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?

Thanks in advance.

[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
Thank you for your quick reply,killer1387.

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.