May 20 10:00 PM PDT  11:00 PM PDT Practice the one most important Quant section  Integer Properties, and rapidly improve your skills. May 24 10:00 PM PDT  11:00 PM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. May 25 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. May 27 01:00 AM PDT  11:59 PM PDT All GMAT Club Tests are free and open on May 27th for Memorial Day!
Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 07 Sep 2010
Posts: 256

The integers r, s and t all have the same remainder when div
[#permalink]
Show Tags
Updated on: 23 Sep 2013, 05:58
Question Stats:
69% (02:01) correct 31% (02:16) wrong based on 748 sessions
HideShow timer Statistics
The integers r, s and t all have the same remainder when divided by 5. What is the value of t? (1) r + s = t (2) 20 <= t <= 24
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by imhimanshu on 23 Sep 2013, 05:55.
Last edited by Bunuel on 23 Sep 2013, 05:58, edited 1 time in total.
Renamed the topic and edited the question.




Math Expert
Joined: 02 Sep 2009
Posts: 55188

Re: The integers r, s and t all have the same remainder when div
[#permalink]
Show Tags
23 Sep 2013, 06:31
The integers r, s and t all have the same remainder when divided by 5. What is the value of t?\(r=5a+x\) \(s=5b+x\) \(t=5c+x\) Where the remainder x is \(0\leq{x}<5\). (1) r + s = t > \((5a+x)+(5b+x)=5c+x\) > \(x=5(cab)\) > the remainder (x) is a multiple of 5, thus it's 0 > r, s and t are multiples of 5. Not sufficient. (2) 20 <= t <= 24. Clearly insufficient. (1)+(2) There is only one multiple of 5 between 20 and 24, inclusive, namely 20. Sufficient. Answer: C. Hope it's clear.
_________________




Intern
Joined: 29 Jun 2012
Posts: 1

Re: The integers r, s and t all have the same remainder when div
[#permalink]
Show Tags
26 Dec 2013, 22:50
rh410 wrote: I still don't understand how 1) r+s = t tells us that these must be multiples of 5. (And thus the remainder is 0)
Could someone please explain? Thanks! The question: when r,t,s are divided by 5, they yield the same remainder. Remember that when X is divided by 5, the remainder must be 0,1,2,3,4 ( remainder must always be smaller than divisor) If r and s has the same remainder, for example 1, then t can not have remainder 1 (21+11=32, remainder of the total (32) is the sum of remainders of 11 and 21, it equals 2 actually). So for the remainder to be the same, r,t and s must be multiples of 5 (20+10=30)




Manager
Joined: 30 May 2013
Posts: 152
Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.82

Re: The integers r, s and t all have the same remainder when div
[#permalink]
Show Tags
23 Sep 2013, 07:32
imhimanshu wrote: The integers r, s and t all have the same remainder when divided by 5. What is the value of t?
(1) r + s = t (2) 20 <= t <= 24 For this r,s ant t can be any values which have same remainder when divided by 5 so r=6 s=1 t=21 or r=2, s=47 and t=1002 From statement 1: r + s = t => so for this only same remainder is "0". But r+s=t can be any value 5+10=15 where all the numbers have remainder "0" or 10+20=30 or etc . . .. So insufficient From statement 2: 20<=t<=24 so t can be 20, 21,22,23,24 Hence not sufficient From combining both the statements From 1 : r, s and t has to multiple of 5 so remainder is "0" From 2: t = 20,21,22,23,24 so from both the multiple of 5 is 20 t=20 sufficient hence both the statement are sufficient. answer is (c)



Intern
Joined: 26 Dec 2012
Posts: 1

Re: The integers r, s and t all have the same remainder when div
[#permalink]
Show Tags
26 Dec 2013, 21:34
I still don't understand how 1) r+s = t tells us that these must be multiples of 5. (And thus the remainder is 0)
Could someone please explain? Thanks!



Manager
Joined: 08 Feb 2014
Posts: 204
Location: United States
Concentration: Finance
WE: Analyst (Commercial Banking)

Re: The integers r, s and t all have the same remainder when div
[#permalink]
Show Tags
01 Dec 2014, 18:47
Bunuel wrote: (1) r + s = t > \((5a+x)+(5b+x)=5c+x\) > \(x=5(cab)\) . Can someone explain these steps? Thanks!



Math Expert
Joined: 02 Sep 2009
Posts: 55188

Re: The integers r, s and t all have the same remainder when div
[#permalink]
Show Tags
02 Dec 2014, 02:21
JackSparr0w wrote: Bunuel wrote: (1) r + s = t > \((5a+x)+(5b+x)=5c+x\) > \(x=5(cab)\) . Can someone explain these steps? Thanks! \((5a+x)+(5b+x)=5c+x\); \(2x+5a+5b=5c+x\); \(x=5c5a5b\); \(x=5(cab)\). Hope it's clear.
_________________



Manager
Joined: 08 Feb 2014
Posts: 204
Location: United States
Concentration: Finance
WE: Analyst (Commercial Banking)

Re: The integers r, s and t all have the same remainder when div
[#permalink]
Show Tags
02 Dec 2014, 09:24
Bunuel wrote: JackSparr0w wrote: Bunuel wrote: (1) r + s = t > \((5a+x)+(5b+x)=5c+x\) > \(x=5(cab)\) . Can someone explain these steps? Thanks! \((5a+x)+(5b+x)=5c+x\); \(2x+5a+5b=5c+x\); \(x=5c5a5b\); \(x=5(cab)\). Hope it's clear. Thanks, I kept getting my signs mixed up...



Intern
Joined: 08 Oct 2015
Posts: 8

The integers r, s and t all have the same remainder when div
[#permalink]
Show Tags
12 Oct 2015, 11:11
I don't get how the answer to this is not B?
Between 20 and 24, 20 is the only number that can be comprised of numbers for which when divided by 5 give equal remainders:
Think about the numbers for t that fit in the inequality and any numbers below t that give the same remainder:
t= 20... 5, 10, 15, 20 t= 21... 6, 11, 16, 21 t= 22... 7, 12, 17, 22
and so on... The pattern becomes clear that only 20 works. What am i missing here?



Math Expert
Joined: 02 Sep 2009
Posts: 55188

Re: The integers r, s and t all have the same remainder when div
[#permalink]
Show Tags
12 Oct 2015, 21:42
dubyap wrote: I don't get how the answer to this is not B?
Between 20 and 24, 20 is the only number that can be comprised of numbers for which when divided by 5 give equal remainders:
Think about the numbers for t that fit in the inequality and any numbers below t that give the same remainder:
t= 20... 5, 10, 15, 20 t= 21... 6, 11, 16, 21 t= 22... 7, 12, 17, 22
and so on... The pattern becomes clear that only 20 works. What am i missing here? You are using info from (1) when evaluating (2).
_________________



Current Student
Joined: 01 Jan 2016
Posts: 16
Location: Brazil
WE: Marketing (Education)

Re: The integers r, s and t all have the same remainder when div
[#permalink]
Show Tags
06 Aug 2016, 15:17
Bunuel wrote: dubyap wrote: I don't get how the answer to this is not B?
Between 20 and 24, 20 is the only number that can be comprised of numbers for which when divided by 5 give equal remainders:
Think about the numbers for t that fit in the inequality and any numbers below t that give the same remainder:
t= 20... 5, 10, 15, 20 t= 21... 6, 11, 16, 21 t= 22... 7, 12, 17, 22
and so on... The pattern becomes clear that only 20 works. What am i missing here? You are using info from (1) when evaluating (2). Damn! I was so deep drilling (2) that by the time solved it I was sure I hadn't used info from (1). And I thought I was avoiding C trap! Thanks!



Senior Manager
Joined: 26 Dec 2015
Posts: 253
Location: United States (CA)
Concentration: Finance, Strategy
WE: Investment Banking (Venture Capital)

Re: The integers r, s and t all have the same remainder when div
[#permalink]
Show Tags
29 Jan 2018, 17:46
here's the way i saw this question...
 since we're told r, s, and t all have the same remainder, it got me thinking: they would all have the same remainder if they were all multiples of 5.
(1) r+s=t r=10, s=10, t=20. works r=20, s=40, t=60. works ** we have 2 possible values for t, so insufficient.
(2) t is between 20 and 24 t can literally equal 20, 21, 22, 23 or 24...clearly insufficient
(3) we know t should be a multiple of 5 and within the range 2024. there's a # here (20) that fits these 2 criteria. sufficient.



NonHuman User
Joined: 09 Sep 2013
Posts: 10956

Re: The integers r, s and t all have the same remainder when div
[#permalink]
Show Tags
07 Feb 2019, 06:38
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: The integers r, s and t all have the same remainder when div
[#permalink]
07 Feb 2019, 06:38






