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(a^2 + 5a + 6[/m]](/forum/styles/gmatclub_light/imageset/icon_post_target_unread.svg "For positive integer a, is the expression [m](a - 4)(a^2 + 5a + 6[/m]"){kind=icon}
18 Apr 2019, 09:48
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A
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Difficulty:
25%
(medium)
Question Stats:
73% (01:38) correct
27%
(02:11)
wrong
based on 59
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For positive integer a, is the expression \((a - 4)(a^2 + 5a + 6\)) divivsible by 4?
1. a is divisible by 8.
2. a is an odd integer.
1. a is divisible by 8.
2. a is an odd integer.
18 Apr 2019, 11:38
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Rewrite the given expression as: \((a-4)(a+3)(a+2)\).
Statement 1: \(a\) is divisible by 8. Hence, \(a\) will be a multiple of \(8 = 2^3 = 4 *2\). Taking into account \(a-4\), we instantaneously derive it will be divided by 4 for every value of a, since it is 4 + 4 - 4 for a = 8; 4 + 4 + 4 + 4 - 4 for a = 16, and so on...
Statement 2: rewrite the expression as: \((2n + 1 - 4)(2n + 1 +3)(2n + 1 +2) = (2n - 3)(2n + 4)(2n +3)\), where \(n = a\). If \(n = 1\), this is not divisible by 4.
Pick A.
Statement 1: \(a\) is divisible by 8. Hence, \(a\) will be a multiple of \(8 = 2^3 = 4 *2\). Taking into account \(a-4\), we instantaneously derive it will be divided by 4 for every value of a, since it is 4 + 4 - 4 for a = 8; 4 + 4 + 4 + 4 - 4 for a = 16, and so on...
Statement 2: rewrite the expression as: \((2n + 1 - 4)(2n + 1 +3)(2n + 1 +2) = (2n - 3)(2n + 4)(2n +3)\), where \(n = a\). If \(n = 1\), this is not divisible by 4.
Pick A.
23 Apr 2019, 04:30
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btrg
Statement 1- a is multiple of 8 so the smallest value of a-4 will be divisible by 4. Need not to worry about the rest of the equation.---Sufficient
Statement 2- if a is odd then we can test the equation for 1 and 3 and can get two different solutions. One divisible by 4 and other not----Not Sufficient.
