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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.

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]

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04 Mar 2017, 01:01

1

This post received KUDOS

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. The correct answer is C.
_________________

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.

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.
_________________

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

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30 May 2016, 03:33

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