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

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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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C
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If j and k are positive integers where k > j, what is the 25 Sep 2010, 04:55
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sachinrelan
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
Show more

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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ramgmat
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If j and k are positive integers where k > j, what is the 25 Sep 2010, 05:00
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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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Bunuel
sachinrelan
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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Thanks for the gr8 explanation !!
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Bunuel
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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.

Answer: C.
Show more

Hi Bunuel,

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

Consider the examples for the first statement given in my solution proving that this statement is not sufficient.
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Very tricky. Nice question! As always, great explanation Bunuel!!
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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.

Answer: C.
Show more

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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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!
Show more

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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Bunuel
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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

Merging similar topics. Please ask if anything remains unclear.
Show more
Hi Bunnel,

If 2) j<5, will the Answer be E?

Thank you
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Bunuel
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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

Merging similar topics. Please ask if anything remains unclear.
Hi Bunnel,

If 2) j<5, will the Answer be E?

Thank you
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Yes, that's correct.
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sachinrelan
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

Show 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
Show more


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

Answer C
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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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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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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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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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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.
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Prompt analysi
k and j are positive integers such that k>j

Superset
The answer will be a positive integer

Translation
In order to find the answer, we need:
1# exact value of x and y
2# any relation between x and y
3# some property of x and y

Statement analysis
St 1: k =jm +5 . we can say the 5 is the remainder only if j>5. since there is no such condition give the statement is INSUFFICIENT

St 2: j>5. Cannot be said anything about the remainder. INSUFFICIENT

St 1 & St 2: k = jm +5 and j>5. we can say that 5 is the remainder.ANSWER

Option C
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I did a much more brute way:

Statement 1:
\(k=mj+5\)

Consider the case of m=any integer, j=1. In this case, the remainder will always be 0.
Consider the case of m=any, j!=1. In this case, the remainder will not always be 0.

INS.

Statement 2:

Clearly INS.

Both:
We know that j>5.
Lets test a few cases:
if m=1, j=6 k=11, and k/j has R5
if m=1, j=7, k=12, k/j has R5
if m=2, j=6, k=17, 17/6 is R5.

So there is a clear pattern established - the remainder is constantly 5.

C is the correct answer
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If j and k are positive integers where k > j, what is the 26 Oct 2023, 00:03
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sachinrelan
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

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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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Such a simple thing but still so tricky!!

We routinely write divisor and dividend in the form Dividend = Quotient*Divisor + Remainder
But we know that the remainder must always be less than the divisor (discussed in the link below)

(1) There exists a positive integer m such that k = jm + 5.
k = jm + 5
seems to be in the format Dividend = Quotient*Divisor + Remainder so it may prompt us to think that the remainder is 5 but note that this is true only if the divisor 'j' is greater than 5.
Say if j = 1, we can write many numbers k as 8 = 3*1 + 5 or 12 = 7*1 + 5 etc. But here when k is divided by j, the remainder is actually 1.
Hence this is not sufficient alone.

(2) j > 5
No info on k. Not sufficient alone.

Both Together, we know that k = jm + 5 and j > 5 so then it makes sense that when we divide k by j, the remainder is 5.

Answer (C)

Check this video on Division and Remainders: https://youtu.be/A5abKfUBFSc
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If j and k are positive integers where k > j, what is the 29 Jan 2025, 02:05
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