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Is p odd

by j_shreyans » Fri Sep 19, 2014 9:09 am
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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by nipunranjan » Mon Nov 03, 2014 11:11 am
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.

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by [email protected] » Mon Nov 03, 2014 5:31 pm
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.

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