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

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SVP
Joined: 11 Sep 2015
Posts: 1908

Kudos [?]: 2747 [1], given: 364

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

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30 Mar 2017, 07:35
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5% (low)

Question Stats:

87% (01:10) correct 13% (01:27) wrong based on 71 sessions

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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

_________________

Brent Hanneson – Founder of gmatprepnow.com

Kudos [?]: 2747 [1], given: 364

Math Expert
Joined: 02 Aug 2009
Posts: 5346

Kudos [?]: 6117 [2], given: 121

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

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30 Mar 2017, 07:51
2
KUDOS
Expert's post
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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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 6117 [2], given: 121

Director
Joined: 05 Mar 2015
Posts: 966

Kudos [?]: 301 [1], given: 41

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

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30 Mar 2017, 09:46
1
KUDOS
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

Kudos [?]: 301 [1], given: 41

Manager
Status: GMAT...one last time for good!!
Joined: 10 Jul 2012
Posts: 71

Kudos [?]: 6 [1], given: 18

Location: India
Concentration: General Management
GMAT 1: 660 Q47 V34
GPA: 3.5
Re: When positive integer x is divided by 44, the remainder is 28 [#permalink]

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30 Mar 2017, 10:46
1
KUDOS
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
_________________

Kudos for a correct solution

Kudos [?]: 6 [1], given: 18

Director
Joined: 07 Dec 2014
Posts: 859

Kudos [?]: 291 [1], given: 16

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

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30 Mar 2017, 10:54
1
KUDOS
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

Kudos [?]: 291 [1], given: 16

Senior Manager
Joined: 07 Jan 2016
Posts: 322

Kudos [?]: 34 [1], given: 28

Location: India
Schools: Duke '20 (S)
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, 12:09
1
KUDOS
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

Kudos [?]: 34 [1], given: 28

Manager
Joined: 12 Jun 2016
Posts: 225

Kudos [?]: 46 [0], given: 149

Location: India
WE: Sales (Telecommunications)
Re: When positive integer x is divided by 44, the remainder is 28 [#permalink]

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04 Aug 2017, 08:45
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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Kudos [?]: 46 [0], given: 149

Re: When positive integer x is divided by 44, the remainder is 28   [#permalink] 04 Aug 2017, 08:45
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