If a and b are positive integers, is ab an even?
1) (a+1)b=even
2) (a+1)^b=odd
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If a and b are positive integers, is ab an even?
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Max@Math Revolution
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dustystormy
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IMO: B
St 1) (a+1)b --> even
either [(a+1) or b] is even or [(a+1) and b] both are even
a+1 can be (odd+odd = even) or (even+odd = odd)
further b can also be even or odd
Therefore St 1 is insufficient
St 2) (a+1)^b --> odd
irrespective of b we can say (a+1) as odd. {one can check by plugging different values or a & b)
therefore (a+1) -->odd, implies (even + odd)
a is even. Therefore ab is even.
Hence Sufficient.
St 1) (a+1)b --> even
either [(a+1) or b] is even or [(a+1) and b] both are even
a+1 can be (odd+odd = even) or (even+odd = odd)
further b can also be even or odd
Therefore St 1 is insufficient
St 2) (a+1)^b --> odd
irrespective of b we can say (a+1) as odd. {one can check by plugging different values or a & b)
therefore (a+1) -->odd, implies (even + odd)
a is even. Therefore ab is even.
Hence Sufficient.
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Max@Math Revolution
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Since there are 2 variables in the original condition, the answer is C. However, we have to apply common mistake type 4(A) because it is one of key questions. In case of con 2), from a+1=odd, a=even, the answer is always yes and the condition is sufficient. Hence, the correct answer is B.
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Brent@GMATPrepNow
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Target question: Is ab evenMax@Math Revolution wrote:If a and b are positive integers, is ab an even?
1) (a+1)(b) is even
2) (a+1)^b is odd
Statement 1: (a+1)(b) is even
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of a and b that satisfy statement 1. Here are two:
Case a: a = 1 and b = 2. Here, (a+1)(b) = (1+1)(2) = 4, and 4 is even. In this case ab = (1)(2) = 2. So, ab IS even
Case b: a = 1 and b = 1. Here, (a+1)(b) = (1+1)(1) = 2, and 2 is even. In this case ab = (1)(1) = 1. So, ab is NOT even
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values
Statement 2: (a+1)^b is odd
In other words, the product (a+1)(a+1)...(a+1) [multiplied b times] is ODD
This means that each value (a+1) in the product must be ODD
If a+1 is ODD, then a is EVEN
If a is EVEN, then ab = (EVEN)(b) = EVEN
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer = B
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
