This GMAT Free Math question is a Probability Data Sufficiency question. Though the question is from probability, this is, in essence a Number Properties DS question. A GMAT 700 level hard math question.

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 10: Set A contains distinct integers: A = {2, 4, 6, -8, x, y}. When two numbers from this set are selected and multiplied, what is the probability that the product is less than zero?

**Statement 1**: x × y is not equal to zero.

**Statement 2**: |x| = |y|

From INR

**Statement 1**: x × y is not equal to zero

Inference: Neither x nor y is zero.

__Possibility 1__: Both x and y are positive. The set will contain 5 positive and 1 negative number.

__Possibility 2__: Both x and y are negative. The set will contain 3 positive and 3 negative numbers.

__Possibility 3__: One of x or y is positive and the other is negative. The set will contain 4 positive and 2 negative number.

The probability will be different for each of these 3 possibilities.

We **cannot compute a unique value** for the probability with information available in statement 1.

Statement 1 ALONE is not sufficient.

__Eliminate answer option A and D__.

Answer options narrow down to B, C, or E.

**Statement 2**: |x| = |y|

__Possibility 1__: x = y

__Possibility 2__: x = -y (opposite sign, but same magnitude)

Possibility 1 is NOT possible because set A has distinct integers.

Result: Set A has 4 positive and 2 negative numbers.

Statement 2 ALONE is Sufficient.

Using the data in statement 2, we can **compute a unique value** for the probability.

Hence, statement 2 is sufficient.

__Eliminate answer options C and E.__.

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