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16 Aug 2010, 06:57
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
68% (01:31) correct
32%
(01:33)
wrong
based on 486
sessions
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If a and b are integers, is b even?
(1) 3a + 4b is even
(2) 3a + 5b is even
(1) 3a + 4b is even
(2) 3a + 5b is even
16 Aug 2010, 07:05
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jakolik
(1) 3a + 4b is even --> if \(a\) is even, then it's not necessary for \(b\) to be even, may be even or odd. Not sufficient.
(2) 3a + 5b is even --> if \(a\) is even, then \(b\) is even too, but if \(a\) is odd, then \(b\) is odd too. Not sufficient.
(1)+(2) Subtract (1) from (2) --> \((3a+ 5b)-(3a + 4b)=even_2-even_1\) --> \(b=even_2-even_1=even\). Sufficient.
Answer: C.
General Discussion
16 Aug 2010, 07:07
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IMO C.
Let me try to explain my approach for this one.
Addition of 2 numbers will be even when both of them are either even or odd.
Now lets check option 1.
3a + 4b is even. 3a can be either even or odd depending value of a. 4b will be even irrespective b being even or odd. Hence, 3a should be even if the sum has to be even. But, we cannot confirm whether b is odd or even with this statement.
Now lets check option 2.
3a + 5b is even. 3a can be either even or odd depending value of a. 5b can be either even or odd depending value of a. Hence, a and b can be either even or odd. This also not sufficient to conclude whether b is even or off.
Combing these 2 statements.
Both 3a + 4b and 3a + 5b are even.
Then as per first statement 3a should be even.
Then 4b and 5b should be even if the sum has to be even in both the cases.
Then b should be even. Hence, C is the answer.
Please let us know the OA and explanation if I am wrong or ambiguous.
Let me try to explain my approach for this one.
Addition of 2 numbers will be even when both of them are either even or odd.
Now lets check option 1.
3a + 4b is even. 3a can be either even or odd depending value of a. 4b will be even irrespective b being even or odd. Hence, 3a should be even if the sum has to be even. But, we cannot confirm whether b is odd or even with this statement.
Now lets check option 2.
3a + 5b is even. 3a can be either even or odd depending value of a. 5b can be either even or odd depending value of a. Hence, a and b can be either even or odd. This also not sufficient to conclude whether b is even or off.
Combing these 2 statements.
Both 3a + 4b and 3a + 5b are even.
Then as per first statement 3a should be even.
Then 4b and 5b should be even if the sum has to be even in both the cases.
Then b should be even. Hence, C is the answer.
Please let us know the OA and explanation if I am wrong or ambiguous.
