Question: Is the product of a positive and a negative integer less than -10?

(1) The positive integer is greater than 3
(2) The negative integer is less than -2

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are not sufficient.

“Is the product of a positive and a negative integer less than -10?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "The Official Guide for GMAT Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution and Explanation:
Approach Solution 1:
The model answer for this question has only 1 approach
Let's assume the positive integer is 'x' and the negative integer is 'y'. We have to determine if x*y < -10

(1) x > 3. So the minimum value of x is 4 (has to be an integer). But nothing about y, so insufficient.

(2) y < -2. So the maximum value of y is -3 (has to be an integer). But nothing about x, so insufficient.

Combining the two statements, if we take x = 4 and y = -3, then their product = 4*-3 = -12. For any other values of x & y satisfying the two statements, the product will be less than -12 only. (eg, x=5, y=-3 gives us -15 and x=4, y=-4 gives us -16 and so on...)

So if the product is less than -12, it will obviously be less than -10 also. (any number to the left of -12 will also be to the left of -10 on the number line). Sufficient.

Correct Answer: C

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