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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] New post 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

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

Thanks
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Re: Remainder [#permalink] New post 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.

Answer: C.
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Re: Remainder [#permalink] New post 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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Re: Remainder [#permalink] New post 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.

Answer: C.



Thanks for the gr8 explanation !!
Re: Remainder   [#permalink] 25 Sep 2010, 05:09
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