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When x is divided by 4 and y is divided by 5 the remainder is 1 and th

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When x is divided by 4 and y is divided by 5 the remainder is 1 and th  [#permalink]

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New post 06 Oct 2018, 18:10
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  85% (hard)

Question Stats:

38% (02:47) correct 62% (02:41) wrong based on 34 sessions

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When integer x is divided by 4 and integer y is divided by 5, the remainder is 1 and the difference between quotients is 6. What is the sum of x and y?

A. 117
B. 119
C. 126
D. 137
E. 143
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Posts: 6986
Re: When x is divided by 4 and y is divided by 5 the remainder is 1 and th  [#permalink]

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New post 06 Oct 2018, 19:58
1
gracie wrote:
When integer x is divided by 4 and integer y is divided by 5, the remainder is 1 and the difference between quotients is 6. What is the sum of x and y?

A. 117
B. 119
C. 126
D. 137
E. 143


x=4(z+6)+1
y=5z+1
We are looking for x+y
x+y=4z+24+1+5z+1=9z+26
Ofcourse there will not be one value but it will depend on z and therefore the question should be " what CAN be the sum of X and y?"
So x+y=9z+26.......x+y-26=9z

Therefore any choice subtracted by 26 should be a multiple of 9..
Let's see the choices
A. 117..... 117-26=91....no
B. 119.....119-26=93...no
C. 126..... 126-26=100...no
D. 137....... 137-26=111.. no
E. 143......143-26=117..yes

So E

A short cut would be X+y-26 means addition of all digits should be divisible by 9
26 gives -(2+6)=-8, so any choice which gives (sumof digits -8) as 0 or a multiple of 9
117=1+1+7=9....9-8=1
119=1+1+9=11...11-8=3
126=1+2+6=9...9-8=1
137=1+3+7=11...11-8=3
143=1+4+3=8...8-8=0...yes
So 143 is the answer
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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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Re: When x is divided by 4 and y is divided by 5 the remainder is 1 and th  [#permalink]

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New post 06 Oct 2018, 21:01
1
gracie wrote:
When integer x is divided by 4 and integer y is divided by 5, the remainder is 1 and the difference between quotients is 6. What is the sum of x and y?

A. 117
B. 119
C. 126
D. 137
E. 143


another approach:
(x-1)/4-(y-1)/5=6
→5x-4y=121
→5x/11-4y/11=11
if x and y are integers, they must both be multiples of 11
and their sum must be a multiple of 11 also
143 is the only multiple of 11
E
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Re: When x is divided by 4 and y is divided by 5 the remainder is 1 and th &nbs [#permalink] 06 Oct 2018, 21:01
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