## Primes & Divisibility

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### Primes & Divisibility

by shanice » Thu Apr 05, 2012 10:19 pm
Hello, everyone. I'll be taking my GMAT within 2 months and I'm struggling with the Primes & Divisibility topic. I heard about your site and hope you guys could help me out.

My question is on Remainders. I know this is the formula for remainders - [b]y=xn+r[/b]. I know that r is the remainder, n is the divisor, x is the quotient and y is dividend. I don't understand how to apply this formula to a question below:-

If x is an integer and y=3x+2, which of the following cannot be a divisor of y?

A) 4
B) 5
C) 6
D) 7
E) 8

I read the explanation on this site but I still don't understand. What is the connection of remainder to divisor or dividend and vice-versa.What does the formula mean?

[Moderator Edit: Moved the post to a relevant forum - neelgandham]

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by killer1387 » Thu Apr 05, 2012 10:38 pm
If x is an integer and y=3x+2, which of the following cannot be a divisor of y?

A) 4
B) 5
C) 6
D) 7
E) 8

you have a number y that is 3x+2,

put x=0,1,2,3.......
you have y= 2,5,8,11,14=> these numbers are divisible by 4,5,8,7

hence 6 will be the answer

hope this helps..!!

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by shanice » Fri Apr 06, 2012 12:53 am

Is there any other way than plugging in numbers? Please explain in detail.

By the way,when the question says "x is an integer", it means x is a whole number (non-fraction or non-decimal right) right?

Thank you.

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by seal4913 » Fri Apr 06, 2012 4:40 pm
shanice wrote:By the way,when the question says "x is an integer", it means x is a whole number (non-fraction or non-decimal right) right?
Yes, an interger is a whole number therefore a number that is not a fraction. Non decimal, I mean 1 is an interger and 1.0 is the same... but 1.1 isn't an interger

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by shanice » Fri Apr 06, 2012 5:37 pm
Thank you very much, Seal4913.

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by Mr Smith » Fri Apr 06, 2012 8:03 pm
Strictly speaking,
Whole numbers are integers but all integers are not whole numbers.
Whole Numbers: 0,1,2,3,4,5,6,7,8,9,10,11,12,13....100.. etc.
Integers: .........-100, .....-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0, 1,2,3,4,5,6,7,8,9,10,11,12,13....100..
Whole numbers are a subset of the numbers.

Ok regarding the original question:
Since y = 3x +2 where x is integer, y is 2 plus a multiple of 3. clearly y is not divisible by 3 and thus not by divisible by the multiples of 3 too.
6 is a multiple of 3, hence 6 is not the divisor of the number.

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by shanice » Sat Apr 07, 2012 2:02 am
Thank you for the explanation, Mr.Smith.

Everyone in "Beat The Gmat" are so supportive and helpful. I'm glad I joined it.

Thanks, again.

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