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

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

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New post 08 Jun 2013, 02:08
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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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New post 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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New post 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.

Answer: A.

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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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New post 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.

Answer: A.

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if-m-is-an-integer-is-m-odd-129702.html
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if-x-and-y-are-integers-is-the-value-of-x-y-1-even-149236.html
if-x-y-and-z-are-integers-and-xy-z-is-an-odd-integer-is-81562.html
if-a-and-b-are-integers-is-b-even-99211.html
if-x-is-an-integer-is-x-even-142751.html
is-a-b-c-even-130399.html
is-x-y-z-t-even-133065.html

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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New post 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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New post 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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