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30 Dec 2010, 21:34
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
50% (01:54) correct
50%
(01:40)
wrong
based on 146
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If a, b and c are all positive integers, is abc an even number?
(1) a + b is a prime number
(2) b + c is an even number
(1) a + b is a prime number
(2) b + c is an even number
bullzeye
Joined: 09 Sep 2010
Last visit: 11 Jul 2016
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Given Kudos: 6
Location: India
Concentration: Operations, General Management
Schools: Rotman '16 (A) Schulich '16 (S) ISB '16 (II)
GMAT 1: 640 Q47 V34
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WE:Information Technology (Aerospace and Defense)
30 Dec 2010, 22:02
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Why is the answer E?
I thought it was A.
a+b is a prime no. Except 2 all other primes are odd, hence, to get an additive result odd, one of the nos. should be even. Hence, in the product, abc, if either of a or b is even then the product is even. Isn't it? Where am I going wrong?
An after thought:
To get the addition result of 2, the possibilities are 0+2, 1+1.
The first one (0+2) cannot be possible, since a,b,c are positive integers. So another one could be 1 and 1. But it is not mentioned in the question that they are different positive integers, so you mean to say that both a,b can take the same value? And hence Statement A is not sufficient?
Statement B is obviously not sufficient.
I thought it was A.
a+b is a prime no. Except 2 all other primes are odd, hence, to get an additive result odd, one of the nos. should be even. Hence, in the product, abc, if either of a or b is even then the product is even. Isn't it? Where am I going wrong?
An after thought:
To get the addition result of 2, the possibilities are 0+2, 1+1.
The first one (0+2) cannot be possible, since a,b,c are positive integers. So another one could be 1 and 1. But it is not mentioned in the question that they are different positive integers, so you mean to say that both a,b can take the same value? And hence Statement A is not sufficient?
Statement B is obviously not sufficient.
31 Dec 2010, 02:05
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ezinis
For \(abc\) to be an even number at least one of the multiples must be even (since a, b and c are all positive integers), so the question basically asks whether either of unknown is even.
(1) a+b is a prime number --> if \(a+b=odd \ prime\), for example 3, then either \(a\) or \(b\) must be even and the answer to the question will be YES (the sum of two integers to be odd one must be odd and the other even) BUT if \(a+b=2=prime\) then \(a=b=1\) and in case \(c=odd\) the answer to the question will be NO. Not sufficient.
(2) b+c is an even number --> either both are even or both are odd. Not sufficient.
(1)+(2) Still not sufficient: if \(a=1\) and \(b=c=2\) (\(a+b=3=prime\) and \(b+c=4=even\)) then the answer will be YES but if \(a=b=c=1\)(\(a+b=2=prime\) and \(b+c=2=even\)) then the answer will be NO. Not sufficient.
Answer: E.
