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# If a, b and c are integers such that ab + c is an odd integer, is a an

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Joined: 24 May 2016
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Kudos [?]: 124 [0], given: 33

If a, b and c are integers such that ab + c is an odd integer, is a an [#permalink]

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26 May 2016, 02:19
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36% (01:32) correct 64% (02:36) wrong based on 45 sessions

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If a, b and c are integers such that ab + c is an odd integer, is a an even integer?

(1) ab + ac is an even integer.
(2) b + ac is an odd integer.
[Reveal] Spoiler: OA

Last edited by Bunuel on 26 May 2016, 02:24, edited 1 time in total.
Renamed the topic and edited the question.

Kudos [?]: 124 [0], given: 33

Math Expert
Joined: 02 Sep 2009
Posts: 41654

Kudos [?]: 124268 [2], given: 12077

Re: If a, b and c are integers such that ab + c is an odd integer, is a an [#permalink]

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26 May 2016, 02:30
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If a, b and c are integers such that ab + c is an odd integer, is a an even integer?

Given that $$ab + c=odd$$, determine whether a is even.

(1) ab + ac is an even integer. $$ab+ac=even$$. Subtract this equation from the equation above: $$(ab+ac)-(ab + c)=ac-c=even-odd=odd$$ --> $$c(a-1)=odd$$ --> both multiples must be odd --> $$a-1=odd$$ --> $$a=odd+1=even$$. Sufficient.

(2) b + ac is an odd integer. a=even, b=odd and c=odd OR a=odd, b=odd and c=even. Not sufficient.

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Kudos [?]: 124268 [2], given: 12077

Math Expert
Joined: 02 Sep 2009
Posts: 41654

Kudos [?]: 124268 [0], given: 12077

Re: If a, b and c are integers such that ab + c is an odd integer, is a an [#permalink]

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26 May 2016, 02:31
Bunuel wrote:
If a, b and c are integers such that ab + c is an odd integer, is a an even integer?

Given that $$ab + c=odd$$, determine whether a is even.

(1) ab + ac is an even integer. $$ab+ac=even$$. Subtract this equation from the equation above: $$(ab+ac)-(ab + c)=ac-c=even-odd=odd$$ --> $$c(a-1)=odd$$ --> both multiples must be odd --> $$a-1=odd$$ --> $$a=odd+1=even$$. Sufficient.

(2) b + ac is an odd integer. a=even, b=odd and c=odd OR a=odd, b=odd and c=even. Not sufficient.

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Hope it helps.
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Re: If a, b and c are integers such that ab + c is an odd integer, is a an [#permalink]

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31 Aug 2017, 07:59
we know , ab+c=odd
1) ab+ac = even
ab+c +ac -ac
ab+ac + c-ac
even + c-ac
c-ac = odd
c(1-a) = odd
oddxodd=odd
1-a=odd
a = even

so A or D can be the answer

2) Now b+ac =odd
ok
b+ac + ab+c = even { ab+c = odd , odd+odd = even}
b+ab + ac+c = even
b(a+1) +c(a+1) = even
(b+c) (a+1) = even

either b+c = even a+1 = odd so a is even
or a+1 is even so a is odd

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Re: If a, b and c are integers such that ab + c is an odd integer, is a an   [#permalink] 31 Aug 2017, 07:59
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