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 Post subject: GMAT Guide: AlgebraPosted: Sun Oct 09, 2011 9:57 am

Joined: Sun May 30, 2010 3:15 am
Posts: 424
(a) If 2 ≤ x ≤ 5 and y > 6, what is the range of values for
xy?

Solution

(a) Compare the minimum values and multiply.
The minimum value for x is 2 and the minimum for y is 6,
so the minimum for xy is 12.

Compare the maximum values and multiply.
The maximum value for x is 5 and y has no maximum, so
xy has no maximum. The range is xy > 12.
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Sorry but there is a Mistake in this point.
Mistake: the answer is a range of xy > 14 given that y > 6, 6 is not included so the minimum for y has to be 7 not 6.

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 Post subject: Re: GMAT Guide: inequalities.Posted: Sun Oct 09, 2011 10:09 am

Joined: Sun May 30, 2010 2:23 am
Posts: 498
Quote:
Mistake: the answer is a range of xy > 14 given that y > 6, 6 is not included so the minimum for y has to be 7 not 6.
That would be true, IF y was said to be an integer. However, the question statement does NOT specify this, so it is assumed that x and y are real numbers. E.g. y can be 6.000001 or 6 3/4, etc.

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I also would like to stress the point that you need to be more accurate, when ranges allow values of different signs. For example, if we have ranges
-4 < x < 4 and -2 < y < 3
we try out all combinations of the boundary values:
(-4) × (-2) = 8
(-4) × 3 = -12
4 × (-2) = -8
4 × 3 = 12

Then we take the minimum and the maximum results:
-12 < xy < 12

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