GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 26 Jan 2020, 08:25

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

Hide Tags

VP
Joined: 07 Dec 2014
Posts: 1231
When x is divided by 4 and y is divided by 5 the remainder is 1 and th  [#permalink]

Show Tags

06 Oct 2018, 18:10
13
00:00

Difficulty:

95% (hard)

Question Stats:

47% (02:41) correct 53% (02:50) wrong based on 75 sessions

HideShow timer Statistics

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
Math Expert
Joined: 02 Aug 2009
Posts: 8336
Re: When x is divided by 4 and y is divided by 5 the remainder is 1 and th  [#permalink]

Show Tags

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
_________________
VP
Joined: 07 Dec 2014
Posts: 1231
Re: When x is divided by 4 and y is divided by 5 the remainder is 1 and th  [#permalink]

Show Tags

06 Oct 2018, 21:01
3
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
Non-Human User
Joined: 09 Sep 2013
Posts: 14016
Re: When x is divided by 4 and y is divided by 5 the remainder is 1 and th  [#permalink]

Show Tags

24 Nov 2019, 06:29
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: When x is divided by 4 and y is divided by 5 the remainder is 1 and th   [#permalink] 24 Nov 2019, 06:29
Display posts from previous: Sort by