# TANCET 2014 DS 69: Mensuration

## Directions for Data Sufficiency Question

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

Medium Data Sufficiency

What is the surface area of the rectangular solid y?

1. Statement 1: The dimensions of one face of the rectangular solid y are 2 by 3.
2. Statement 2: The area of another face of the rectangular solid y is 6.

Correct Answer    Choice (5). Statements (1) and (2) TOGETHER are not 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 "What is the surface area of the rectangular solid y?"

The answer to the question should be a number followed by square units. For e.g., 40 sq units.

#### When is the data sufficient?

If we are able to come up with a UNIQUE value for the surface area, the data is sufficient.

If we are not able to come up with a UNIQUE value for the surface area of the rectangular solid y, the data is NOT sufficient.

#### How to compute the surface area of the rectangular solid?

For a rectangular solid of length l units, width w units and height h units, the surface area is 2(lw + wh + lh).

#### What is the approach?

Look for a counter example. Try to figure out more than one value for the surface area using the information given in the statements.

If you are able to come up with more than one answer, the data is NOT sufficient. If only one value exists, the data is SUFFICIENT.

• ### Statement (1) ALONE

#### The dimensions of one face of the rectangular solid y are 2 by 3.

Essentially, we have two out of the 3 dimensions required to find the surface area.

The surface area will take different values for different values of the third dimension.

Statement (1) ALONE is NOT sufficient.

If statement (1) ALONE is NOT sufficient, we can eliminate choices 1 and 4.

Choices narrow down to 2, 3, or 5.

• ### Statement (2) ALONE

#### The area of another face of the rectangular solid y is 6.

Remember: When you are evaluating statement (2) ALONE, please do not recall information that you read in statement (1). Anything said about any one face in statement (1) should not be used while evaluating statement (2).

The area of a second face is 6 square units.

There could be multiple possibilities for the two dimensions of this face. It could be 2 * 3 or it could be 6 * 1.

Further, we still do not have information about the 3rd dimension and the final answer is a function of that dimension.

Using statement (2) we were NOT able to determine a unique value for W.

Statement (2) ALONE is NOT sufficient.

If statement (2) ALONE is NOT sufficient, we can eliminate choice 2 as well.

Choices narrow down to 3, or 5.

• ### Statements Together

+

#### area of another face of the rectangular solid y is 6.

The two faces mentioned could be two opposite faces of a rectangular solid.

In a rectangular solid, opposite faces have the same dimension and hence the same area.

Essentially, it again boils down to the fact that we only have two out of the 3 dimensions required to find the surface area. We do not have the third dimension and it is required to get a unique answer.

Statements (1) and (2) together are NOT sufficient to determine the surface area of the rectangular solid y.

Hence, choice (5) is the answer.

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