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08 Jun 2013, 02:08
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
40% (02:16) correct
60%
(02:29)
wrong
based on 316
sessions
History
Date
Time
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Not Attempted Yet
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
(1) ac + ab is even
(2) b + c is odd
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
\(ac+b=odd\)
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
General Discussion
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.
Similar questions to practice:
the-product-of-integers-x-y-and-z-is-even-is-z-even-130140.html
if-m-is-an-integer-is-m-odd-129702.html
if-x-and-y-are-integers-is-xy-even-137508.html
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.
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.
Similar questions to practice:
the-product-of-integers-x-y-and-z-is-even-is-z-even-130140.html
if-m-is-an-integer-is-m-odd-129702.html
if-x-and-y-are-integers-is-xy-even-137508.html
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.
Hope you like the shayari, pun intended 
