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ans this data suffi q

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ans this data suffi q

by emiflo » Thu Jul 15, 2010 9:05 am
Hi guys.could someone explain this data sufficiency question to me:

If m,p, and q are positive integers and m<p<q, is the product mpt an even integer?

(1) t-p = p-m

(2) t-m= 16.

ps: OG says the ans is E (12th edition q76). thanks
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by selango » Thu Jul 15, 2010 9:24 am
Can u pl check the question?

I think it's m<p<t
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by selango » Thu Jul 15, 2010 9:31 am
mpt is even?

From stmt1,

t-p=p-m

t+m=2p

Since t+m is multiple of 2,t+m is even.

Odd+Odd=even or Even+Even=Even.


If t and m are even,mpt is even watever p value is

m=2,t=4,mpt=8*p

If t and m are odd,p must be even for mpt to be even.We dont know abt p.

m=1,t=3,mpt=3*p

Insufficient.

From stmt2,

t-m=16

t-m=39-23=16

t-m=32-16=16

t and m can be both odd or t and m can be both even.

Similar to stmt1,we dont know abt p.

Insufficient.

Combining 1 and 2

m and t can be both even or odd.Still insufficient.

Hence E
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by Rahul@gurome » Thu Jul 15, 2010 8:46 pm
If the question is: If m,p, and t are positive integers and m<p<t, is the product mpt an even integer?

(1) t-p = p-m

(2) t-m= 16.

(1) t-p = p-m implies t = 2p - m
2p will always be even whether p is even or odd since 2(even) = even and 2(odd) = even
m can be even or odd.
If m is even then t = even - even = even
If m is odd then t = even - odd = odd
So, (1) is NOT SUFFICIENT.

(2) t-m= 16 implies t = 16 + m
m can be even or odd.
If m is even then t = 16 + even = even
If m is odd then t = 16 + odd = odd
So, (2) is NOT SUFFICIENT.

Combining (1) and (2), 2p - m = 16 + m or 2p = 16 + 2m or p = 8 + m. This also doesn't imply if p and m are even or odd.

The correct answer is (E).
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