**Directions (1-5):**Each of the questions below consists of a question and three statements numbered A, B and C given below it. You have to decide whether the data provided in the statements are sufficient to answer the questions. Read all the statements and given an answer:

**1. What is the cost of painting two adjacent walls of a room which have no window or door?**

**B.**The breadth, height and the length of the room are in the ratio of 4: 5: 7

**C.**The cost of painting per m² is rs. 50.

1. Both A and B

2. All A, B and C

3. Only C

4. Both B and C

5. Only B

**2. How much profit did Naman earn on the cost price of an article by selling it?**

**A.**He got 10% discount on the marked price at the time of purchase.

**B.**He sold it for Rs. 3120.

**C.**He earned 4% profit on the marked price.

1. All A, B and C

2. Only A

3. Only B

4. Both A and B

5. Only C

**3. What is the present population of the city?**

**A.**The population of the city was 1690000, two years ago.

**B.**The population of the city increases at the rate of 25% per year.

**C.**The population of the city decreases by 1/25 of its total population per year.

1. Only C

2. Both A and B

3. All A, B and C

4. Only A

5. Both B and C

**4. In how many days will the work be completed by Aryan and Ankush?**

**A.**Aryan is twice as efficient as Ankush.

**B.**Ankush can complete the work in 32 days.

**C.**Aryan joins the work after 4 days of the start of work.

1. Only A

2. Only B

3. Both A and B

4. Both B and C

5. All A, B and C

**5. What is the area of the hte rectangular field?**

**A.**The perimeter of the field is 240 metres.

**B.**The width is 10 meters less than the length.

**C.**The ratio of the length to breadth is 13: 11

1. Both A and B

2. Both B and C

3. Only A

4. Only B

5. Any two of the three

*Download Data Sufficiency Workbook here*### Answer :

**1. 2;**

From A, B and C, we get

Area of the room = 664

⇒ 2 (20x² + 28x² + 35x²) = 664

⇒ 116x² = 664

∴ x = 2

∴ Cost of painting

= (

*I*h + bh) x 50
= (14 + 8 ) x 10 x 50

= Rs. 11000

**2. 1;**

Let the marked price be Rs. 100

From A, B and C, we get

Cost Price = Rs. 90

By selling the article for Rs. 3120, he gained 4% on the marked price.

∴ Sp is 104, when MP is Rs. 100

SP is 3120, when MP = 100/104 x 3120 = Rs. 3000

∴ Cost price = 3000 x 90/100 = Rs. 2700

So we need all three statements to answer the question.

**3. 3;**

From A, B and C:

Population of the city two years ago = 1,69,0000

Rate of increase = 25% per year

Rate of decrease = 1/25 x 100 = 4% per year

Hence, total growth of population = 25 - 4 = 31%

So, present population = 1690000 (1+21/100)²

= 2474329

Hence, all the statements are necessary.

**4. 5;**

From Statement A; Ratio of efficiency of Aryan to that of Ankush = 2: 1

Ratio of time taken by Aryan to that of Ankush = 1:2

From A, B and C;

If Ankush can complete the work in 32 days.

Then, 4 days work of Ankush

So, the remaining work

After 4 days, Aryan and Ankush both are working together.

Hence 1 day's work of Ankush and Aryan

Number of days required to complete the work

Total number of days

So,all the three statements are required.

**5. 5;**

From A; 2(

*I +*b) = 240 ⇒*I +*b = 120
From B;

*I =*(b + 10) ⇒*I -*b = 10
These are three equations are of length and breadth. We may solve them by making pair of any two.

∴ Any two of the three will give answer.

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