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For integers a and b, is the expression ab – b even?

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For integers a and b, is the expression ab – b even?  [#permalink]

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New post 06 Jun 2017, 11:42
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

61% (01:14) correct 39% (01:09) wrong based on 148 sessions

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Re: For integers a and b, is the expression ab – b even?  [#permalink]

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New post 06 Jun 2017, 11:55
Top Contributor
Bunuel wrote:
For integers a and b, is the expression ab – b even?

(1) a is odd

(2) b is odd


Target question: Is the expression ab – b even?

HINT: notice that ab – b = b(a - 1)

Statement 1: a is odd
What does does this tell us about the expression ab – b?
Well, ab – b = b(a - 1)
= b(ODD - 1)
= b(EVEN) [since an odd integer minus 1 gives us a EVEN integer]
= EVEN
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: b is odd
There are several values of a and b that satisfy statement 2. Here are two:
Case a: a = 3 and b = 1. In this case ab – b = (3)(1) - 1 = 2. So, ab – b is EVEN
Case b: a = 2 and b = 1. In this case ab – b = (2)(1) - 1 = 1. So, ab – b is ODD
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer:

Cheers,
Brent
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Re: For integers a and b, is the expression ab – b even?  [#permalink]

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New post 25 Jul 2017, 17:49
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ab-b can be converted into b(a-1),

We have to find either b or a-1 to be even.

st-1 says a is odd. then a-1 is even. So the term b(a-1) will be even. sufficient.

st-2 says b is odd. No info about a. so not sufficient.

Answer is A.
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Re: For integers a and b, is the expression ab – b even?  [#permalink]

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New post 16 Jan 2019, 13:20
Bunuel wrote:
For integers a and b, is the expression ab – b even?

(1) a is odd

(2) b is odd


b(a-1) even?

(1) a odd, then a-1 is even, then we have even *b = even sufficient

(2) b odd. Let be =1 1(a-1) even? let a=1. Then ab-b = 1(0) = 0 Yes even. Let a=2 then ab-b 1(2-1) =1 No. Odd. NS

Answer is A
GMAT Club Bot
Re: For integers a and b, is the expression ab – b even?   [#permalink] 16 Jan 2019, 13:20
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