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08 May 2020, 07:52
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
34% (02:23) correct
66%
(02:20)
wrong
based on 365
sessions
History
Date
Time
Result
Not Attempted Yet
(|a| - 3) (|b| + 4) = 12. How many pairs of integers (a, b) satisfy this equation?
A) 4
B) 6
C) 8
D) 10
E) 12
A) 4
B) 6
C) 8
D) 10
E) 12
Source: www.GMATinsight.com
yashikaaggarwal
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08 May 2020, 08:24
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Answer is supposedly 10.
Factors of 12 = 3*4,6*2,12*1
(|a| - 3) (|b| + 4) = 12.
Let the factors of 12 be 3*4
Since second bracket already have 4 in there, b has to be zero. And a will have 2 values. +6,-6 who when solved using bodmas will give 3.
The ordered pairs will be (6,0)(-6,0) = 2
Let the factors of 12 be 2*6
Since second bracket already have 4 in there, b has to be 2 (+2,-2), who will give the sum of 6 when solved using bodmas. And a will also have 2 values. (+5,-5) who when solved using bodmas will give 2.
The ordered pairs will be (-5,-2)(5,2)(-5,2)&(5,-2) = 4
Let the factors of 12 be 1*12
Since second bracket already have 4 in there, b has to be 8 (+8,-8), who will give the sum of 12 when solved using bodmas. And a will also have 2 values. (+4,-4) who when solved using bodmas will give 2.
The ordered pairs will be (-4,-8)(4,8)(-4,8)&(4,-8) = 4
4+4+2=10 ordered pairs.
So IMO is D
Posted from my mobile device
Factors of 12 = 3*4,6*2,12*1
(|a| - 3) (|b| + 4) = 12.
Let the factors of 12 be 3*4
Since second bracket already have 4 in there, b has to be zero. And a will have 2 values. +6,-6 who when solved using bodmas will give 3.
The ordered pairs will be (6,0)(-6,0) = 2
Let the factors of 12 be 2*6
Since second bracket already have 4 in there, b has to be 2 (+2,-2), who will give the sum of 6 when solved using bodmas. And a will also have 2 values. (+5,-5) who when solved using bodmas will give 2.
The ordered pairs will be (-5,-2)(5,2)(-5,2)&(5,-2) = 4
Let the factors of 12 be 1*12
Since second bracket already have 4 in there, b has to be 8 (+8,-8), who will give the sum of 12 when solved using bodmas. And a will also have 2 values. (+4,-4) who when solved using bodmas will give 2.
The ordered pairs will be (-4,-8)(4,8)(-4,8)&(4,-8) = 4
4+4+2=10 ordered pairs.
So IMO is D
Posted from my mobile device
General Discussion
ArunSharma12
Joined: 25 Oct 2015
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08 May 2020, 08:46
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GMATinsight
- \(12 \times 1\): (4,8),(4,-8),(-4,8),(-4,-8)
\(6 \times 2\): (5,2),(5,-2),(-5,2),(-5,-2)
\(4 \times 3\):(6,0),(-6,0)
