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# a and b are integers, is b even? (1) 3a+4b is even. (2)

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Senior Manager
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a and b are integers, is b even? (1) 3a+4b is even. (2) [#permalink]  06 Jan 2005, 11:04
46. a and b are integers, is b even?

(1) 3a+4b is even.

(2) 4a+6b is even.

I think its E
Manager
Joined: 31 Aug 2004
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Re: even or Odd [#permalink]  06 Jan 2005, 11:36
pb_india wrote:
46. a and b are integers, is b even?

(1) 3a+4b is even.

(2) 4a+6b is even.

I think its E

Odd integer + Even integer = Odd integer
Even integer + Even integer = Even integer

For 1), we need both an even integer for both 3a and 4b. 3a can only be even when a is an even integer. 4b can be an even integer when b is odd or even. So 1) alone cannot give us an anwer whenther b is even. So eliminate D & A.

For 2), we know 4a is an even number with either a is odd or even. Same logic applys to 6b, as an odd b or even b will give 6b an even number. So 2) alone is not sufficient to answer the question. We can eliminate B.

1) + 2) together cannot help us answer the question, so C is gone too, and this left us with E as the correct answer.
VP
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E it is both the statements r insuff and even together they r insuff. Hence "E". What's the OA?
Director
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its E because

the oonly way we get an even number bby addition is

odd + even
or odd + odd
Director
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odd+odd= even odd-odd=even
even+even= even even-even=even

E..
Manager
Joined: 06 Dec 2004
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rxs0005 wrote:
its E because

the oonly way we get an even number bby addition is

odd + even
or odd + odd

you state odd + even = even

I think this is a typo

5 + 2 = 7

5+ 4 = 9

9 + 6 = 15

In each case odd + even = odd

I believe you ment

Even = even + even or
Even = Odd + Odd
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# a and b are integers, is b even? (1) 3a+4b is even. (2)

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