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30 Oct 2019, 02:17
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C
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Is ab(b - 4) a positive integer?
(1) Both a and b are positive integers
(2) b - 1 = 63/(b + 1)
(1) Both a and b are positive integers
(2) b - 1 = 63/(b + 1)
30 Oct 2019, 06:51
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Bunuel
Is ab(b - 4) a positive integer?
(1) Both a and b are positive integers
(2) b - 1 = 63/(b + 1)
(1) Both a and b are positive integers
(2) b - 1 = 63/(b + 1)
(1) Both a and b are positive integers
So ab will be always positive, and
b-4 will be positive when b>4....ab(b - 4)=1*5(5-4)=5>0
while b-4 will be negative when b\(\leq\)4....ab(b - 4)=1*2(2-4)=-4<0
Insuff
(2) b - 1 = 63/(b + 1)
\(b - 1 = \frac{63}{(b + 1)}......(b-1)(b+1)=63...b^2-1=63.....b^2=64.......b=8, -8\)
Nothing about a..
If a >0..yes...1*8(8-4)=32>0...and 1*(-8)(-8-4)=96
If \(a\leq{0}\)..no...-1*8(8-4)=-32<0 and -1(-8)(-8-4)=-96<0
Insuff
Combined
b>0 and a>0, so YES
C
30 Oct 2019, 07:32
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Bunuel
Is ab(b - 4) a positive integer?
(1) Both a and b are positive integers
(2) b - 1 = 63/(b + 1)
(1) Both a and b are positive integers
(2) b - 1 = 63/(b + 1)
Target question: Is ab(b - 4) a positive integer?
Statement 1: Both a and b are positive integers
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of a and b that satisfy statement 1. Here are two:
Case a: a = 1 and b = 1. In this case, ab(b - 4) = (1)(1)(1 - 4) = -3. So, the answer to the target question is NO, ab(b - 4) is NOT positive
Case b: a = 1 and b = 5. In this case, ab(b - 4) = (1)(5)(5 - 4) = 5. So, the answer to the target question is YES, ab(b - 4) IS positive
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Aside: For more on this idea of testing values when a statement doesn't feel sufficient, read my article: https://www.gmatprepnow.com/articles/dat ... lug-values
Statement 2: b - 1 = 63/(b + 1)
Multiply both sides by (b + 1) to get: b² - 1 = 63
Add 1 to both sides: b² = 64
So, EITHER b = 8 OR b = -8
So, here are two possible cases:
Case a: a = 1 and b = 8. In this case, ab(b - 4) = (1)(8)(8 - 4) = 32. So, the answer to the target question is YES, ab(b - 4) IS positive
Case b: a = -1 and b = -8. In this case, ab(b - 4) = (-1)(-8)(-8 - 4) = -96. So, the answer to the target question is NO, ab(b - 4) is NOT positive
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
From statement 2, we concluded that EITHER b = 8 OR b = -8
From statement 1, we know that b must be 8 and a must be positive
So, we can write: ab(b - 4) = (some positive integer)(8)(8 - 4)
= (some positive integer)(8)(4)
= (some positive integer)(32)
= a positive integer
So, the answer to the target question is YES, ab(b - 4) IS a positive integer
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
