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

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If j and k are positive integers where k > j, what is the [#permalink]  25 Sep 2010, 03:33
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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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Re: Remainder [#permalink]  25 Sep 2010, 03:55
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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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Re: Remainder [#permalink]  25 Sep 2010, 04:00
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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Re: Remainder [#permalink]  25 Sep 2010, 04:09
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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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If j and k are positive integers such that k > j [#permalink]  05 Sep 2013, 22:32
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
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Posts: 23398
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Kudos [?]: 28838 [0], given: 2854

Re: If j and k are positive integers such that k > j [#permalink]  05 Sep 2013, 22:35
Expert's post
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

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Re: Remainder [#permalink]  16 Sep 2013, 20:11
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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Posts: 23398
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Kudos [?]: 28838 [0], given: 2854

Re: Remainder [#permalink]  16 Sep 2013, 23:49
Expert's post
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]  16 Dec 2013, 05:40
Very tricky. Nice question! As always, great explanation Bunuel!!
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Re: Remainder [#permalink]  26 Dec 2013, 00:07
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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Re: Remainder [#permalink]  26 Dec 2013, 02:19
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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]  10 May 2014, 12:16
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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Re: If j and k are positive integers such that k > j [#permalink]  11 May 2014, 05:14
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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]  08 Jun 2014, 11:58
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]  18 Sep 2014, 07:34
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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Re: If j and k are positive integers where k > j, what is the [#permalink]  18 Sep 2014, 07:41
Expert's post
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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Re: If j and k are positive integers where k > j, what is the   [#permalink] 18 Sep 2014, 07:41
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