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If a and b are integers, is b an even integer?�

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Source: — Data Sufficiency |
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by kvcpk » Mon Jul 12, 2010 5:05 am
gmatmachoman wrote:"If a and b are integers, is b an even
integer?"


1. 3a + 4b is even integer.
2. 3a + 5b is even integer.
3a +4b is even.
put a=2, b=1
3a+4b=10, b=1....NO

pur a=2,b=2
3a+4b = 14, b=2..YES

INSUFF

3a + 5b is even integer

put a=2, b=2
3a+5b = 16, b=2...YES
put a= 5, b=1
3a+5b = 20, b=1..NO

INSUFF

Combining:
3a + 4b is even integer.
3a + 5b is even integer
subtract 1 from 2
we get b. difference of 2 even integers is even.
pick C
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by Patrick_GMATFix » Mon Jul 12, 2010 5:15 am
gmatmachoman wrote:"If a and b are integers, is b an even
integer?"


1. 3a + 4b is even integer.
2. 3a + 5b is even integer.
I agree with kvcpk

(1) 4b must be even. Since 3a+4b is even, 3a must be even, so a must be even. We know nothing about b. NOT SUFFICIENT

(2) Two possibilities:
  • 3a and 5b are both odd, which means a and b are both odd.
  • 3a and 5b are both even which means a and b are both even.
Therefore, b could be odd, but could also be even. NOT SUFFICIENT

MERGE STATEMENTS:
(1) guarantees that a is even. (2) guarantees that a and b have the same property. Together, they guarantee that b is also even. SUFFICIENT

The answer is C

gmatmachoman, something tells me that you could solve this on your own before you ever posted it :-)

-Patrick
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