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A very interesting GMAT hard math data sufficiency question. A GMAT 675+ level DI question testing your understanding of multiple concepts – positive and negative numbers, computing probability, and interpreting the import of absolute values of two variables being the same.
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 July 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.
Set A contains distinct integers: A = {2, 4, 6, -8, x, y}. When two numbers from this set are picked and multiplied, what is the probability that the product is less than zero?
(1) x * y is not equal to zero.
(2) |x| = |y|
Correct Answer is choice B. Statement 2 alone is sufficient.
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Here is a summary and interpretation of what is given in the question stem
Can we determine whether x and y are positive or negative or zero using the information in the two statements.
Neither x nor y is zero. Though a valuable information, it still leaves more things unsaid. Is x or y positive and is x or y negative is not answered.
Statement 1 alone is therefore, not sufficient.
Eliminate answer options A and D.
This one is a very interesting statement.
If |x| = |y|, then we have the following inferences
Possibilities 1, 2 and 3, that both x and y are zero or both x and y are positive or both x and y are negative are not possible scenarios because the question stem states that the 6 numbers are distinct integers. So, x cannot be equal to y.
In possibility 4, we have one of x or y being positive and the other being negative. So, the set will comprise 4 positive numbers and 2 negative numbers.
The number of outcomes in which the product will be negative is when one of the two negative numbers is selected and one of the 4 positive numbers is selected. i.e., in 2 * 4 = 8 ways.
That being the case, the probability will be 8/15
Because we are able to find a unique answer to the question using statement 2, statement 2 alone is sufficient to answer the question.