# TANCET 2014 DS 64: Number Properties

## Directions

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

What is the value of xy?

1. Statement 1: x2 = 4.
2. Statement 2: y = 0.

Correct Answer    Choice (2). Statement (2) ALONE is sufficient.

## Explanatory Answer - step by step

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

Before evaluating the two statements, answer the following questions to gain clarity.

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

The question is "What is the value of xy?"

The answer should give an exact value for xy -- the answer is essentially a number.

#### When is the data sufficient?

If we are able to come up with a unique value for xy, the data is sufficient.

If we are not able to come up with a unique answer for xy, the data is NOT sufficient.

• ### Statement (1) ALONE

#### x2 = 4.

We can deduce that x is either 2 or -2. However, we do not have any information about y.

We cannot find the value of xy from the information given in statement (1).

Statement (1) ALONE is NOT sufficient.

The moment we realize that statement (1) is NOT sufficient, we can eliminate choices 1 and 4.

We can narrow down our choices to 2, 3 and 5.

• ### Statement (2) ALONE

#### y = 0.

Remember: When you are evaluating statement (2) ALONE, please do not recall information that you read in statement (1). It might be a good idea to read the question stem once and statement (2) alone to erase any information that you may retain about statement (1).

We know that y is 0.

We need to find the value of xy. If y is 0, xy will be 0 - irrespective of what value x takes.

We could find a UNIQUE value for xy from the information given in statement (2).

Statement (2) ALONE is sufficient. Hence, choice 2 is the answer.

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