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If \(0 < x < 7\) and \(y < 9\), then the lowest pos

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by Brent@GMATPrepNow » Sun Dec 01, 2019 6:14 am
VJesus12 wrote:If \(0 < x < 7\) and \(y < 9\), then the lowest possible value for \(xy\) is

A. between 60 and 70
B. between 0 and 60
C. 0
D. between 0 and -70
E. less than -70

[spoiler]OA=E[/spoiler]

Source: Manhattan GMAT
If 0 < x < 7 and y < 9, then it COULD be the case that x = 5 and y = -1000, in which case xy = -5000
Of course y can be much smaller than -1000, which means xy can be much smaller than -5000

Answer: E

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by Scott@TargetTestPrep » Mon Dec 09, 2019 5:35 pm
VJesus12 wrote:If \(0 < x < 7\) and \(y < 9\), then the lowest possible value for \(xy\) is

A. between 60 and 70
B. between 0 and 60
C. 0
D. between 0 and -70
E. less than -70

[spoiler]OA=E[/spoiler]

Source: Manhattan GMAT
Since y is less than 9, y can be any negative number. Let's let y be -20 and x be 6; we see that xy can be -120, and thus the lowest possible value of xy is less than -70.

Answer: E

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by [email protected] » Tue Dec 10, 2019 12:10 pm
Hi All,

We're told that 0 < X < 9 and Y < 9. We're asked for the SMALLEST possible value of (X)(Y). This question is ultimately about Number Properties, so we can answer it in a number of different ways - including by TESTing VALUES or logic.

We know that X must be POSITIVE and Y can be positive (but less than 9), 0 or ANY negative. To make the product (X)(Y) as SMALL as possible, Y would have to be AS NEGATIVE AS POSSIBLE. Multiplying that type of extreme negative value by any positive value would lead to another extreme negative value (re: negative infinity).

Final Answer: E

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