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When positive integer x is divided by 44, the remainder is 28

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Joined: 12 Sep 2015
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When positive integer x is divided by 44, the remainder is 28 [#permalink]

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30 Mar 2017, 08:35
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When positive integer x is divided by 44, the remainder is 28. When positive integer y is divided by 22, the remainder is 14. If N = x+y, what is the remainder when N is divided by 11?

A) 1
B) 3
C) 5
D) 7
E) 9

*kudos for all correct solutions
[Reveal] Spoiler: OA

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Brent Hanneson – Founder of gmatprepnow.com

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Joined: 02 Aug 2009
Posts: 5724
Re: When positive integer x is divided by 44, the remainder is 28 [#permalink]

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30 Mar 2017, 08:51
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GMATPrepNow wrote:
When positive integer x is divided by 44, the remainder is 28. When positive integer y is divided by 22, the remainder is 14. If N = x+y, what is the remainder when N is divided by 11?

A) 1
B) 3
C) 5
D) 7
E) 9

*kudos for all correct solutions

Good Question Brent..

When x is divided by 44, remainder is 28...
So the number x is 44t+28, where t is integer..

When y is divided by 22, remainder is 14..
So the number y is 22s+14, where s is integer..

N=x+y = 44t+28+22s+14
So when N is divided by 11, $$\frac{44t+22s+42}{11}$$
44t and 22s are div by 11..
42=11*3+9..
So 9 is the remainder

E
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Re: When positive integer x is divided by 44, the remainder is 28 [#permalink]

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30 Mar 2017, 10:46
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GMATPrepNow wrote:
When positive integer x is divided by 44, the remainder is 28. When positive integer y is divided by 22, the remainder is 14. If N = x+y, what is the remainder when N is divided by 11?

A) 1
B) 3
C) 5
D) 7
E) 9

*kudos for all correct solutions

x = 44a+28( a = any integer)
Let a =1 then x = 44+28= 72
similarly
y=22b+14 (b=any integer)
let b=1
then y= 36

thus N=x+y =72+36=108
108/11 = 9 9/11

ans E
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Re: When positive integer x is divided by 44, the remainder is 28 [#permalink]

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30 Mar 2017, 11:46
1
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GMATPrepNow wrote:
When positive integer x is divided by 44, the remainder is 28. When positive integer y is divided by 22, the remainder is 14. If N = x+y, what is the remainder when N is divided by 11?

A) 1
B) 3
C) 5
D) 7
E) 9

*kudos for all correct solutions

x=44a+28;y=14+22b
For a=1 and b=1
x=72,y=36
n=x+5=108
remainder-9
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Director
Joined: 07 Dec 2014
Posts: 927
Re: When positive integer x is divided by 44, the remainder is 28 [#permalink]

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30 Mar 2017, 11:54
1
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GMATPrepNow wrote:
When positive integer x is divided by 44, the remainder is 28. When positive integer y is divided by 22, the remainder is 14. If N = x+y, what is the remainder when N is divided by 11?

A) 1
B) 3
C) 5
D) 7
E) 9

*kudos for all correct solutions

least values of x and y are 28 and 14 respectively
x+y=42=N
N/11 gives a remainder of 9
E
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Joined: 07 Jan 2016
Posts: 647
Location: India
GMAT 1: 710 Q49 V36
Re: When positive integer x is divided by 44, the remainder is 28 [#permalink]

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30 Mar 2017, 13:09
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remainder 28 when divided by 44

so 44a + 28

remainder 14 when divided by 22

so 22b + 14

now N = x+y

44a + 22b + 42

N/11

as we know 44 and 22 are divisible by 11 only 42 is remaining

42/11 remainder = -2 or 9

44- 2 = 42
33+9 = 42

E
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Posts: 224
Location: India
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Re: When positive integer x is divided by 44, the remainder is 28 [#permalink]

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04 Aug 2017, 09:45
HI!

Did it by number picking

Possible value of x = 28, 72, 100...
Possible values of y = 14, 36, 58....

Since there can be only one unique solution, add to find the smallest possible value of n = 28 + 14 = 42. Remainder of 42/11 = 9

Is the Kudos for correct solution still valid?
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Re: When positive integer x is divided by 44, the remainder is 28   [#permalink] 04 Aug 2017, 09:45
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