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# If | x + 1 | <= 5 and | y — 1| <= 5, what is the least

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If | x + 1 | <= 5 and | y — 1| <= 5, what is the least [#permalink]  05 Mar 2017, 13:03
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Question Stats:

60% (01:07) correct 40% (01:23) wrong based on 10 sessions

If | x + 1 | <= 5 and |y — 1| <= 5, what is the least possible value of the product xy ?

[Reveal] Spoiler:
-36

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Joined: 07 Jun 2014
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GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Kudos [?]: 1612 [0], given: 375

Re: If | x + 1 | <= 5 and | y — 1| <= 5, what is the least [#permalink]  11 Mar 2017, 21:07
Expert's post
Explanation

Find $$| x + 1 | \leq 5$$:

$$-5 \leq x + 1 \leq 5$$ or $$-6 \leq x \leq 4$$

Now calculate $$| y - 1 | \leq 5$$:

$$-5 \leq y - 1 \leq 5$$ or $$-4 \leq y \leq 6$$

To find the least possible value of the product xy, put numbers from the extremes of x and y. Keep in mind that two positive numbers and two negative numbers will result in a positive number.

Since we want the least value, we are looking for a negative number and must use one positive and one negative value to obtain it.

If x = 4 and y = –4, then xy = –16
If x = –6 and y = 6, then xy = –36

The least possible value is –36.
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Re: If | x + 1 | <= 5 and | y — 1| <= 5, what is the least   [#permalink] 11 Mar 2017, 21:07
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