Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 11 Aug 2014
Posts: 3

When the positive integer k is divided by the positive integ
[#permalink]
Show Tags
Updated on: 20 Sep 2017, 05:43
Question Stats:
85% (01:31) correct 15% (01:59) wrong based on 480 sessions
HideShow timer Statistics
When the positive integer k is divided by the positive integer n , the remainder is 11. If k/n = 81.2 , what is the value of n? A. 9 B. 20 C. 55 D. 70 E. 81 Can someone break this down for me please?
Here is a response from Beat The GMAT (/trickyremainderproblemt270176.html)
Before I past the question, I am confused with how the user came up with K = 81n +11. Where did the .2 go for this representation?
"If, when k is divided by n, the remainder is 11, we could say that some multiple of n plus 11 equals k: xn + 11 = k
If k/n = 81.2, that means that "some multiple of n" (aka the quotient) is 81, and the remainder is represented by the 0.2.
k = 81.2n
and
k = 81n + 11
Now, we can simply set these expressions equal to each other, since they're both equal to k:
81.2n = 81n + 11 0.2n = 11 n = 55"
Thank you for your help!!
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by joaomario on 12 Aug 2014, 05:00.
Last edited by abhimahna on 20 Sep 2017, 05:43, edited 2 times in total.
Edited the question




Math Expert
Joined: 02 Sep 2009
Posts: 50007

Re: When the positive integer k is divided by the positive integ
[#permalink]
Show Tags
12 Aug 2014, 05:44
joaomario wrote: When the positive integer k is divided by the positive integer n , the remainder is 11. If k/n = 81.2 , what is the value of n?
A. 9 B. 20 C. 55 D. 70 E. 81
Can someone break this down for me please?
Here is a response from Beat The GMAT (/trickyremainderproblemt270176.html)
Before I past the question, I am confused with how the user came up with K = 81n +11. Where did the .2 go for this representation?
"If, when k is divided by n, the remainder is 11, we could say that some multiple of n plus 11 equals k: xn + 11 = k
If k/n = 81.2, that means that "some multiple of n" (aka the quotient) is 81, and the remainder is represented by the 0.2.
k = 81.2n
and
k = 81n + 11
Now, we can simply set these expressions equal to each other, since they're both equal to k:
81.2n = 81n + 11 0.2n = 11 n = 55"
Thank you for your help!! If \(x\) and \(y\) are positive integers, there exist unique integers \(q\) and \(r\), called the quotient and remainder, respectively, such that \(y =divisor*quotient+remainder= xq + r\) and \(0\leq{r}<x\).For example, when 15 is divided by 6, the quotient is 2 and the remainder is 3 since \(15 = 6*2 + 3\). Hence, the positive integer k is divided by the positive integer n, the remainder is 11, could be written as k = nq + 11. Divide by n: k/n = q + 11/n. We are also given that k/n = 81.2 = 81 + 0.2. So, the quotient, q, is 81 and 11/n is 0.2: 11/n = 0.2 > n = 55. Answer: C. Similar questions to practice: whenpositiveintegerxisdividedbypositiveintegery106493.htmlifsandtarepositiveintegerssuchthatst6412which135190.htmlP.S. Please read carefully and follow: rulesforpostingpleasereadthisbeforeposting133935.html Pay attention to rule 3. Thank you.
_________________
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: 17 May 2014
Posts: 5
Location: United Kingdom
Concentration: General Management, Finance
GPA: 3.4
WE: Accounting (Retail)

Re: When the positive integer k is divided by the positive integ
[#permalink]
Show Tags
17 Dec 2014, 04:36
joaomario wrote: When the positive integer k is divided by the positive integer n , the remainder is 11. If k/n = 81.2 , what is the value of n?
A. 9 B. 20 C. 55 D. 70 E. 81
Can someone break this down for me please?
Here is a response from Beat The GMAT (/trickyremainderproblemt270176.html)
Before I past the question, I am confused with how the user came up with K = 81n +11. Where did the .2 go for this representation?
"If, when k is divided by n, the remainder is 11, we could say that some multiple of n plus 11 equals k: xn + 11 = k
If k/n = 81.2, that means that "some multiple of n" (aka the quotient) is 81, and the remainder is represented by the 0.2.
k = 81.2n
and
k = 81n + 11
Now, we can simply set these expressions equal to each other, since they're both equal to k:
81.2n = 81n + 11 0.2n = 11 n = 55"
Thank you for your help!! If K/N is 81,2 and the remainder is 11 we can say that 11=0,2n 11/0,2=55 N=55 Answer C



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12687
Location: United States (CA)

Re: When the positive integer k is divided by the positive integ
[#permalink]
Show Tags
21 Dec 2014, 20:09
Hi joaomario, Here's an approach that's based on Number Properties and a bit of "brute force" math: We're told that K and N are both INTEGERS. Since K/N = 81.2, we can say that K = 81.2(N) N has to "multiply out" the .2 so that K becomes an INTEGER. With the answers that we have to work with, N has to be a multiple of 5. Eliminate A and E. With the remaining answers, we can TEST THE ANSWERS and find the one that fits the rest of the info (K/N = 81.2 and K/N has a remainder of 11) Answer B: If N = 20, then K = 1624; 1624/20 has a remainder of 4 NOT A MATCH Answer C: If N = 55, then K = 4466; 4466/55 has a remainder of 11 MATCH. 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!*****



Manager
Joined: 10 May 2014
Posts: 138

Re: When the positive integer k is divided by the positive integ
[#permalink]
Show Tags
29 Dec 2014, 17:18
Yes, I am aware that my answer goes after the 800scorer Rich, but I´ll try my best! Once you really understood the pattern in which Gmat works with this type of problem, it all boils down to a very simple system of 3 equations and 3 variables. That´s the "trick" you should know.Here is my reasoning: The System of Equations1st Equation: k = nq + 11 > k/n = q + 11/n 2nd Equation: k/n = 81.2 > k/n = 81 + 1/5 3rd Equation: q = 81 Plug in q (from equation 3) in equation 1k/n = 81 + 11/n Rewrite Equations 1 and 2k/n – 81 = 11/n k/n – 81 = 1/5 Set Equalities in Equations 1 and 211/n = 1/5 n = 55 There are many ways to find the system of equations. I just found this approach "elegant". Hope it helps!
_________________
Consider giving me Kudos if I helped, but don´t take them away if I didn´t!
What would you do if you weren´t afraid?



Manager
Joined: 20 Jan 2016
Posts: 195

Re: When the positive integer k is divided by the positive integ
[#permalink]
Show Tags
28 Sep 2017, 04:00
Bunuel wrote: joaomario wrote: When the positive integer k is divided by the positive integer n , the remainder is 11. If k/n = 81.2 , what is the value of n?
A. 9 B. 20 C. 55 D. 70 E. 81
Can someone break this down for me please?
Here is a response from Beat The GMAT (/trickyremainderproblemt270176.html)
Before I past the question, I am confused with how the user came up with K = 81n +11. Where did the .2 go for this representation?
"If, when k is divided by n, the remainder is 11, we could say that some multiple of n plus 11 equals k: xn + 11 = k
If k/n = 81.2, that means that "some multiple of n" (aka the quotient) is 81, and the remainder is represented by the 0.2.
k = 81.2n
and
k = 81n + 11
Now, we can simply set these expressions equal to each other, since they're both equal to k:
81.2n = 81n + 11 0.2n = 11 n = 55"
Thank you for your help!! If \(x\) and \(y\) are positive integers, there exist unique integers \(q\) and \(r\), called the quotient and remainder, respectively, such that \(y =divisor*quotient+remainder= xq + r\) and \(0\leq{r}<x\).For example, when 15 is divided by 6, the quotient is 2 and the remainder is 3 since \(15 = 6*2 + 3\). Hence, the positive integer k is divided by the positive integer n, the remainder is 11, could be written as k = nq + 11. Divide by n: k/n = q + 11/n. We are also given that k/n = 81.2 = 81 + 0.2. So, the quotient, q, is 81 and 11/n is 0.2: 11/n = 0.2 > n = 55. Answer: C. Similar questions to practice: http://gmatclub.com/forum/whenpositive ... 06493.htmlhttp://gmatclub.com/forum/ifsandtar ... 35190.htmlP.S. Please read carefully and follow: http://gmatclub.com/forum/rulesforpos ... 33935.html Pay attention to rule 3. Thank you. Hi Bunuel, "We are also given that k/n = 81.2 = 81 + 0.2. So, the quotient, q, is 81 and 11/n is 0.2: 11/n = 0.2 > n = 55." I was wondering, why can't q = 0.2 and 81=11/n ?



Math Expert
Joined: 02 Sep 2009
Posts: 50007

Re: When the positive integer k is divided by the positive integ
[#permalink]
Show Tags
28 Sep 2017, 04:20
pra1785 wrote: Bunuel wrote: joaomario wrote: When the positive integer k is divided by the positive integer n , the remainder is 11. If k/n = 81.2 , what is the value of n?
A. 9 B. 20 C. 55 D. 70 E. 81
Can someone break this down for me please?
Here is a response from Beat The GMAT (/trickyremainderproblemt270176.html)
Before I past the question, I am confused with how the user came up with K = 81n +11. Where did the .2 go for this representation?
"If, when k is divided by n, the remainder is 11, we could say that some multiple of n plus 11 equals k: xn + 11 = k
If k/n = 81.2, that means that "some multiple of n" (aka the quotient) is 81, and the remainder is represented by the 0.2.
k = 81.2n
and
k = 81n + 11
Now, we can simply set these expressions equal to each other, since they're both equal to k:
81.2n = 81n + 11 0.2n = 11 n = 55"
Thank you for your help!! If \(x\) and \(y\) are positive integers, there exist unique integers \(q\) and \(r\), called the quotient and remainder, respectively, such that \(y =divisor*quotient+remainder= xq + r\) and \(0\leq{r}<x\).For example, when 15 is divided by 6, the quotient is 2 and the remainder is 3 since \(15 = 6*2 + 3\). Hence, the positive integer k is divided by the positive integer n, the remainder is 11, could be written as k = nq + 11. Divide by n: k/n = q + 11/n. We are also given that k/n = 81.2 = 81 + 0.2. So, the quotient, q, is 81 and 11/n is 0.2: 11/n = 0.2 > n = 55. Answer: C. Similar questions to practice: http://gmatclub.com/forum/whenpositive ... 06493.htmlhttp://gmatclub.com/forum/ifsandtar ... 35190.htmlP.S. Please read carefully and follow: http://gmatclub.com/forum/rulesforpos ... 33935.html Pay attention to rule 3. Thank you. Hi Bunuel, "We are also given that k/n = 81.2 = 81 + 0.2. So, the quotient, q, is 81 and 11/n is 0.2: 11/n = 0.2 > n = 55." I was wondering, why can't q = 0.2 and 81=11/n ? The point is that the quotient must be an integer. For example, 15 divided by 6 gives the quotient of 2 and the remainder of 3: 15 = 2*6 + 3. The quotient (2 in our case) is the greatest whole number of times a divisor (6 in our case) may be subtracted from a dividend (15) without the remainder becoming negative.
_________________
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



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830

Re: When the positive integer k is divided by the positive integ
[#permalink]
Show Tags
03 Oct 2017, 09:30
joaomario wrote: When the positive integer k is divided by the positive integer n , the remainder is 11. If k/n = 81.2 , what is the value of n?
A. 9 B. 20 C. 55 D. 70 E. 81 We can create two remainder equations: k/n = 81 + 2/10 k/n = 81 + 1/5 and k/n = 81 + 11/n Thus: 1/5 = 11/n n = 55 Answer: C
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions




Re: When the positive integer k is divided by the positive integ &nbs
[#permalink]
03 Oct 2017, 09:30






