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# when a positive integer X is divided by 5 the remainder is 1.

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VP
Joined: 31 Oct 2013
Posts: 1003
Concentration: Accounting, Finance
GPA: 3.68
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when a positive integer X is divided by 5 the remainder is 1.  [#permalink]

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Updated on: 23 Jan 2018, 17:39
00:00

Difficulty:

45% (medium)

Question Stats:

88% (01:35) correct 13% (01:02) wrong based on 8 sessions

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when a positive integer X is divided by 5 the remainder is 1. when X is divided by 8 the remainder is 4 . what is the smallest positive integer y such that, (X+Y) is divisible by 40 ?

a)3
b)4
c)9
d)13
e) none of these

looking for short-cut solution.

--== Message from the GMAT Club Team ==--

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Originally posted by selim on 23 Jan 2018, 15:10.
Last edited by chetan2u on 23 Jan 2018, 17:39, edited 3 times in total.
updated topic name and added OA
Intern
Joined: 11 Nov 2017
Posts: 2
Re: when a positive integer X is divided by 5 the remainder is 1.  [#permalink]

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23 Jan 2018, 15:35
1
The first thing I did when attempting this problem is to find the lowest value that satisfies the information given.
We can quickly compare some values (6, 11, 16, 21, 26, 31, 36, 41) and (4, 12, 20, 28, 36, 44) and find out quickly that 36 is the lowest value which fits both the facts we are given.

from 36 we can look at the answer choices and see that 4 can be added to make it 40.
Math Expert
Joined: 02 Aug 2009
Posts: 7211
Re: when a positive integer X is divided by 5 the remainder is 1.  [#permalink]

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23 Jan 2018, 17:35
selim wrote:
when a positive integer X is divided by 5 the remainder is 1. when X is divided by 8 the remainder is 4 . what is the smallest positive integer y such that, (X+Y) is divisible by 40 ?

a)3
b)4
c)9
d)13
e) none of these

looking for short-cut solution.

Please post question with correct topic name as first few words of the Question and with OA

x+y has to be divisible by 40, then x+y has to be EVEN..
x is even as it leaves a Remainder of 4 when div by 8..
So y has to be even.. only 4 is possible other than none of these
Eliminate a,c,d

For proper orLogical method..

When divided by 5, it leaves a Remainder of 1.
So x will have units digit 1 or 6

When divided by 8, x leaves a remainder of 4..
So units digit has to be even and thus 6..

Look for 6-4=2 as units digit in MULTIPLE of 8..
First such is 8*4=32..
So x is 32+4=36
Next number after 36 divisible by 40 is 40 itself..
So x+y=40....36+y=40...y=40-36=4

B
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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VP
Joined: 07 Dec 2014
Posts: 1152
Re: when a positive integer X is divided by 5 the remainder is 1.  [#permalink]

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23 Jan 2018, 19:15
selim wrote:
when a positive integer X is divided by 5 the remainder is 1. when X is divided by 8 the remainder is 4 . what is the smallest positive integer y such that, (X+Y) is divisible by 40 ?

a)3
b)4
c)9
d)13
e) none of these

looking for short-cut solution.

x=5q+1
x=8p+4
8p+3=5q
least value of p that makes q an integer is 4
p=4; q=7; x=36
40-36=4
B
Math Expert
Joined: 02 Sep 2009
Posts: 52385
Re: when a positive integer X is divided by 5 the remainder is 1.  [#permalink]

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23 Jan 2018, 19:41
1
selim wrote:
when a positive integer X is divided by 5 the remainder is 1. when X is divided by 8 the remainder is 4 . what is the smallest positive integer y such that, (X+Y) is divisible by 40 ?

a)3
b)4
c)9
d)13
e) none of these

looking for short-cut solution.

This is a copy of the following OG question: when-positive-integer-n-is-divided-by-5-the-remainder-is-166831.html

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________
Re: when a positive integer X is divided by 5 the remainder is 1. &nbs [#permalink] 23 Jan 2018, 19:41
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# when a positive integer X is divided by 5 the remainder is 1.

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