Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 12 Jul 2007
Posts: 47

When the positive integer n is divided by 25, the remainder [#permalink]
Show Tags
15 Sep 2007, 11:19
3
This post was BOOKMARKED
Question Stats:
73% (02:09) correct
27% (01:04) wrong based on 280 sessions
HideShow timer Statistics
When the positive integer n is divided by 25, the remainder is 13. What is the value of n? (1) n < 100 (2) When n is divided by 20, the remainder is 3. it is c, and i got 63 as n using both statements, but wasn't certain there didn't exist another one.
any quick way to do this.
thx
Official Answer and Stats are available only to registered users. Register/ Login.



VP
Joined: 08 Jun 2005
Posts: 1145

When the positive integer n is divided by 25, the remainder is 13.
n = 25*x+13
statement 1
n < 100
n = 13,38,63,88
insufficient
statement 2
when n is divided by 20, the remainder is 3.
n = 20*y + 3
20*y + 3 = 25*x+13
insufficient
both statements
n = 13,38,63,88
n = 20*y + 3 > 3,23,43,63,83
n = 63
sufficient
the answer is (C)



Director
Joined: 01 May 2007
Posts: 793

DS: GMATPrep Remainder [#permalink]
Show Tags
03 Feb 2008, 13:07
1
This post received KUDOS
When the positive integer n is divided by 25, the remainder is 13. What is the value of n?
1. n < 100 2. When n is divided by 20, the remainder is 3.



CEO
Joined: 17 Nov 2007
Posts: 3584
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth)  Class of 2011

Re: DS: GMATPrep Remainder [#permalink]
Show Tags
03 Feb 2008, 14:22
C1. 38,63,88. insuff. 2. 63,163. insuff. 1&2. 63. suff.
_________________
HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android)  The OFFICIAL GMAT CLUB PREP APP, a musthave app especially if you aim at 700+  PrepGame



Director
Joined: 01 May 2007
Posts: 793

Re: DS: GMATPrep Remainder [#permalink]
Show Tags
03 Feb 2008, 14:26
I tried solving this via the remainder formula. Is their anyway to do this without picking #s?
I got as far as:
n = 25k + 13 n = 20k +3
No idea if I was on the right track with this one. I hate remainder problems.



CEO
Joined: 17 Nov 2007
Posts: 3584
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth)  Class of 2011

Re: DS: GMATPrep Remainder [#permalink]
Show Tags
03 Feb 2008, 14:29
I also hate remainder problems Smart number approach seems to be faster way.
_________________
HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android)  The OFFICIAL GMAT CLUB PREP APP, a musthave app especially if you aim at 700+  PrepGame



CEO
Joined: 17 Nov 2007
Posts: 3584
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth)  Class of 2011

Re: DS: GMATPrep Remainder [#permalink]
Show Tags
03 Feb 2008, 14:57
n = 25k + 13 n = 20m +3 25k + 13 = 20m +3 25k + 10 = 20m 5k + 2 = 4m m=(5k+2)/4  m has to be integer. k has to be even and not divisible by 4 k=2,6,10 ==> 63, 163, 263  our magic integers
_________________
HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android)  The OFFICIAL GMAT CLUB PREP APP, a musthave app especially if you aim at 700+  PrepGame



Director
Joined: 01 May 2007
Posts: 793

Re: DS: GMATPrep Remainder [#permalink]
Show Tags
03 Feb 2008, 17:39
I missing you at this part:
m=(5k+2)/4  m has to be integer. k has to be even and not divisible by 4
Why does k have to be even, and not divisible by 4?



CEO
Joined: 17 Nov 2007
Posts: 3584
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth)  Class of 2011

Re: DS: GMATPrep Remainder [#permalink]
Show Tags
03 Feb 2008, 23:43
jimmyjamesdonkey wrote: I missing you at this part:
m=(5k+2)/4  m has to be integer. k has to be even and not divisible by 4
Why does k have to be even, and not divisible by 4? 1. m has to be an integer. 2. (5k+2) has to be even and divisible by 4 3. (5k+2) is even when 5k is even. Therefore k is even. 4. if 5k is divisible by 4, (5k+2) will not divisible by 4: 5*4i+2=4*(5i)+2. Therefore, (5k+2) has not to be divisible by 4 => 5k has not to be divisible by 4 5. k is even and indivisible by 4. 6: 2,6,10....
_________________
HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android)  The OFFICIAL GMAT CLUB PREP APP, a musthave app especially if you aim at 700+  PrepGame



Director
Joined: 05 Jan 2008
Posts: 687

Re: DS: GMATPrep Remainder [#permalink]
Show Tags
04 Feb 2008, 03:31
1
This post received KUDOS
My approach is : n=25x+13 multiples of 25 are > 25,50,75 thus n would be >38,63,88 Apply 1> I have 3 values > Not sufficient Apply 2> I will have one value >63, there could be more above 100, thus applying both 1&2 you get n=63
_________________
Persistence+Patience+Persistence+Patience=G...O...A...L



Senior Manager
Joined: 16 Feb 2011
Posts: 258

Re: DS GMAT prep Remainder [#permalink]
Show Tags
04 Sep 2011, 02:47
per ques stem, we can get values > 13,38,63,88,113 etc so not a single value of n is derived..
per stat 1 , we dnt get to knw anything.. per stat 2, we can get values > 3,23,43,63,83,103 etc
Now, there is only one value (63) which satisfies both the ques stenm condition and stat 2 condition..
somebody pls help me understand what am i missing to get the answer...



Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2010

Re: DS GMAT prep Remainder [#permalink]
Show Tags
04 Sep 2011, 03:15
DeeptiM wrote: per ques stem, we can get values > 13,38,63,88,113 etc so not a single value of n is derived..
per stat 1 , we dnt get to knw anything.. per stat 2, we can get values > 3,23,43,63,83,103 etc
Now, there is only one value (63) which satisfies both the ques stenm condition and stat 2 condition..
somebody pls help me understand what am i missing to get the answer... St1 & Stem: n can be: 13, 38, 63, 88 Not Sufficient. St2 & Stem: n can be: 63, 163, 263... Not Sufficient. Using both, we have just one integer in common "63". 63 must be the value because it satisfies both statements and the stem. Sufficient. Ans: "C"
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings



Director
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 520
Location: India
GMAT 1: 640 Q43 V34 GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)

Re: When the positive integer n is divided by 25, the remainder [#permalink]
Show Tags
25 Jan 2013, 23:58
1
This post was BOOKMARKED
I used the number pluggin approach until I got this no: 63. When I was about to hit B as the answer, I saw the option A .. Highly unlikely that A couldn't have been there for a reason. . thought that there must be numbers greater than 100 which will satisfy B. So Chose C :D
_________________
hope is a good thing, maybe the best of things. And no good thing ever dies.
Who says you need a 700 ?Check this out : http://gmatclub.com/forum/whosaysyouneeda149706.html#p1201595
My GMAT Journey : http://gmatclub.com/forum/endofmygmatjourney149328.html#p1197992



Math Expert
Joined: 02 Sep 2009
Posts: 39661

Re: When the positive integer n is divided by 25, the remainder [#permalink]
Show Tags
26 Jan 2013, 04:38
When the positive integer n is divided by 25, the remainder is 13. What is the value of n?Given that \(n=25q+13\), so n could be 13, 38, 63, 88, 113, ... (1) n < 100. n could be 13, 38, 63, or 88. Not sufficient. (2) When n is divided by 20, the remainder is 3 > \(n=20p+3\). n could be 3, 23, 43, 63, 83, 103, ... Not sufficient. (1)+(2) The only value of n which both statements is 63. Sufficient. Answer: C.
_________________
New to the Math Forum? Please read this: 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



Director
Joined: 29 Nov 2012
Posts: 878

Re: When the positive integer n is divided by 25, the remainder [#permalink]
Show Tags
06 Oct 2013, 01:55
Bunuel wrote: When the positive integer n is divided by 25, the remainder is 13. What is the value of n?
Given that \(n=25q+13\), so n could be 13, 38, 63, 88, 113, ...
(1) n < 100. n could be 13, 38, 63, or 88. Not sufficient.
(2) When n is divided by 20, the remainder is 3 > \(n=20p+3\). n could be 3, 23, 43, 63, 83, 103, ... Not sufficient.
(1)+(2) The only value of n which both statements is 63. Sufficient.
Answer: C. Out of the highlighted values only 63 satisfies we need to find another value isn't it otherwise we can't claim insufficiency? How do we find the other number quickly... 3,23,43,83 and 103 don't satisfy the 1st equation
_________________
Click +1 Kudos if my post helped...
Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/
GMAT Prep software What if scenarios http://gmatclub.com/forum/gmatprepsoftwareanalysisandwhatifscenarios146146.html



Math Expert
Joined: 02 Sep 2009
Posts: 39661

Re: When the positive integer n is divided by 25, the remainder [#permalink]
Show Tags
06 Oct 2013, 03:24
fozzzy wrote: Bunuel wrote: When the positive integer n is divided by 25, the remainder is 13. What is the value of n?
Given that \(n=25q+13\), so n could be 13, 38, 63, 88, 113, ...
(1) n < 100. n could be 13, 38, 63, or 88. Not sufficient.
(2) When n is divided by 20, the remainder is 3 > \(n=20p+3\). n could be 3, 23, 43, 63, 83, 103, ... Not sufficient.
(1)+(2) The only value of n which both statements is 63. Sufficient.
Answer: C. Out of the highlighted values only 63 satisfies we need to find another value isn't it otherwise we can't claim insufficiency? How do we find the other number quickly... 3,23,43,83 and 103 don't satisfy the 1st equation Can you please elaborate what you mean? Thank you.
_________________
New to the Math Forum? Please read this: 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



Director
Joined: 29 Nov 2012
Posts: 878

Re: When the positive integer n is divided by 25, the remainder [#permalink]
Show Tags
06 Oct 2013, 03:33
What I meant was we are given n = 25q + 13 => possible values 13,38,63,88,113 statement 2 n=20p + 3 => 3,23,43,63,83,103For the second statement all the values in red don't satisfy the first equation only 63 does... How do you find another value quickly to claim insufficiency? don't we have to match the equations here?
_________________
Click +1 Kudos if my post helped...
Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/
GMAT Prep software What if scenarios http://gmatclub.com/forum/gmatprepsoftwareanalysisandwhatifscenarios146146.html



Math Expert
Joined: 02 Sep 2009
Posts: 39661

Re: When the positive integer n is divided by 25, the remainder [#permalink]
Show Tags
06 Oct 2013, 03:47
2
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
fozzzy wrote: What I meant was we are given n = 25q + 13 => possible values 13,38,63,88,113
statement 2
n=20p + 3 => 3,23,43,63,83,103
For the second statement all the values in red don't satisfy the first equation only 63 does... How do you find another value quickly to claim insufficiency?
don't we have to match the equations here? Well, there cannot be only one value that satisfies both \(n=25q+13\) (13, 38, 63, 88, 113, ...) and \(n=20p+3\) (3, 23, 43, 63, 83, 103, ...). Next, there is a way to derive general formula for \(n\) (of a type \(n=mx+r\), where \(x\) is a divisor and \(r\) is a remainder) based on above two statements:Divisor \(x\) would be the least common multiple of above two divisors 25 and 20, hence \(x=100\). Remainder \(r\) would be the first common integer in above two patterns, hence \(r=63\). Therefore general formula based on both statements is \(n=100m+63\). Hence n can be 63, 163, 263, ... For more about this concept check: manhattanremainderproblem93752.html#p721341, whenpositiveintegernisdividedby5theremainderis90442.html#p722552, whenthepositiveintegeraisdividedby5and125591.html#p1028654Hope this helps.
_________________
New to the Math Forum? Please read this: 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



Director
Joined: 29 Nov 2012
Posts: 878

Re: When the positive integer n is divided by 25, the remainder [#permalink]
Show Tags
06 Oct 2013, 03:58
Really neat trick... I'm gonna save this absolutely brilliant... Thanks Bunuel!
_________________
Click +1 Kudos if my post helped...
Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/
GMAT Prep software What if scenarios http://gmatclub.com/forum/gmatprepsoftwareanalysisandwhatifscenarios146146.html



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15951

Re: When the positive integer n is divided by 25, the remainder [#permalink]
Show Tags
13 Feb 2015, 11:53
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




Re: When the positive integer n is divided by 25, the remainder
[#permalink]
13 Feb 2015, 11:53



Go to page
1 2
Next
[ 21 posts ]




