GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Mar 2019, 12:15 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. ### Request Expert Reply # If j and k are positive integers where k > j, what is the

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Intern  Joined: 27 Jun 2010
Posts: 33
If j and k are positive integers where k > j, what is the  [#permalink]

### Show Tags

5
26 00:00

Difficulty:   75% (hard)

Question Stats: 50% (01:34) correct 50% (01:25) wrong based on 759 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
Math Expert V
Joined: 02 Sep 2009
Posts: 53709

### Show Tags

17
18
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 non-negative 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.

_________________
##### General Discussion
Intern  Joined: 21 Aug 2009
Posts: 41

### Show Tags

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: 33

### Show Tags

1
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 non-negative 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.

Thanks for the gr8 explanation !!
Intern  Joined: 15 Sep 2013
Posts: 1

### Show Tags

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 non-negative 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.

Hi Bunuel,

Could you please elaborate as to why A is not the right answer. Would really appreciate it. Thanks
Math Expert V
Joined: 02 Sep 2009
Posts: 53709

### Show Tags

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 non-negative 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.

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.
_________________
Manager  Joined: 25 Oct 2013
Posts: 145
Re: If j and k are positive integers where k > j, what is the  [#permalink]

### Show Tags

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: 180
Location: France
Concentration: Finance, General Management
Schools: EMLYON FT'16
GMAT 1: 650 Q47 V32 GPA: 3.44

### Show Tags

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 non-negative 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.

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 V
Joined: 02 Sep 2009
Posts: 53709

### Show Tags

1
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 non-negative 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.

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.
_________________
Intern  Joined: 12 Mar 2011
Posts: 15
Re: If j and k are positive integers such that k > j  [#permalink]

### Show Tags

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 V
Joined: 02 Sep 2009
Posts: 53709
Re: If j and k are positive integers such that k > j  [#permalink]

### Show Tags

1
yenpham9 wrote:
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

Yes, that's correct.
_________________
Intern  B
Joined: 04 Jun 2008
Posts: 8
Re: If j and k are positive integers where k > j, what is the  [#permalink]

### Show Tags

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 -> sufficient

Intern  Joined: 26 Aug 2014
Posts: 2
Re: If j and k are positive integers where k > j, what is the  [#permalink]

### Show Tags

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 V
Joined: 02 Sep 2009
Posts: 53709
Re: If j and k are positive integers where k > j, what is the  [#permalink]

### Show Tags

sudipt23 wrote:
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

Have you read this:
(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.
_________________
Intern  Joined: 23 Apr 2014
Posts: 20
If j and k are positive integers where k > j, what is the  [#permalink]

### Show Tags

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  G
Joined: 26 Oct 2016
Posts: 634
Location: United States
Concentration: Marketing, International Business
Schools: HBS '19
GMAT 1: 770 Q51 V44 GPA: 4
WE: Education (Education)
Re: If j and k are positive integers where k > j, what is the  [#permalink]

### Show Tags

1
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

Director  S
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 542
Location: India
Re: If j and k are positive integers where k > j, what is the  [#permalink]

### Show Tags

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 Non-Human User Joined: 09 Sep 2013
Posts: 10141
Re: If j and k are positive integers where k > j, what is the  [#permalink]

### Show Tags

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.
_________________ Re: If j and k are positive integers where k > j, what is the   [#permalink] 15 Mar 2018, 02:50
Display posts from previous: Sort by

# If j and k are positive integers where k > j, what is the

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.  