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
- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- EACH statement ALONE is sufficient.
- 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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