# TANCET 2014 DS 76: Mensuration

## Directions for TANCET Data Sufficiency Questions

The question is followed by two statements labeled (1) and (2) in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the problem plus your knowledge of mathematics and everyday facts, choose the answer as:

1. Choice 1 if statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Choice 2 if statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. Choice 3 if both the statements (1) and (2) TOGETHER are sufficient, but NEITHER statement alone is sufficient.
4. Choice 4 if each statement ALONE is sufficient.
5. Choice 5 if statements (1) and (2) TOGETHER are not sufficient, and additional data is needed.

## Question

Square G has sides of length 4 cm. Is the area of the Square H exactly one-half the area of Square G?

1. Statement 1: The length of the diagonal of Square H equals the length of one side of Square G.
2. Statement 2: The perimeter of Square H is twice the length of the diagonal of Square G.

Correct Answer    Choice (4). Each statement is INDEPENDENTLY sufficient.

## Explanatory Answer - step by step

• ### What should we know from the Question Stem?

Before evaluating the two statements, answer the following questions to get clarity on when the data is sufficient.

#### What kind of an answer will the question fetch?

The question is "Is the area of square H exactly one-half the area of square G?"

The question is an "is" question. The answer to the question is either an 'yes' or a 'no'.

#### When is the data sufficient?

If we are able to come up with a CONCLUSIVE answer – a DEFINITE YES or a DEFINITE NO, the data is sufficient.

If we are not able to come up with a DEFINITE answer – if we find that the area of square H is exactly half that of square G in some cases and not equal to half that of square G in other cases the data is NOT sufficient.

#### What data do we know from the question stem?

Square G has sides of length 4 cm.

So, area of square G is 16 sq cm.

• ### Statement (1) ALONE

#### The length of the diagonal of Square H equals the length of one side of Square G.

The diagonal of Square H = side of Square G = 4 cm.

Area of a square = a2, where a is the area.

Area of a square = $$frac{d^2}{2}\\$, where d is the diagonal. We know the diagonal of Square H; so, area of Square H = $\frac{d^2}{2} = \frac{4^2}{2}\\$ = 8 sq cm. Area of Square H = $\frac{1}{2}\\$ area of Square G. We could get a UNIQUE YES as an answer to the question using data from statement$1).

Statement (1) ALONE is sufficient.

The moment we realize that statement (1) is sufficient, we can narrow down our choices to 1 or 4.

To determine whether the answer is choice 1 or choice 4, we need to evaluate statement (2). Remember that you have to evaluate statement (2) even if statement (1) is sufficient.

• ### Statement (2) ALONE

#### The perimeter of Square H is twice the length of the diagonal of Square G.

Remember: When you are evaluating statement (2) ALONE, please do not recall information that you read in statement (1). Anything said about the relation between Square H and Square G in statement (1) should not be used while evaluating statement (2).

Diagonal of Square G = $$sqrt{2}\\$$side of Square G) = 4$$sqrt{2}\\$ Perimeter of Square H = 2$the diagonal of Square G) = 2 (4$$sqrt{2}\\$) = 8$\sqrt{2}\\$ Therefore, side of Square H = $\frac{Perimeter}{4}\\$ = $\frac{8\sqrt{2}}{4}\\$ = 2$\sqrt{2}\\$. Area of Square H =$side)2 = (2$$sqrt{2}\\$)2 = 8 sq cm. Area of Square H = $\frac{1}{2}\\$ area of Square G. We could get a UNIQUE YES as an answer to the question using data from statement 2. Statement$2) ALONE is ALSO sufficient.

If statement (1) ALONE is sufficient and statement (2) ALONE is ALSO sufficient, each statement is INDEPENDENTLY sufficient.

Hence, choice (4) is the answer.

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