Number properties

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Number properties

by kannans3 » Fri May 20, 2011 7:27 am
Source OG

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

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by GMATGuruNY » Fri May 20, 2011 8:11 am
kannans3 wrote:Source OG

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
When positive integer n is divided by 5, the remainder is 1.
The smallest possible value of n that satisfies the statement above is the given remainder of 1.
To determine the other possible values of n, just keep adding multiples of the divisor 5:
1,6,11,16,21,26,31...

When positive integer n is divided by 7, the remainder is 3.
The smallest possible value of n that satisfies the statement above is the given remainder of 3.
To determine the other possible values of n, just keep adding multiples of the divisor 7:
3,10,17,24,31...

The smallest value included in both lists is n=31.

Now we can plug in the answers, which represent the smallest possible value of k.
When the correct answer is added to n=31, the sum will be a multiple of 35.
Since we need the smallest possible value of k, we should start with the smallest answer choice.

Answer choice A: k=3
n+k = 31+3 = 34. Not a multiple of 35.
Eliminate A.

Answer choice B: k=4
n+k = 31+4 = 35. Success!

The correct answer is B.
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by pemdas » Fri May 20, 2011 8:18 am
n>0, n is integer
n/5=a+1/5, a is integer
n/7=b+3/7, b is integer
find k (smallest integer) when (k+n) is divisible by 35?

solution: if we add 4 to n, both remainders will be gone, so k must be 4
kannans3 wrote:Source OG

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
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