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If |a + 3| ≤ 6 and |b + 4| ≤ 12, what is the maximum value of ab?

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If |a + 3| ≤ 6 and |b + 4| ≤ 12, what is the maximum value of ab?  [#permalink]

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New post 21 Jan 2019, 01:25
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Question Stats:

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If |a + 3| ≤ 6 and |b + 4| ≤ 12, what is the maximum value of ab?


A. 24
B. 120
C. 144
D. 192
E. 256
Spoiler: OA

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Re: If |a + 3| ≤ 6 and |b + 4| ≤ 12, what is the maximum value of ab?  [#permalink]

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New post 21 Jan 2019, 01:53
|a+3| ≤ 6
-6 ≤ a+3 ≤6
subtract 3 on both sides
-9 ≤ a ≤ 3

|b+4| ≤ 12
-12 ≤ b+4 ≤ 12
subtract 4 on both sides
-16 ≤ b ≤ 8

Max value of ab can be -16*-9 = 144

C is the answer.
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Re: If |a + 3| ≤ 6 and |b + 4| ≤ 12, what is the maximum value of ab?  [#permalink]

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New post 21 Jan 2019, 02:32
Bunuel wrote:
If |a + 3| ≤ 6 and |b + 4| ≤ 12, what is the maximum value of ab?


A. 24
B. 120
C. 144
D. 192
E. 256



|a + 3| ≤ 6

-6≤a+3≤6

-9≤a≤9

again,

|b + 4| ≤ 12

-12≤b + 4 ≤12

-16≤b≤8

organize the data:

-9≤a≤9

-16≤b≤8

ab*** max.

ab =(-9) ( -16) = 144.

C is the correct answer.
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Re: If |a + 3| ≤ 6 and |b + 4| ≤ 12, what is the maximum value of ab?  [#permalink]

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New post 21 Jan 2019, 07:52
Bunuel wrote:
If |a + 3| ≤ 6 and |b + 4| ≤ 12, what is the maximum value of ab?


A. 24
B. 120
C. 144
D. 192
E. 256


solve for a & b
a we get a<=3 ; a>=9 and b <=8 and b>=16
ab max = 9*16
= 144
IMO C
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Re: If |a + 3| ≤ 6 and |b + 4| ≤ 12, what is the maximum value of ab?   [#permalink] 21 Jan 2019, 07:52
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