Positive integers a, b, c, m, n, and p are defined as follows: m=2^a3^b , n=2^c and p=2m/n. Is p odd?
(1) a<b
(2) a<c
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Is p odd
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j_shreyans
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nipunranjan
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p=2m/n=(2*2^a*3^b)/(2^c)=2^(a+1-c)*3^b
Now,
since b is a positive integer, we need not worry about 3^b.
If, the power of 2 is positive then p will be even(not odd).
from statement (1) we cannot make out whether the power of 2, i.e., (a+1-c) is positive or not.
Statement (2)
a<c
a-c<0
a+1-c<1
since a,c both are integers, (a+1-c) will be 0,-1,-2,-3 etc. In any case it can't be positive
Since p is integer, (a+1-c) can't be negative, or else p will become fraction.
So the only value which (a+1-c) can attain is 0.
Since, the power of 2 is 0 as per statement (2), 2^0=1 and hence, we can tell for sure that p is odd.
Hence B is the correct answer.
Now,
since b is a positive integer, we need not worry about 3^b.
If, the power of 2 is positive then p will be even(not odd).
from statement (1) we cannot make out whether the power of 2, i.e., (a+1-c) is positive or not.
Statement (2)
a<c
a-c<0
a+1-c<1
since a,c both are integers, (a+1-c) will be 0,-1,-2,-3 etc. In any case it can't be positive
Since p is integer, (a+1-c) can't be negative, or else p will become fraction.
So the only value which (a+1-c) can attain is 0.
Since, the power of 2 is 0 as per statement (2), 2^0=1 and hence, we can tell for sure that p is odd.
Hence B is the correct answer.
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Hi j_shreyans,
Can you use parentheses to clarify any of the ambiguous terms in this question?
For example:
m=2^a3^b is probably meant to be m = (2^a)(3^b). Without the clear definition of terms though, it's tough to be sure that we're answering the original prompt correctly.
GMAT assassins aren't born, they're made,
Rich
Can you use parentheses to clarify any of the ambiguous terms in this question?
For example:
m=2^a3^b is probably meant to be m = (2^a)(3^b). Without the clear definition of terms though, it's tough to be sure that we're answering the original prompt correctly.
GMAT assassins aren't born, they're made,
Rich
