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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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New post 21 Jan 2019, 02:38
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E

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Question Stats:

74% (01:05) correct 26% (01:03) wrong based on 128 sessions

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

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New post 21 Jan 2019, 02:46
Product will be maximum when both x and y are either positive or negative.
X = -15
Y = -11
Hence answer is 165 (E)

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

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New post 21 Jan 2019, 03:21
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

1) x + 3 is positive:

x + 3 = 12

x = 9.

2) x + 3 is negative:

-x - 3 = 12

x = -15.

again,

|y + 2| = 9

1) y + 2 is positive:

y + 2 = 9
y=7.

2) y + 2 is negative :

-y -2 = 9

y = -11

..........

x= 9, -15

y = 7, -11

we are looking for max value of xy***

x*y = (-15)*(-11) = 165.

E is the correct answer.
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If |x + 3| = 12 and |y +2| = 9, the maximum value of xy =  [#permalink]

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New post 21 Jan 2019, 04:58
1
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

Answer (E)

Check out this way of dealing with absolute values here:
https://www.veritasprep.com/blog/2011/0 ... edore-did/
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Re: If |x + 3| = 12 and |y +2| = 9, the maximum value of xy =  [#permalink]

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New post 21 Jan 2019, 09:28
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]

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New post 21 Jan 2019, 09:34
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] 21 Jan 2019, 09:34
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