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is b an integer?

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by sanju09 » Wed Jan 05, 2011 5:12 am
If a is an integer, is b an integer?

[1] The average (arithmetic mean) of a and b is not an integer.

[2] The average (arithmetic mean) of 3a, 2b, and a + 12, is 2b.




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Source: — Data Sufficiency |

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by Anurag@Gurome » Wed Jan 05, 2011 5:21 am
sanju09 wrote:If a is an integer, is b an integer?

[1] The average (arithmetic mean) of a and b is not an integer.

[2] The average (arithmetic mean) of 3a, 2b, and a + 12, is 2b.
Statement 1: (a + b)/2 is not integer.
If b is not integer => (a + b)/2 is also not integer.
If b is an integer and (a + b) is odd => (a + b)/2 is not integer.

Not Sufficient

Statement 2: (3a + 2b + a + 12)/3 = 2b
Implies, (4a + 2b + 12) = 6b
=> 4b = (4a + 12)
=> b = (a + 3) => Integer.

Sufficient

The correct answer is B.
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by arora007 » Wed Jan 05, 2011 5:22 am
1 and .5 will have average .75 b here is not an integer 1 and 2 will have average 1.5 here b is an integer... A is insufficient

(3a +2b+a+12 )/3 = 2b

4a+2b+12 = 6b

4a+12=4b

a+3=b

now if a is an integer b is gotta be an integer....

pick B!
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