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Math Expert V
Joined: 02 Sep 2009
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If a, b, and c are integers and a(b - c) is odd, which of the followin  [#permalink]

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Question Stats: 70% (01:24) correct 30% (01:27) wrong based on 40 sessions

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If a, b, and c are integers and a(b - c) is odd, which of the following must be odd?

A. b
B. c
C. ab
D. ab + c
E. abc

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VP  V
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Posts: 1339
Location: India
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Re: If a, b, and c are integers and a(b - c) is odd, which of the followin  [#permalink]

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Bunuel wrote:
If a, b, and c are integers and a(b - c) is odd, which of the following must be odd?

A. b
B. c
C. ab
D. ab + c
E. abc

a(b - c) is odd
--> a = odd & b - c = odd

So, Possible combinations of (a, b, c) = (o, e, o) or (o, o, e)

A. b --> can be odd or even --> No
B. c --> can be odd or even --> No
C. ab = o*o or o*e --> No
D. ab + c = o*o + e = o or o*e + o = o --> Odd always --> Yes
E. abc = o*o*e = e or o*e*o = e --> No

Option D
GMAT Club Legend  V
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If a, b, and c are integers and a(b - c) is odd, which of the followin  [#permalink]

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Top Contributor
Bunuel wrote:
If a, b, and c are integers and a(b - c) is odd, which of the following must be odd?

A. b
B. c
C. ab
D. ab + c
E. abc

Another approach here is to test some values that satisfy the initial condition

If a(b - c) is odd, then it COULD be the case that a = 1, b = 2 and c = 1
Now let's plug these values into our answer choices...

A. b = 2
2 is NOT odd, so eliminate A

B. c = 1
1 is odd, so keep B

C. ab = (1)(2) = 2
2 is NOT odd, so eliminate C

D. ab + c = (1)(2) + 1 = 3
3 is odd, so keep D

E. abc = (1)(2)(1) = 2
2 is NOT odd, so eliminate E

At this point, we're left with answer choices B and D
So that's test another set of values

If a(b - c) is odd, then it COULD be the case that a = 2, b = 1 and c = 1
Now let's plug these values into the remaining answer choices...

B. c = 2
2 is NOT odd, so eliminate B

By the process of elimination, the correct answer must be D

Cheers,
Brent
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Re: If a, b, and c are integers and a(b - c) is odd, which of the followin  [#permalink]

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Here Odd = o and Even =e
a………..b………..c……….a(b-c)
o………..o……….e……….o*(o-e) =o……..First case
o………..e……….o……….o*(e-o) = o…….Second Case

From the cases above, ab +c = o + e = o
ab + c = e + o = o
Ans:D
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Re: If a, b, and c are integers and a(b - c) is odd, which of the followin  [#permalink]

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Question:
If a, b, and c are integers and a(b - c) is odd, which of the following must be odd?
A. b
B. c
C. ab
D. ab + c
E. abc

Solution:

a(b - c) is odd
=> a is odd AND (b - c) is odd
=> a is odd AND b is even and c is odd ... (possibility 1)
OR a is odd AND b is odd and c is even ... (possibility 2)

Let us check the options:
A) b : As discussed above, b could be even or odd - hence, incorrect
B) c : As discussed above, b could be even or odd - hence, incorrect
C) ab: As discussed above, b could be even or odd => hence, ab could be even or odd - hence, incorrect
D) ab + c:
According to Possibility (i): odd x even + odd = odd
According to Possibility (ii): odd x odd + even = odd
Hence, this option is correct
E) abc: It is clear that since b or c may be even or odd, abc could also be even or odd - hence, incorrect

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Re: If a, b, and c are integers and a(b - c) is odd, which of the followin  [#permalink]

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Bunuel wrote:
If a, b, and c are integers and a(b - c) is odd, which of the following must be odd?

A. b
B. c
C. ab
D. ab + c
E. abc

The only way to obtain an odd product is for both of the factors to be odd, since odd x odd = odd.

Since a(b - c) is odd, then a must be odd and (b - c) must be odd, which means b is odd when c is even, or vice versa. Thus, ab will be even when c is odd, or ab will be odd when c is even. In any case, ab + c is odd.

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: If a, b, and c are integers and a(b - c) is odd, which of the followin   [#permalink] 29 Jan 2020, 04:51
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