annual income of boss be x, then Mr. Krishnamurthy’s annual income

= 70% of x

But we do not know the value of x. Hence, this statement is not sufficient. From statement II, Initial income = Z’ 12000

Increase = 10% per month

Time = 12 months

Income in May

= Rs. 12000 + 10% of 12000

= Rs. (12000 + 1200)

= Rs. 13200

Similarly, the income for other months can be calculated.

7) (c)

From statement I,

If the radius of the circular field be r metres, then

2r= x

This relation gives us the value of radius.

Area = it x (Radius)^{2}

Hence, statement I alone is sufficient to answer the question

From statement II,

Diameter = y

Area = π × (Diametre/2)^{2}

Hence, statement II alone is also sufficient to answer the question.

8) (e)

Let the speed of boat in still water be x kmph and that of cur-rent be y kmph

Rate upstream = (x – y) kmph

Rate downstream = (x + y) kmph

From statement I,

x+y = 35/5

x + y = 7 kmph

From statement II,

x – y = 35/7

x-y= 5 kmph

From combined statements I and H, we can get the required answer.

9) (e)

From statement I,

Let the number of boys and girls be 5x and 6x respectively.

From statement II,

6x – 5x = 7

x = 7 5x = 35 and 6x = 42

Clearly, both statements are required to answer the question.

10) (a)

From statement I,

SP = Rs. 1740

% Profit = 20

CP=(100×1740)/120=Rs. 1450

Profit = Rs. (1740 – 1450)

= Rs. 290

Information in statement II is not required.

Hence, statement I alone is sufficient to answer the question.