A GMAT DS practice question in Number Properties and Number Theory. Concept covered includes absolute value of numbers and positive and negative numbers.

This data sufficiency problem consists of a question and 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 statements, plus your knowledge of mathematics and everyday facts (such as the number of days in a leap year or the meaning of the word counterclockwise), you must indicate whether -

- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
- EACH statement ALONE is sufficient to answer the question asked.
- Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

All numbers used are real numbers.

A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2)

Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight

You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.

All figures lie in a plane unless otherwise indicated.

In data sufficiency problems that ask for the value of a quantity, the data given in the statement are sufficient only when it is possible to determine exactly one numerical value for the quantity.

Question 13: Is xy < 0?

- 5|x| + |y| = 0
- |x| + 5|y| = 0

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

The question is an **"Is"** question. Answer to an "is" question is either YES or NO.

**When is the data sufficient?**

The data is sufficient if we are able to get a DEFINITE YES or a DEFINITE NO from the information given in the statements.

If the answer is __MAYBE__ or __DONOT KNOW__, the data is NOT sufficient.

**When is the answer YES and when is it NO?**

If xy < 0, the answer is YES. If xy ≥ 0, the answer is NO.

__Note__: If xy = 0, the answer is NO.

Evaluate Statement (1) ALONE: 5|x| + |y| = 0

Modulus of any real number will always be non-negative.

So, if 5|x| + |y| = 0, then the only possibility is that x = 0 and y = 0.

Therefore, xy = 0.

Or xy is not negative.

The answer is a DEFINITE NO.

**Statement 1 ALONE is sufficient.**

Eliminate choices B, C and E. Choices narrow down to A or D.

Evaluate Statement (2) ALONE: |x| + 5|y| = 0

Modulus of any real number will always be non-negative.

So, if |x| + 5|y| = 0, then the only possibility is that x = 0 and y = 0.

Therefore, xy = 0.

Or xy is not negative.

The answer is a DEFINITE NO.

**Statement 2 ALONE is also sufficient.**

Eliminate choice A.

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