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by shanice » Fri Apr 06, 2012 6:26 pm
When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k+n is a multiple of 35?

(A)3 (B)4 (c)12 (D)32 (E)35

The answer is B.

I understand the 1st and 2nd sentence of the question but having problem understanding the 3rd sentence - "What is the smallest positive integer k such that k+n is a multiple of 35?". What does the question mean?

Thank you in advance.
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by Bill@VeritasPrep » Fri Apr 06, 2012 6:30 pm
The sum of k and n must be a multiple of 35, i.e. 35, 70, etc. Since we're looking for k, we need to solve for the value of n, then see what we must add to that value to make the sum a multiple of 35.
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by shanice » Fri Apr 06, 2012 6:57 pm
Thank you, Bill.
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by eaakbari » Thu Nov 08, 2012 10:40 pm
Solution please?
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by Brent@GMATPrepNow » Fri Nov 09, 2012 7:38 am
eaakbari wrote:Solution please?
When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k+n is a multiple of 35?

(A)3
(B)4
(C)12
(D)32
(E)35

Here's one approach:

There's a nice rule that says, If, when N is divided by D, the remainder is R, then the possible values of N include: R, R+D, R+2D, R+3D,. . .

First we're told that when n is divided by 5, the remainder is 1.
So, possible values of n are 1, 6, 11, 16, 21, 26, 31, 36, 41, 46, 51, 56, 61, 66, 71, 76, etc.

Next we're told that when n is divided by 7, the remainder is 3.
So, possible values of n are 3, 10, 17, 24, 31, 38, 45, 52, 59, 66, 73, etc.

So, we can see that n could equal 31, or 66, or an infinite number of other values.

Important: Since the Least Common Multiple of 7 and 5 is 35, we can conclude that if we list the possible values of n, each value will be 35 greater than the last value.

So, n could equal 31, 66, 101, 136, and so on.

Notice that, if we take any of these values, we need to add 4 to it so that the sum will be a multiple of 35. So, the smallest value of k is 4 such that k+n is a multiple of 35.

Answer = B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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