Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49206

How many twodigit whole numbers yield a remainder of 1 when divided
[#permalink]
Show Tags
19 Jan 2015, 05:25
Question Stats:
67% (00:56) correct 33% (00:56) wrong based on 315 sessions
HideShow timer Statistics




Math Expert
Joined: 02 Sep 2009
Posts: 49206

Re: How many twodigit whole numbers yield a remainder of 1 when divided
[#permalink]
Show Tags
20 Jan 2015, 03:31
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




Manager
Joined: 02 May 2014
Posts: 106

Re: How many twodigit whole numbers yield a remainder of 1 when divided
[#permalink]
Show Tags
19 Jan 2015, 06:00
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: 132

Re: How many twodigit whole numbers yield a remainder of 1 when divided
[#permalink]
Show Tags
19 Jan 2015, 06:01
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: 1835
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, 03:13
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: 1835
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, 03:21
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



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, 04:44
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: 34

Re: How many twodigit whole numbers yield a remainder of 1 when divided
[#permalink]
Show Tags
15 Mar 2015, 21:47
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: 49206

Re: How many twodigit whole numbers yield a remainder of 1 when divided
[#permalink]
Show Tags
15 Mar 2015, 22:34



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, 09:26
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.



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12409
Location: United States (CA)

How many twodigit whole numbers yield a remainder of 1 when divided
[#permalink]
Show Tags
28 Feb 2018, 22:20
Hi All, This type of question is rooted in patternmatching. Once you find the patterns behind this question, it won't be hard to solve. Instead of trying to do every step all at once, I suggest that you break the prompt into "pieces": First, name the 2digit numbers that are evenly divisible by 10: 10, 20, 30, ......90 Now, name the 2digit numbers that have a remainder of 1 when divided by 10: 11, 21, 31,.....91 Now that we've established the numbers that fit the first 2 "restrictions" in the prompt, let's factor in numbers that are ALSO divisible by 6: 30, 60, 90 And ALSO have a remainder of 1 when divided by 6: 31, 61, 91 Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************



VP
Status: It's near  I can see.
Joined: 13 Apr 2013
Posts: 1256
Location: India
Concentration: International Business, Operations
GPA: 3.01
WE: Engineering (Consulting)

Re: How many twodigit whole numbers yield a remainder of 1 when divided
[#permalink]
Show Tags
29 Mar 2018, 23:06
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. Two digit numbers divided my 10 yielding remainder 1 = 11,21,31,41,51,61,71,81,91 Two digit numbers divided my 6 yielding remainder 1 = 31,61,91 Three common numbers. Hence (D)
_________________
"Do not watch clock; Do what it does. KEEP GOING."



Intern
Joined: 02 Oct 2016
Posts: 25

Re: How many twodigit whole numbers yield a remainder of 1 when divided
[#permalink]
Show Tags
08 Apr 2018, 07:01
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.




Re: How many twodigit whole numbers yield a remainder of 1 when divided &nbs
[#permalink]
08 Apr 2018, 07:01






