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# If a, b, and c are integers and ac + b is odd, is b odd?

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Manager
Joined: 09 Feb 2013
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If a, b, and c are integers and ac + b is odd, is b odd?  [#permalink]

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08 Jun 2013, 02:08
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95% (hard)

Question Stats:

42% (01:53) correct 58% (01:28) wrong based on 210 sessions

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If a, b, and c are integers and ac + b is odd, is b odd?

(1) ac + ab is even
(2) b + c is odd

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Re: If a, b, and c are integers and ac + b is odd, is b odd?  [#permalink]

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08 Jun 2013, 02:17
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If a, b, and c are integers and ac + b is odd, is b odd?
$$ac+b=odd$$

A) ac + ab is even
$$ac+b+ac+ab=odd+even$$, $$2ac+b(1+a)=odd$$. The first term will be even so the second term must be odd in order to obtain even+odd=odd.
$$b(1+a)=odd$$, since an odd number results from odd*odd, both terms must be odd.
Sufficient

B) b + c is odd
B could be even or odd.
Not sufficient
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Re: If a, b, and c are integers and ac + b is odd, is b odd?  [#permalink]

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08 Jun 2013, 02:49
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If a, b, and c are integers and ac + b is odd, is b odd?

Given that $$ac + b=odd$$, determine whether b is odd.

(1) ac + ab is even --> $$ac+ab=even$$. Subtract this equation from the equation above: $$b-ab=odd-even=odd$$ --> $$b(1-a)=odd$$ --> $$b=odd$$. Sufficient.

(2) b + c is odd. Clearly insufficient.

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Re: If a, b, and c are integers and ac + b is odd, is b odd?  [#permalink]

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08 Jun 2013, 18:34
Bunuel wrote:
If a, b, and c are integers and ac + b is odd, is b odd?

Given that $$ac + b=odd$$, determine whether b is odd.

(1) ac + ab is even --> $$ac+ab=even$$. Subtract this equation from the equation above: $$b-ab=odd-even=odd$$ --> $$b(1-a)=odd$$ --> $$b=odd$$. Sufficient.

(2) b + c is odd. Clearly insufficient.

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Hope it helps.

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Re: If a, b, and c are integers and ac + b is odd, is b odd?  [#permalink]

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15 Jul 2015, 21:52
A) ac + ab is even
ac+b+ac+ab=odd+even, 2ac+b(1+a)=odd. The first term will be even so the second term must be odd in order to obtain even+odd=odd.
b(1+a)=odd, since an odd number results from odd*odd, both terms must be odd.
Sufficient

B) b + c is odd
B could be even or odd.
Not sufficient
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Re: If a, b, and c are integers and ac + b is odd, is b odd?  [#permalink]

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13 Apr 2018, 03:55
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Re: If a, b, and c are integers and ac + b is odd, is b odd? &nbs [#permalink] 13 Apr 2018, 03:55
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# If a, b, and c are integers and ac + b is odd, is b odd?

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