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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

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.

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.

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.

Hi Bunuel,

Could you please elaborate as to why A is not the right answer. Would really appreciate it. Thanks

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.

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. _________________

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.

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.

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.

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.

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

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. _________________

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