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# If |x + 3| = 12 and |y +2| = 9, the maximum value of xy =

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If |x + 3| = 12 and |y +2| = 9, the maximum value of xy = [#permalink]
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Bunuel wrote:
If |x + 3| = 12 and |y +2| = 9, the maximum value of xy =

A 63
B 84
C 99
D 132
E 165

|x + 3| = 12
means x is 12 units away from -3. It will be either at -15 or at 9.

|y +2| = 9
means y is 9 units away from -2. It will be either at -11 or at 7.

xy will be maximum when it is positive so x and y are both positive or both negative and when absolute values of x and y are maximum.
So x = -15 and y = -11 will give positive xy and x and y will have maximum absolute values.
xy = -15*-11 = 165

Originally posted by KarishmaB on 21 Jan 2019, 04:58.
Last edited by KarishmaB on 20 Oct 2022, 05:20, edited 1 time in total.
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Re: If |x + 3| = 12 and |y +2| = 9, the maximum value of xy = [#permalink]
Bunuel wrote:
If |x + 3| = 12 and |y +2| = 9, the maximum value of xy =

A 63
B 84
C 99
D 132
E 165

solve for x & y values
x= -15 & 9
y=-11, 7
max values
(-)15*(-)11
= 165
IMO E
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Re: If |x + 3| = 12 and |y +2| = 9, the maximum value of xy = [#permalink]
Bunuel wrote:
If |x + 3| = 12 and |y +2| = 9, the maximum value of xy =

A 63
B 84
C 99
D 132
E 165

IMO E

Product of two negative numbers results in a positive number. SO now if we solve the question, we can realize that the negative values of the mod, will give the maximum value
x = -15 and y = -11
xy = 165
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Re: If |x + 3| = 12 and |y +2| = 9, the maximum value of xy = [#permalink]
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Re: If |x + 3| = 12 and |y +2| = 9, the maximum value of xy = [#permalink]
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