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

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Manager
Joined: 10 Oct 2008
Posts: 56
If a and b are integers, is b even? (1) 3a + 4b is even. (2) [#permalink]

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05 Nov 2008, 18:39
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

If a and b are integers, is b even?
(1) 3a + 4b is even.
(2) 3a + 5b is even.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
SVP
Joined: 17 Jun 2008
Posts: 1529
Re: a and b (30) [#permalink]

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05 Nov 2008, 22:08
C.

From stmt1: either (3a and 4b are even) or, (3a and 4b are odd----not possible as 4b cannot be odd).

Hence, 3a and 4b are even
or, a is even and b is even/odd. Insufficient.

Similarly, from stmt2:
either (a is even and b is even) or (a is odd and b is odd). Insufficient.

Combining both, a is even and b is even. Sufficient.

Alternatively,
(3a+4b) is even and (3a+5b) is even. Hence, (3a+4b) + b is even. Or, b is even.
Manager
Joined: 14 Jun 2007
Posts: 166
Location: Vienna, Austria
Re: a and b (30) [#permalink]

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05 Nov 2008, 23:22
guys

why does using C point to the fact that a must be even? the choices for be a are odd/even, but i don´t get why using C makes it straight that a must be even?

thanks
Re: a and b (30)   [#permalink] 05 Nov 2008, 23:22
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# If a and b are integers, is b even? (1) 3a + 4b is even. (2)

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