Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 27 Jun 2010
Posts: 39

If j and k are positive integers where k > j, what is the
[#permalink]
Show Tags
25 Sep 2010, 04:33
Question Stats:
53% (00:52) correct 47% (00:54) wrong based on 730 sessions
HideShow timer Statistics
If j and k are positive integers where k > j, what is the value of the remainder when k is divided by j? (1) There exists a positive integer m such that k = jm + 5. (2) j > 5 Got the answer as E , can someone testify ..whether the answer ..i am getting is right or wrong and also post the explanation.
Thanks
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 47946

Re: Remainder
[#permalink]
Show Tags
25 Sep 2010, 04:55
sachinrelan wrote: If j and k are positive integers where k > j, what is the value of the remainder when k is divided by j?
(1) There exists a positive integer m such that k = jm + 5.
(2) j > 5
Got the answer as E , can someone testify ..whether the answer ..i am getting is right or wrong and also post the explanation.
Thanks 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).So according to above \(k\) is divided by \(j\) yields a remainder of \(r\) can be expressed as: \(k=qj+r\), where \(0\leq{r}<j=divisor\). Question: \(r=?\) (1) There exists a positive integer m such that k = jm + 5 > it's tempting to say that this statement is sufficient and \(r=5\), as given equation is very similar to \(k=qj+r\). But we don't know whether \(5<j\): remainder must be less than divisor. For example: If \(k=6\) and \(j=1\) then \(6=1*1+5\) and the remainder upon division 6 by 1 is zero; If \(k=11\) and \(j=6\) then \(11=1*6+5\) and the remainder upon division 11 by 6 is 5. Not sufficient. (2) \(j > 5\) > clearly insufficient. (1)+(2) \(k = jm + 5\) and \(j > 5\) > direct formula of remainder as defined above > \(r=5\). Sufficient. Or: \(k = jm + 5\) > first term \(jm\) is clearly divisible by \(j\) and 5 divided by \(j\) as (\(j>5\)) yields remainder of 5. Answer: C.
_________________
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: 21 Aug 2009
Posts: 47

Re: Remainder
[#permalink]
Show Tags
25 Sep 2010, 05:00
Ans: C
Statement 1: k=jm+5 This is of the form "Quotient x J + Remainder". However J could be 2, 3, 4, in which case the remainder would not be 5.
Statement 2: j>5 Insufficient. Just the value of J is not sufficient to find what the remainder is.
Combining both the equations we get that the remainder is 5.



Intern
Joined: 27 Jun 2010
Posts: 39

Re: Remainder
[#permalink]
Show Tags
25 Sep 2010, 05:09
Bunuel wrote: sachinrelan wrote: If j and k are positive integers where k > j, what is the value of the remainder when k is divided by j?
(1) There exists a positive integer m such that k = jm + 5.
(2) j > 5
Got the answer as E , can someone testify ..whether the answer ..i am getting is right or wrong and also post the explanation.
Thanks 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).So according to above \(k\) is divided by \(j\) yields a remainder of \(r\) can be expressed as: \(k=qj+r\), where \(0\leq{r}<j=divisor\). Question: \(r=?\) (1) There exists a positive integer m such that k = jm + 5 > it's tempting to say that this statement is sufficient and \(r=5\), as given equation is very similar to \(k=qj+r\). But we don't know whether \(5<j\): remainder must be less than divisor. For example: If \(k=6\) and \(j=1\) then \(6=1*1+5\) and the remainder upon division 6 by 1 is zero; If \(k=11\) and \(j=6\) then \(11=1*6+5\) and the remainder upon division 11 by 6 is 5. Not sufficient. (2) \(j > 5\) > clearly insufficient. (1)+(2) \(k = jm + 5\) and \(j > 5\) > direct formula of remainder as defined above > \(r=5\). Sufficient. Or: \(k = jm + 5\) > first term \(jm\) is clearly divisible by \(j\) and 5 divided by \(j\) as (\(j>5\)) yields remainder of 5. Answer: C. Thanks for the gr8 explanation !!



Intern
Joined: 15 Sep 2013
Posts: 1

Re: Remainder
[#permalink]
Show Tags
16 Sep 2013, 21:11
Bunuel wrote: sachinrelan wrote: If j and k are positive integers where k > j, what is the value of the remainder when k is divided by j?
(1) There exists a positive integer m such that k = jm + 5.
(2) j > 5
Got the answer as E , can someone testify ..whether the answer ..i am getting is right or wrong and also post the explanation.
Thanks 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).So according to above \(k\) is divided by \(j\) yields a remainder of \(r\) can be expressed as: \(k=qj+r\), where \(0\leq{r}<j=divisor\). Question: \(r=?\) (1) There exists a positive integer m such that k = jm + 5 > it's tempting to say that this statement is sufficient and \(r=5\), as given equation is very similar to \(k=qj+r\). But we don't know whether \(5<j\): remainder must be less than divisor. For example: If \(k=6\) and \(j=1\) then \(6=1*1+5\) and the remainder upon division 6 by 1 is zero; If \(k=11\) and \(j=6\) then \(11=1*6+5\) and the remainder upon division 11 by 6 is 5. Not sufficient. (2) \(j > 5\) > clearly insufficient. (1)+(2) \(k = jm + 5\) and \(j > 5\) > direct formula of remainder as defined above > \(r=5\). Sufficient. Or: \(k = jm + 5\) > first term \(jm\) is clearly divisible by \(j\) and 5 divided by \(j\) as (\(j>5\)) yields remainder of 5. Answer: C. Hi Bunuel, Could you please elaborate as to why A is not the right answer. Would really appreciate it. Thanks



Math Expert
Joined: 02 Sep 2009
Posts: 47946

Re: Remainder
[#permalink]
Show Tags
17 Sep 2013, 00:49
sadhusaint wrote: Bunuel wrote: sachinrelan wrote: If j and k are positive integers where k > j, what is the value of the remainder when k is divided by j?
(1) There exists a positive integer m such that k = jm + 5.
(2) j > 5
Got the answer as E , can someone testify ..whether the answer ..i am getting is right or wrong and also post the explanation.
Thanks 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).So according to above \(k\) is divided by \(j\) yields a remainder of \(r\) can be expressed as: \(k=qj+r\), where \(0\leq{r}<j=divisor\). Question: \(r=?\) (1) There exists a positive integer m such that k = jm + 5 > it's tempting to say that this statement is sufficient and \(r=5\), as given equation is very similar to \(k=qj+r\). But we don't know whether \(5<j\): remainder must be less than divisor. For example: If \(k=6\) and \(j=1\) then \(6=1*1+5\) and the remainder upon division 6 by 1 is zero; If \(k=11\) and \(j=6\) then \(11=1*6+5\) and the remainder upon division 11 by 6 is 5. Not sufficient. (2) \(j > 5\) > clearly insufficient. (1)+(2) \(k = jm + 5\) and \(j > 5\) > direct formula of remainder as defined above > \(r=5\). Sufficient. Or: \(k = jm + 5\) > first term \(jm\) is clearly divisible by \(j\) and 5 divided by \(j\) as (\(j>5\)) yields remainder of 5. Answer: C. Hi Bunuel, Could you please elaborate as to why A is not the right answer. Would really appreciate it. Thanks Consider the examples for the first statement given in my solution proving that this statement is not sufficient.
_________________
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: 25 Oct 2013
Posts: 158

Re: If j and k are positive integers where k > j, what is the
[#permalink]
Show Tags
16 Dec 2013, 06:40
Very tricky. Nice question! As always, great explanation Bunuel!!
_________________
Click on Kudos if you liked the post!
Practice makes Perfect.



Manager
Status: Student
Joined: 26 Aug 2013
Posts: 220
Location: France
Concentration: Finance, General Management
GPA: 3.44

Re: Remainder
[#permalink]
Show Tags
26 Dec 2013, 01:07
Bunuel wrote: sachinrelan wrote: If j and k are positive integers where k > j, what is the value of the remainder when k is divided by j?
(1) There exists a positive integer m such that k = jm + 5.
(2) j > 5
Got the answer as E , can someone testify ..whether the answer ..i am getting is right or wrong and also post the explanation.
Thanks 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).So according to above \(k\) is divided by \(j\) yields a remainder of \(r\) can be expressed as: \(k=qj+r\), where \(0\leq{r}<j=divisor\). Question: \(r=?\) (1) There exists a positive integer m such that k = jm + 5 > it's tempting to say that this statement is sufficient and \(r=5\), as given equation is very similar to \(k=qj+r\). But we don't know whether \(5<j\): remainder must be less than divisor. For example: If \(k=6\) and \(j=1\) then \(6=1*1+5\) and the remainder upon division 6 by 1 is zero; If \(k=11\) and \(j=6\) then \(11=1*6+5\) and the remainder upon division 11 by 6 is 5. Not sufficient. (2) \(j > 5\) > clearly insufficient. (1)+(2) \(k = jm + 5\) and \(j > 5\) > direct formula of remainder as defined above > \(r=5\). Sufficient. Or: \(k = jm + 5\) > first term \(jm\) is clearly divisible by \(j\) and 5 divided by \(j\) as (\(j>5\)) yields remainder of 5. Answer: C. I do not understand why the reminder is still 5.... If you have 25=20*2 + 5 than reminder is 5. But if K/J than the reminder is 5/10: 0.5 not 5. And indeed 25/10=2.5 and 2+0.5=2.5 Therefore, the value of the reminder when K is divided by J is correlated with the value of J. This is why I answered E because we do not know the value of J. Where did I get wrong? Thanks!
_________________
Think outside the box



Math Expert
Joined: 02 Sep 2009
Posts: 47946

Re: Remainder
[#permalink]
Show Tags
26 Dec 2013, 03:19
Paris75 wrote: Bunuel wrote: sachinrelan wrote: If j and k are positive integers where k > j, what is the value of the remainder when k is divided by j?
(1) There exists a positive integer m such that k = jm + 5.
(2) j > 5
Got the answer as E , can someone testify ..whether the answer ..i am getting is right or wrong and also post the explanation.
Thanks 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).So according to above \(k\) is divided by \(j\) yields a remainder of \(r\) can be expressed as: \(k=qj+r\), where \(0\leq{r}<j=divisor\). Question: \(r=?\) (1) There exists a positive integer m such that k = jm + 5 > it's tempting to say that this statement is sufficient and \(r=5\), as given equation is very similar to \(k=qj+r\). But we don't know whether \(5<j\): remainder must be less than divisor. For example: If \(k=6\) and \(j=1\) then \(6=1*1+5\) and the remainder upon division 6 by 1 is zero; If \(k=11\) and \(j=6\) then \(11=1*6+5\) and the remainder upon division 11 by 6 is 5. Not sufficient. (2) \(j > 5\) > clearly insufficient. (1)+(2) \(k = jm + 5\) and \(j > 5\) > direct formula of remainder as defined above > \(r=5\). Sufficient. Or: \(k = jm + 5\) > first term \(jm\) is clearly divisible by \(j\) and 5 divided by \(j\) as (\(j>5\)) yields remainder of 5. Answer: C. I do not understand why the reminder is still 5.... If you have 25=20*2 + 5 than reminder is 5. But if K/J than the reminder is 5/10: 0.5 not 5. And indeed 25/10=2.5 and 2+0.5=2.5 Therefore, the value of the reminder when K is divided by J is correlated with the value of J. This is why I answered E because we do not know the value of J. Where did I get wrong? Thanks! The remainder when k=25 is divided by j=20 is 5. The remainder when k=5 is divided by j=10 is 5 too. 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



Intern
Joined: 12 Mar 2011
Posts: 19

Re: If j and k are positive integers such that k > j
[#permalink]
Show Tags
10 May 2014, 13:16
Bunuel wrote: AkshayChittoria wrote: If j and k are positive integers such that k > j, what is the value of the remainder when k is divided by j?
(1) There exists a positive integer m such that k = jm + 5. (2) j > 5 Merging similar topics. Please ask if anything remains unclear. Hi Bunnel, If 2) j<5, will the Answer be E? Thank you



Math Expert
Joined: 02 Sep 2009
Posts: 47946

Re: If j and k are positive integers such that k > j
[#permalink]
Show Tags
11 May 2014, 06:14



Intern
Joined: 04 Jun 2008
Posts: 9

Re: If j and k are positive integers where k > j, what is the
[#permalink]
Show Tags
08 Jun 2014, 12:58
sachinrelan wrote: If j and k are positive integers where k > j, what is the value of the remainder when k is divided by j? (1) There exists a positive integer m such that k = jm + 5. (2) j > 5 Got the answer as E , can someone testify ..whether the answer ..i am getting is right or wrong and also post the explanation.
Thanks 1) K = jm + 5 > K/j = m + 5/j > remainder of 5/j is the remainder, without knowing J value remainder could be anything > insufficient 2) j>5 remainder could be anything  insufficient (1)(2) if J>5 remainder of 5/j is 5 > sufficientAnswer C



Intern
Joined: 26 Aug 2014
Posts: 2

Re: If j and k are positive integers where k > j, what is the
[#permalink]
Show Tags
18 Sep 2014, 08:34
Hi, would be grateful if someone could elaborate on first statement. Can't understand how given statement 'k=jm+5' is not the same as 'a=qd+r'.
Thanks



Math Expert
Joined: 02 Sep 2009
Posts: 47946

Re: If j and k are positive integers where k > j, what is the
[#permalink]
Show Tags
18 Sep 2014, 08:41



Intern
Joined: 23 Apr 2014
Posts: 21

If j and k are positive integers where k > j, what is the
[#permalink]
Show Tags
26 May 2015, 04:03
Stmt 1: we need to findd k/j so as per the stmt 1 jm+5/j This gives us m + 5/j As m is an integer we need to find the remainder for 5/j Not suff
Stmt 2: j>5 does not tell us anything. So insuff
Combining we get J>5 so 5/j will always give a remainder of 5
So the ans is C



Director
Joined: 26 Oct 2016
Posts: 656
Location: United States
Concentration: Marketing, International Business
GPA: 4
WE: Education (Education)

Re: If j and k are positive integers where k > j, what is the
[#permalink]
Show Tags
04 Mar 2017, 01:01
We are told that k > j > 0, and both k and j are integers. The remainder when k is divided by j may be expressed as r in this formula: k = jq + r In this formula, (a) all of the variables are integers, (b) q (the quotient) is the greatest number of j's such that jx < k, and (c) r < j. (If r were greater than j, then q would not be the greatest number of j's in k.) Thus, the question may be rephrased: “If k = jq + r, and q is maximized such that jq < k and r < j, what is the value of r?” (1) INSUFFICIENT: At first glance, this may seem sufficient since it is in the form of our remainder equation. Certainly, m could equal q (the quotient) and r (the remainder) could be 5. For example, k = 13 and j = 8 yield a remainder of 5 when k is divided by j: 13 = (8)(1) + 5, where m = 1 is the greatest number of 8's such that (8)(1) < 13, and r < j (i.e. 5 < 8). However, this statement does not indicate whether m is the greatest number of j's such that jm < k and r < j, as our rephrased question requires. For example, k = 13 and j = 2 may be expressed in this form: 13 = (2)(4) + 5, where m = 4. However, 5 is not the remainder because 5 > j, and 4 is not the greatest number of 2's in 13. When 13 is divided by 2, the quotient is 6 and the remainder is 1. If j ≤ 5, then 5 cannot be the remainder and m is not the quotient. If j > 5, then 5 must be the remainder and m must be the quotient. (2) INSUFFICIENT: This statement gives us a range of possible values of j. Without information about k, we cannot determine anything about the remainder when k is divided by j. (1) AND (2) SUFFICIENT: Statement (2) tells us that j > 5, so we can conclude from statement (1) that 5 is the remainder and m is the quotient when k is divided by j. The correct answer is C.
_________________
Thanks & Regards, Anaira Mitch



Senior Manager
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 433
Location: India

Re: If j and k are positive integers where k > j, what is the
[#permalink]
Show Tags
04 Mar 2017, 04:43
Prompt analysi k and j are positive integers such that k>j Superset The answer will be a positive integer Translation In order to find the answer, we need: 1# exact value of x and y 2# any relation between x and y 3# some property of x and y Statement analysis St 1: k =jm +5 . we can say the 5 is the remainder only if j>5. since there is no such condition give the statement is INSUFFICIENT St 2: j>5. Cannot be said anything about the remainder. INSUFFICIENT St 1 & St 2: k = jm +5 and j>5. we can say that 5 is the remainder.ANSWER Option C
_________________
GMAT Mentors



NonHuman User
Joined: 09 Sep 2013
Posts: 7732

Re: If j and k are positive integers where k > j, what is the
[#permalink]
Show Tags
15 Mar 2018, 02:50
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: If j and k are positive integers where k > j, what is the &nbs
[#permalink]
15 Mar 2018, 02:50






