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

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If a and b are integers, is b even? (1) 3a + 4b is even. (2) [#permalink] New post 26 Jun 2008, 01:18
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.
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Re: Integer problem [#permalink] New post 26 Jun 2008, 01:22
bhatiagp wrote:
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.


I think 1 or 2 alone is not suff, but 1 and 2 combined is suff

[3a+5b]-[3a+4b]=b even, so b must be even

C
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Re: Integer problem [#permalink] New post 26 Jun 2008, 01:58
The answer is C.

Stmt 1: 3a + 4b is even. This means, either both 3a and 4b are odd or both 3a and 4b are even. But, 4b cannot be odd. Hence, 4b is even. This is true for any value of b (either odd or even). Hence, insufficient.

Stmt 2: With the same logic as above, 5b can either be odd or even. If 5b is odd, b is odd. If 5b is even, b is even. Insufficient.

Combining the two : b is even.
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Re: Integer problem [#permalink] New post 26 Jun 2008, 02:07
bhatiagp wrote:
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.


As my understanding goeas..
1 and 2 both are nt sufficient.
so if check by combing both the:
(1) 3a + 4b is even.
(2) 3a + 5b is even.

for (1) 3a + 4b is even.
if 3a is even then 4b shud be even as teh no. is multiplied by 4 it will always be even irrespectinve of b's value
if 3a is odd then 4b shud be odd to make the stat even which is nt possible so we can conclude that 3a is even

for (2) 3a + 5b is even.
now frm above stat we came to know 3a is even now to make tis statement even 5b shud be even which is only possible wen b is even

so by combining both the statement we can say b is even
and answer is c
Re: Integer problem   [#permalink] 26 Jun 2008, 02:07
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If a and b are integers, is b even? (1) 3a + 4b is even. (2)

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