December 16, 2018 December 16, 2018 07:00 AM PST 09:00 AM PST Get personalized insights on how to achieve your Target Quant Score. December 16, 2018 December 16, 2018 03:00 PM EST 04:00 PM EST Strategies and techniques for approaching featured GMAT topics
Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 10 Mar 2008
Posts: 310

When 10 is divided by the positive integer n, the remainder
[#permalink]
Show Tags
15 Sep 2008, 13:33
Question Stats:
89% (00:47) correct 11% (01:09) wrong based on 703 sessions
HideShow timer Statistics
When 10 is divided by the positive integer n, the remainder is n4. Which of the following could be the value of n ? A) 3 B) 4 C) 7 D) 8 E) 12
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 51223

Re: When 10 is divided by the positive integer n, the remainder
[#permalink]
Show Tags
18 Jun 2010, 00:58
jpr200012 wrote: When 10 is divided by the positive integer n, the remainder is n4. Which of the following could be the value of n?
A. 3 B. 4 C. 7 D. 8 E. 12
My strategy was to create lists below: n = 3, 4, 7, 8, 12 n4 = 1(becomes 9), 0, 3, 4, 8 n/10 = R? = 3, 4, 7, 8, 4
There is no match between n4 and n/10's R.
The solution uses 14 = ..., but I don't understand how they are using 14. Should the question have said a multiple of one of these numbers? Algebraic approach: THEORY:Positive integer \(a\) divided by positive integer \(d\) yields a reminder of \(r\) can always be expressed as \(a=qd+r\), where \(q\) is called a quotient and \(r\) is called a remainder, note here that \(0\leq{r}<d\) (remainder is nonnegative integer and always less than divisor). Original question says that when 10 is divided by the positive integer n, the remainder is n4, so \(10=nq+(n4)\) and also \(n4\geq{0}\) or \(n\geq{4}\) (remainder must be nonnegative). \(10=nq+n4\) > \(14=n(q+1)\) > as \(14=1*14=2*7\) and \(\geq{4}\) then > \(n\) can be 7 or 14. Answer: C. Hope it's clear.
_________________
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: 11 Jan 2008
Posts: 54

Re: When 10 is divided by the positive integer n, the remainder
[#permalink]
Show Tags
15 Sep 2008, 16:08
back solving is easier for this one.
10/7 gives a remainder of 3. n4 = 74 = 3



Current Student
Joined: 28 Dec 2004
Posts: 3230
Location: New York City
Schools: Wharton'11 HBS'12

Re: When 10 is divided by the positive integer n, the remainder
[#permalink]
Show Tags
16 Sep 2008, 06:18
10=NK+N4; assume K=1
10=2N4
14=2N. N has to be a multiple of 7...
C it is..



VP
Joined: 21 Jul 2006
Posts: 1392

Re: When 10 is divided by the positive integer n, the remainder
[#permalink]
Show Tags
17 Sep 2008, 06:04
vksunder wrote: fresinha12  I did the same way as you had described. But is it safe to assume that K=1? well, since we can never have the denominator to be zero, otherwise the fraction will be undefined. so it makes sense to start off with k=1. If that doesn't work, then you just have to keep increasing the value of k until you can match your answer with the correct answer choice.



VP
Joined: 17 Jun 2008
Posts: 1417

Re: When 10 is divided by the positive integer n, the remainder
[#permalink]
Show Tags
17 Sep 2008, 23:18
I approached as follows.
10 = nx + n4 for x = 0,1,2,3,4...... or, n(x+1) = 14 or, n = 14/(x+1)
For x = 0, n = 14, for x = 1, n = 7, x cannot be 2,3,4,5. For x = 6, n = 2. x cannot be greater than 6.
Hence, possible values of n are 14, 7, 2. Answer choice has 7. Hence, 7 is the answer.



Manager
Joined: 30 May 2010
Posts: 176

Re: When 10 is divided by the positive integer n, the remainder
[#permalink]
Show Tags
17 Jun 2010, 23:12
When 10 is divided by the positive integer n, the remainder is n4. Which of the following could be the value of n?
A. 3 B. 4 C. 7 D. 8 E. 12
My strategy was to create lists below: n = 3, 4, 7, 8, 12 n4 = 1(becomes 9), 0, 3, 4, 8 n/10 = R? = 3, 4, 7, 8, 4
There is no match between n4 and n/10's R.
The solution uses 14 = ..., but I don't understand how they are using 14. Should the question have said a multiple of one of these numbers?



Manager
Joined: 07 Oct 2006
Posts: 61
Location: India

Re: When 10 is divided by the positive integer n, the remainder
[#permalink]
Show Tags
17 Jun 2010, 23:56
As per my approach, it is easy to reach the solution by going thorough each one of the options. You can eliminate 12,8,4 and 3 at one look. Then you just need to check for 7. It took me less than 1 minute to get to the answer. So that should be fine I guess.



SVP
Status: Three Down.
Joined: 09 Jun 2010
Posts: 1855
Concentration: General Management, Nonprofit

Re: When 10 is divided by the positive integer n, the remainder
[#permalink]
Show Tags
18 Jun 2010, 05:29
It says that the remainder when you divide 10 by n is n4 This basically can be translated into the following statement algebraically: \(10 = kn + (n4)\) This is simplified as follows: \(10 = kn + n 4 = n *(k+1)  4\) Further simplifying: \(10 + 4 = n*(k+1) 14 = n*(k+1) 7*2 = n*(k+1)\) So n can be 7 or 2. Only 7 is listed as an option here, so the answer is C. Hope this helps! jpr200012 wrote: When 10 is divided by the positive integer n, the remainder is n4. Which of the following could be the value of n?
A. 3 B. 4 C. 7 D. 8 E. 12
My strategy was to create lists below: n = 3, 4, 7, 8, 12 n4 = 1(becomes 9), 0, 3, 4, 8 n/10 = R? = 3, 4, 7, 8, 4
There is no match between n4 and n/10's R.
The solution uses 14 = ..., but I don't understand how they are using 14. Should the question have said a multiple of one of these numbers?



Math Expert
Joined: 02 Sep 2009
Posts: 51223

Re: When 10 is divided by the positive integer n, the remainder
[#permalink]
Show Tags
18 Jun 2010, 05:46



SVP
Status: Three Down.
Joined: 09 Jun 2010
Posts: 1855
Concentration: General Management, Nonprofit

Re: When 10 is divided by the positive integer n, the remainder
[#permalink]
Show Tags
18 Jun 2010, 05:52
Oh, yeah, that's right. I just saw the 7 and 2, and looked at the answer choices and chose 7. Thanks, Bunuel. Your explanation will come in handy in case both 2 and 7 were listed as answer choices!



Director
Joined: 23 Apr 2010
Posts: 547

Re: When 10 is divided by the positive integer n, the remainder
[#permalink]
Show Tags
16 Jul 2010, 03:22
Quote: remainder is always nonnegative Bunuel, I have to disagree with you on that: http://en.wikipedia.org/wiki/Remainder



Math Expert
Joined: 02 Sep 2009
Posts: 51223

Re: When 10 is divided by the positive integer n, the remainder
[#permalink]
Show Tags
16 Jul 2010, 06:14



Director
Joined: 23 Apr 2010
Posts: 547

Re: When 10 is divided by the positive integer n, the remainder
[#permalink]
Show Tags
16 Jul 2010, 13:00
Thanks for clarification. But you can use that property (negative remainder) to solve remainder problems (as it has been done in several posts).



Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 739

Re: When 10 is divided by the positive integer n, the remainder
[#permalink]
Show Tags
05 Mar 2011, 00:24
If division by n leaves reminder. Then i.e. Dividend  Remainder is a multiple of divider. Here 10 (n4) must be a multiple of n. Or Is [10  (n4)] / n = integer?Now plug in the values of n from the options. A  n4 will give negative remainder. Illogical B  (100)/4 is not integer C  (103)/7 is integer D  (104)/8 is not integer E  (108)/12 is not integer Answer C. Baten80 wrote: When 10 is divided by the positive integer n, the remainder is n4. Which of the following could be the value of n ?
A) 3 B) 4 C) 7 D) 8 E) 12



Retired Moderator
Joined: 20 Dec 2010
Posts: 1820

Re: When 10 is divided by the positive integer n, the remainder
[#permalink]
Show Tags
05 Mar 2011, 00:44
\(10=nQ+n4\) where Q is the quotient \(n(Q+1)=14\), where n and Q are both integers. Factors of 14; n*(Q+1) 1*14; n=1, Q=13; Not possible because 1 won't leave any remainder with 10 2*7; n=2, Q=6; Not possible because 2 won't leave any remainder with 10 7*2; n=7, Q=1; Possible 14*1; n=14, Q=0; Possible So; n can be 7 or 14. Ans: "C"
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings



Director
Joined: 01 Feb 2011
Posts: 659

Re: When 10 is divided by the positive integer n, the remainder
[#permalink]
Show Tags
06 Mar 2011, 14:04
Nice explanation there Bunuel. Bunuel wrote: jpr200012 wrote: When 10 is divided by the positive integer n, the remainder is n4. Which of the following could be the value of n?
A. 3 B. 4 C. 7 D. 8 E. 12
My strategy was to create lists below: n = 3, 4, 7, 8, 12 n4 = 1(becomes 9), 0, 3, 4, 8 n/10 = R? = 3, 4, 7, 8, 4
There is no match between n4 and n/10's R.
The solution uses 14 = ..., but I don't understand how they are using 14. Should the question have said a multiple of one of these numbers? Algebraic approach: THEORY:Positive integer \(a\) divided by positive integer \(d\) yields a reminder of \(r\) can always be expressed as \(a=qd+r\), where \(q\) is called a quotient and \(r\) is called a remainder, note here that \(0\leq{r}<d\) (remainder is nonnegative integer and always less than divisor). Original question says that when 10 is divided by the positive integer n, the remainder is n4, so \(10=nq+(n4)\) and also \(n4\geq{0}\) or \(n\geq{4}\) (remainder must be nonnegative). \(10=nq+n4\) > \(14=n(q+1)\) > \(n\) is an factor of 14 and \(\geq{4}\) > \(n\) can be 7 or 14. Answer: C. Hope it's clear.



Director
Joined: 01 Feb 2011
Posts: 659

Re: When 10 is divided by the positive integer n, the remainder
[#permalink]
Show Tags
Updated on: 06 Mar 2011, 15:27
I thought of the same , why cant a remainder be negative? I guess in some cases , as Bunel is suggesting we need to make an assumption that we are dealing with just positive integers. nonameee wrote: Quote: remainder is always nonnegative Bunuel, I have to disagree with you on that: http://en.wikipedia.org/wiki/Remainder
Originally posted by Spidy001 on 06 Mar 2011, 14:48.
Last edited by Spidy001 on 06 Mar 2011, 15:27, edited 1 time in total.



Math Expert
Joined: 02 Sep 2009
Posts: 51223

Re: When 10 is divided by the positive integer n, the remainder
[#permalink]
Show Tags
06 Mar 2011, 14:55



Director
Joined: 01 Feb 2011
Posts: 659

Re: When 10 is divided by the positive integer n, the remainder
[#permalink]
Show Tags
06 Mar 2011, 15:41
Bunuel, I know in this case we don't have to make any assumption, because the question clearly states these are two positive integers. i was referring more to scenarios like negative number division 25 /7 25 = 7(3)+(4) Here remainder is 4 which is negative. so lets say if question is like x,y are integers x/y . we cannot generalize and say remainder >=0 ,unless we assume that we are only talking about positive integers. nonameee wrote: Quote: remainder is always nonnegative Bunuel, I have to disagree with you on that: http://en.wikipedia.org/wiki/Remainder[/quote] It's not an assumption. Remainder is a nonnegative by definition (at least on the GMAT).[/quote]




Re: When 10 is divided by the positive integer n, the remainder &nbs
[#permalink]
06 Mar 2011, 15:41



Go to page
1 2 3
Next
[ 43 posts ]



