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When positive integer n is divided by 5, the remainder is 1.

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S
Joined: 09 Jun 2010
Posts: 1395

Kudos [?]: 168 [0], given: 916

Re: When positive integer n is divided by 5, the remainder is 1. [#permalink]

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New post 05 Aug 2016, 01:55
[quote="Bunuel"]The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

I come to a solution without using any fomulae

n=5x+1
but becaue n can be divided by 7 and remainder is 3 . this mean 5x can be divided by 7 with remainder of 2
x =4 is one variable which is ok.
so n=31.

we we add 35 to 31 , the we alway have n which satisfy the two things.

now k =4 and k is unchanged. there is no SMALLEST K.

am i correct?
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Kudos [?]: 168 [0], given: 916

Director
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G
Joined: 07 Dec 2014
Posts: 836

Kudos [?]: 265 [0], given: 15

When positive integer n is divided by 5, the remainder is 1. [#permalink]

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New post 31 Aug 2016, 16:42
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

n=r1+d1(d2-1)
n=1+5(7-1)=31
35-31=4
B

Last edited by gracie on 19 Dec 2016, 15:15, edited 2 times in total.

Kudos [?]: 265 [0], given: 15

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Joined: 13 Nov 2016
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Re: When positive integer n is divided by 5, the remainder is 1. [#permalink]

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New post 19 Dec 2016, 03:01
A number which leaves a remainder x-a when divided by x and leaves a remainder y-a when divided by y can be written as : LCM(x,y)-a
Here the number leaves a remainder 1 when divided by 5 , thus x=5 x-a=1 , therfore a=4
the same number leaves a remainder 3 when divided by 7 , thus y-7 and x-a=3 thus a=4

So the number is LCM(5,7)- 4 which is 35-4 =31 , the smallest number required to get a multiple of 35 is 31+4 =35

Therefore the answer is 4 which is B

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Director
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Joined: 07 Dec 2014
Posts: 836

Kudos [?]: 265 [0], given: 15

When positive integer n is divided by 5, the remainder is 1. [#permalink]

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New post 06 Sep 2017, 16:26
Quote:
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


let x=difference between quotients
(n-1)/5-(n-3)/7=x➡
n+4=35x/2
because x must be even, start with x=2
n+4=35*2/2=35
n=31
k=4
B

Kudos [?]: 265 [0], given: 15

When positive integer n is divided by 5, the remainder is 1.   [#permalink] 06 Sep 2017, 16:26

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