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by lenagmat » Thu Oct 27, 2011 12:28 am
For any positive integer n, <n> denotes the remainder when 5n^2+1 is divided by 2. If m is a positive integer, what is the value of <m>?

1). m is even number.
2). m is divided by 5.

Please, could you say first of all the answer for very silly question - what this mean <n>, <m>,<>??
Because I did not understand the question at all.

answer is A.
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by GmatKiss » Thu Oct 27, 2011 1:24 am
lenagmat wrote:For any positive integer n, <n> denotes the remainder when 5n^2+1 is divided by 2. If m is a positive integer, what is the value of <m>?

1). m is even number.
2). m is divided by 5.

Please, could you say first of all the answer for very silly question - what this mean <n>, <m>,<>??
Because I did not understand the question at all.

answer is A.
what does the red portion say.
Something is wrong in the question.

And for god sake, pls reveal the answer only with spoiler.

-GK
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by neelgandham » Thu Oct 27, 2011 2:37 am
lenagmat wrote:For any positive integer n, <n> denotes the remainder when 5n^2+1 is divided by 2. If m is a positive integer, what is the value of <m>?

1). m is even number.
2). m is divided by 5.Assuming the statement m is divided by 5 is the same as m is divisible by 5

<m> = Remainder of ((5*(m^2))+1 )/2 is 1 if m=even and is 0 if m =odd

from 1) m = even => remainder = 1 Sufficient
from 2) m = 5 or 10 or 15 => remainder can be 1 or 0 or 1.. Insufficient

Hence Option A

Please, could you say first of all the answer for very silly question - what this mean <n>, <m>,<>??
Because I did not understand the question at all.

When one says "Let D be the distance" or "Let X be the number", it is just his/her assumption. In the same way the author or the question-creator asked us to assume that <n> denotes the remainder when 5n^2+1 is divided by 2.
Answers inline (red) ! Can you please not reveal the answer without the spoiler?
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by user123321 » Thu Oct 27, 2011 3:42 am
1) if m is even number, then 5.m^2+1 is always odd. and when odd number divided by 2 remainder is 1. so this is sufficient.
2) if m is divisible by 5 then m = 5k, then 5.(5k)^2+1 = 125.k^2 + 1 . and when this is divided by 2 remainder can be 0 when k is odd and 1 when k is even. so insufficient.
hence it is A

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by Brent@GMATPrepNow » Thu Oct 27, 2011 5:13 am
lenagmat wrote: Please, could you say first of all the answer for very silly question - what this mean <n>, <m>,<>??
Don't worry; you aren't meant to have pre-existing knowledge of what <m> means.
I call this a "strange operator." Here, the GMAT introduces some strange operation (in this case <n>) and then defines how the operation works (in this case, <n> denotes the remainder when 5n^2+1 is divided by 2). Once you understand the basic rules for the new operator, you are given a question to solve.

Keep in mind that you have learned many strange operators in the past. For example, there was a time when you didn't know what the square root symbol stood for. Once you understood the basic rules for the new operator, you were given questions to solve.

Cheers,
Brent
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by Brent@GMATPrepNow » Thu Oct 27, 2011 5:24 am
lenagmat wrote:For any positive integer n, <n> denotes the remainder when 5n^2+1 is divided by 2. If m is a positive integer, what is the value of <m>?

1). m is even number.
2). m is divided by 5.
This question is a great candidate for "rephrasing the target question" (see video #6 at https://www.gmatprepnow.com/module/gmat-data-sufficiency - it's free)

At the moment, the target question is basically "What is the remainder when 5m^2 + 1 is divided by 2?"
Since the remainder solely depends on whether 5m^2 + 1 is odd or even, we can rephrase the target question as "Is 5m^2 + 1 odd?"

Statement 1:
If m is even, then m^2 is even, which means 5m^2 is even, which means 5m^2 + 1 must be odd
SUFFICIENT

Statement 2:
If m is divisible by 5 then m can be odd or even.

case a) m is odd
If m is even then m^2 is odd, which means 5m^2 is odd, which means 5m^2 + 1 is even
case b) m is even
If m is even then m^2 is even, which means 5m^2 is even, which means 5m^2 + 1 is odd

Since 5m^2 + 1 can be either even or odd, statement 2 is NOT SUFFICIENT

Answer = A
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