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

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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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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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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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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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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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16 Sep 2013, 23:49
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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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16 Dec 2013, 05:40
Very tricky. Nice question! As always, great explanation Bunuel!!
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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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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]

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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]

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11 May 2014, 05:14
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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, 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]

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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]

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18 Sep 2014, 07:41
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, 03:03
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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