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

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

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25 Sep 2010, 04:33
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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

[Reveal] Spoiler:
Got the answer as E , can someone testify ..whether the answer ..i am getting is right or wrong and also post the explanation.

Thanks
[Reveal] Spoiler: OA
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25 Sep 2010, 04:55
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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.

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Joined: 21 Aug 2009
Posts: 54

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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.
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Joined: 27 Jun 2010
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25 Sep 2010, 05:09
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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 !!
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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 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
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17 Sep 2013, 00:49
Expert's post
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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.
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Re: If j and k are positive integers where k > j, what is the [#permalink]

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16 Dec 2013, 06:40
Very tricky. Nice question! As always, great explanation Bunuel!!
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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 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!
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Joined: 02 Sep 2009
Posts: 39622

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26 Dec 2013, 03:19
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Expert's post
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.
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Re: If j and k are positive integers such that k > j [#permalink]

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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

Hi Bunnel,

If 2) j<5, will the Answer be E?

Thank you
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Joined: 02 Sep 2009
Posts: 39622
Re: If j and k are positive integers such that k > j [#permalink]

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11 May 2014, 06:14
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Expert's post
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

Hi Bunnel,

If 2) j<5, will the Answer be E?

Thank you

Yes, that's correct.
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Re: If j and k are positive integers where k > j, what is the [#permalink]

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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

[Reveal] Spoiler:
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

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Re: If j and k are positive integers where k > j, what is the [#permalink]

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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
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Posts: 39622
Re: If j and k are positive integers where k > j, what is the [#permalink]

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18 Sep 2014, 08:41
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

(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.
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If j and k are positive integers where k > j, what is the [#permalink]

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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
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Re: If j and k are positive integers where k > j, what is the [#permalink]

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Re: If j and k are positive integers where k > j, what is the [#permalink]

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04 Mar 2017, 01:01
1
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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.
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Re: If j and k are positive integers where k > j, what is the [#permalink]

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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
Re: If j and k are positive integers where k > j, what is the   [#permalink] 04 Mar 2017, 04:43
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