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a data from gmat club

by diebeatsthegmat » Mon Aug 29, 2011 1:31 am
If m and n are positive integers, is the remainder of 10^m + n}/3 larger than the remainder of {10^n + m}/3 ?

1. m > n
2. The remainder of n/3is 2

the OA is B and i disagree with it and i also dont understand why it is B.
if the remainder of n/3 is 2 so n could be 2,5,8...
* if n=2 and m=1 >>>> 10^m +n=12/3=4 and the remainder is 0 and 10^n+m=101/3=33 and the remainder is 2
* if n=2 and m=2 the remainder of both fractions will be equally 0
if n=2 and m=3 the remainder of the first fraction will be 0 and the second fraction is 1
according to me, the answer should be E.. could you please show me where i got mistakes?
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by Geva@EconomistGMAT » Mon Aug 29, 2011 6:43 am
diebeatsthegmat wrote:If m and n are positive integers, is the remainder of 10^m + n}/3 larger than the remainder of {10^n + m}/3 ?

1. m > n
2. The remainder of n/3is 2

the OA is B and i disagree with it and i also dont understand why it is B.
if the remainder of n/3 is 2 so n could be 2,5,8...
* if n=2 and m=1 >>>> 10^m +n=12/3=4 and the remainder is 0 and 10^n+m=101/3=33 and the remainder is 2
* if n=2 and m=2 the remainder of both fractions will be equally 0
if n=2 and m=3 the remainder of the first fraction will be 0 and the second fraction is 1
according to me, the answer should be E.. could you please show me where i got mistakes?
You're right in your plug ins, but wrong in your interpretation of what they mean. For all of these cases, the remainder of the first fraction is NOT greater than the remainder of the second fraction - it's either smaller (cases 1 and 3) or equal (case 2), but never greater. Therefore, the answer to the question "is the remainder greater?" is always a "NO" - which means that stat. (2) is sufficient to provide a single answer to the question stem. In DS Yes/No questions, "no" is sufficient: the only way a statement will be insufficient is if it provides both a "yes" and a "no" answer.

As to why the answer is "no": 10 to the power of anything will always be 1 more than a multiple of 3: 10 is one more than 9, 100 is one more than 99, 1000 is one more than 999, etc. So when stat. (2) says that n gives a remainder of 2 when divided by 3, it makes sure that 10^m+n will always be a multiple of 3 (take a number with a remainder of 1, and add 2 more). Therefore, the first fraction will ALWAYS have a remainder of zero - which means that it cannot have a greater remainder than the other fraction, since it is impossible to have a remainder smaller than zero.

Clever question - a bit too clever for the real GMAT, in my estimate.
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by navami » Mon Aug 29, 2011 8:02 am
10/3 reminder 1
100/3 reminder 1
1000/3 reminder 1

so at any case if n/3 reminder = 2
then {10^m + n}/3 reminder would be = 0 .... HOW???
10^m/ 3 = reminder 1
and n/3 = reminder = 2
2+1 = 3 which is divisible by 3 again.

AND : {10^n + m}/3???
10^3/3 reminder will be 1
but m Not equal to n
and hence m/3 reminder will be anything but smaller than the earlier case.
This time no looking back!!!
Navami
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