Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 43867

How many twodigit whole numbers yield a remainder of 1 when divided [#permalink]
Show Tags
19 Jan 2015, 04:25
Question Stats:
64% (00:54) correct 36% (01:00) wrong based on 229 sessions
HideShow timer Statistics



Manager
Joined: 02 May 2014
Posts: 116

Re: How many twodigit whole numbers yield a remainder of 1 when divided [#permalink]
Show Tags
19 Jan 2015, 05:00
1
This post received KUDOS
2
This post was BOOKMARKED
Bunuel wrote: How many twodigit whole numbers yield a remainder of 1 when divided by 10 and also yield a remainder of 1 when divided by 6?
A. None B. One C. Two D. Three E. Four
Kudos for a correct solution. The possible number N can be written as follow: N = Multiple of LCM(6,10) + 1st such number N = 30x + 1 Possible values = 1, 31, 61, 91 Answer : 3 such 2 digit number. D.



Manager
Joined: 31 Jul 2014
Posts: 143

Re: How many twodigit whole numbers yield a remainder of 1 when divided [#permalink]
Show Tags
19 Jan 2015, 05:01
1
This post received KUDOS
Bunuel wrote: How many twodigit whole numbers yield a remainder of 1 when divided by 10 and also yield a remainder of 1 when divided by 6?
A. None B. One C. Two D. Three E. Four
Kudos for a correct solution. n=10p+1 > Number could be 11 21 31 41 51 n=6q+1 > Number could be 7 13 19 25 31 n= 30q+31 so n could be 31,61,91 IMO D



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1839
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: How many twodigit whole numbers yield a remainder of 1 when divided [#permalink]
Show Tags
20 Jan 2015, 02:13
1
This post received KUDOS
Answer = D. Three LCM of 10 & 6 = 30 Twodigit numbers giving remainder 1 for 30 are 31, 61, 91
_________________
Kindly press "+1 Kudos" to appreciate



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1839
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: How many twodigit whole numbers yield a remainder of 1 when divided [#permalink]
Show Tags
20 Jan 2015, 02:21
anupamadw wrote: Bunuel wrote: How many twodigit whole numbers yield a remainder of 1 when divided by 10 and also yield a remainder of 1 when divided by 6?
A. None B. One C. Two D. Three E. Four
Kudos for a correct solution. n=10p+1 > Number could be 11 21 31 41 51 n=6q+1 > Number could be 7 13 19 25 31 n= 30q+31so n could be 31,61,91 IMO D Can you explain the highlighted calculation? How is that obtained?
_________________
Kindly press "+1 Kudos" to appreciate



Math Expert
Joined: 02 Sep 2009
Posts: 43867

Re: How many twodigit whole numbers yield a remainder of 1 when divided [#permalink]
Show Tags
20 Jan 2015, 02:31
2
This post received KUDOS
Expert's post
6
This post was BOOKMARKED
PareshGmat wrote: anupamadw wrote: Bunuel wrote: How many twodigit whole numbers yield a remainder of 1 when divided by 10 and also yield a remainder of 1 when divided by 6?
A. None B. One C. Two D. Three E. Four
Kudos for a correct solution. n=10p+1 > Number could be 11 21 31 41 51 n=6q+1 > Number could be 7 13 19 25 31 n= 30q+31so n could be 31,61,91 IMO D Can you explain the highlighted calculation? How is that obtained? Positive integer n is divided by 10, the remainder is 1 > \(n=10q+1\), where \(q\) is the quotient > 1, 11, 21, 31, 41, ... Positive integer n is divided by 6, the remainder is 1 > \(n=6p+1\), where \(p\) is the quotient > 1, 7, 13, 19, ... There is a way to derive general formula for \(n\) (of a type \(n=mx+r\), where \(x\) is divisor and \(r\) is a remainder) based on above two statements:Divisor \(x\) would be the least common multiple of above two divisors 10 and 6, hence \(x=30\). Remainder \(r\) would be the first common integer in above two patterns, hence \(r=1\). Therefore general formula based on both statements is \(n=30m+1\). Thus n could be 1, 31, 61, 91, ... Since n is a twodigit integer, then n could only be 31, 61, or 91. Check for more here: positiveintegernleavesaremainderof4afterdivisionby93752.html#p721341Hope it helps.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 08 Jan 2015
Posts: 13

Re: How many twodigit whole numbers yield a remainder of 1 when divided [#permalink]
Show Tags
20 Jan 2015, 03:44
Find the least common factor and multiples of the number +1 Least common factor of 10 and 6 is 30 (two digits multiples of 30 are 30,60,90.. Add +1 to the numbers) so totally 3 numbers are possible



Intern
Joined: 08 Dec 2013
Posts: 41

Re: How many twodigit whole numbers yield a remainder of 1 when divided [#permalink]
Show Tags
15 Mar 2015, 20:47
hi Bunuel don`t you think with respect to your answer.. since q is the quotient..how can you put q=0 and get 1 as common from both equations I mean if you put q=0,then n=1 but n is a two digit number so the first common value needs to be 31 i.e N(two digit)=30m+31.. thanks



Math Expert
Joined: 02 Sep 2009
Posts: 43867

Re: How many twodigit whole numbers yield a remainder of 1 when divided [#permalink]
Show Tags
15 Mar 2015, 21:34



NonHuman User
Joined: 09 Sep 2013
Posts: 13801

Re: How many twodigit whole numbers yield a remainder of 1 when divided [#permalink]
Show Tags
25 Jun 2016, 20:11
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Manager
Joined: 18 Jun 2017
Posts: 60

Re: How many twodigit whole numbers yield a remainder of 1 when divided [#permalink]
Show Tags
16 Aug 2017, 08:26
31,61 & 91 are the only three two digit numbers that when divided by 10 and 6 each leaves a remainder of 1. Option D.




Re: How many twodigit whole numbers yield a remainder of 1 when divided
[#permalink]
16 Aug 2017, 08:26






