# Aptitude - Area

### Exercise :: Area - Data Sufficiency 2

Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.

1.

 What is the area of the hall? I. Material cost of flooring per square metre is Rs. 2.50 II. Labour cost of flooring the hall is Rs. 3500 III. Total cost of flooring the hall is Rs. 14,500.

 A. I and II only B. II and III only C. All I, II and III D. Any two of the three E. None of these

Explanation:

I. Material cost = Rs. 2.50 per m2

II. Labour cost = Rs. 3500.

III. Total cost = Rs. 14,500.

Let the area be A sq. metres. Material cost = Rs. (14500 - 3500) = Rs. 11,000. 5A = 11000 A = 11000 x 2 = 4400 m2. 2 5

Thus, all I, II and III are needed to get the answer. Correct answer is (C).

2.

 What is the area of a right-angled triangle? I. The perimeter of the triangle is 30 cm. II. The ratio between the base and the height of the triangle is 5 : 12. III. The area of the triangle is equal to the area of a rectangle of length 10 cm.

 A. I and II only B. II and III only C. I and III only D. III, and either I or II only E. None of these

Explanation:

From II, base : height = 5 : 12.

Let base = 5x and height = 12x.

Then, hypotenuse = (5x)2 + (12x)2 = 13x.

From I, perimeter of the triangle = 30 cm. 5x + 12x + 13x = 30 x = 1.

So, base = 5x = 5 cm, height = 12x = 12 cm. Area = 1 x 5 x 12 cm2 = 30 cm2. 2

Thus, I and II together give the answer.

Clearly III is redundant, since the breadth of the rectangle is not given. Correct answer is (A).

3.

 What is the area of rectangular field? I. The perimeter of the field is 110 metres. II. The length is 5 metres more than the width. III. The ratio between length and width is 6 : 5 respectively.

 A. I and II only B. Any two of the three C. All I, II and III D. I, and either II or III only E. None of these

Explanation:

I. 2(l + b) = 110 l + b = 55.

II. l = (b + 5) l - b = 5.

 III. l = 6 5l - 6b = 0. b 5

These are three equations in l and b. We may solve them pairwise. Any two of the three will give the answer. Correct answer is (B).