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n and k are positive integers. When n is divided by 23, the quotient i

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n and k are positive integers. When n is divided by 23, the quotient i [#permalink]

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n and k are positive integers. When n is divided by 23, the quotient is 2k and the remainder is j. What is the value of j + k?

(1) When n is divided by 15, the quotient is 3k and the remainder is 5j
(2) When n is divided by 9, the quotient is 5k and the remainder is 5j

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n and k are positive integers. When n is divided by 23, the quotient i [#permalink]

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GMATPrepNow wrote:
n and k are positive integers. When n is divided by 23, the quotient is 2k and the remainder is j. What is the value of j + k?

(1) When n is divided by 15, the quotient is 3k and the remainder is 5j
(2) When n is divided by 9, the quotient is 5k and the remainder is 5j



There are two important rules regarding remainders:

Rule #1: "If N divided by D equals Q with remainder R, then N = DQ + R"
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2

Rule #2: When positive integer N is divided by positive integer D, the remainder R is such that 0 < R < D
For example, if we divide some positive integer by 7, the remainder will be 6, 5, 4, 3, 2, 1, or 0

---------------------------

Target question: What is the value of j + k?

Given: When n is divided by 23, the quotient is 2k and the remainder is j
From Rule #1, we can write: n = (23)(2k) + j
Simplify: n = 46k + j

Statement 1: When n is divided by 15, the quotient is 3k and the remainder is 5j
From rule #1, we can write: n = (15)(3k) + 5j
Simplify: n = 45k + 5j
Since we also know that n = 46k + j, we can write: 46k + j = 45k + 5j
Simplify to get: k = 4j

NOTE: From rule #2, we know that the remainder must be LESS THAN 15
Since we're told that j is a positive integer, this means 5j can equal either 5 (if j = 1) or 10 (if j = 2).
This means there are two possible cases:
case a: j = 1: Since k = 4j, this tells us that k = 4, which means j + k = 1 + 4 = 5
case b: j = 2: Since k = 4j, this tells us that k = 8, which means j + k = 2 + 8 = 10
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: When n is divided by 9, the quotient is 5k and the remainder is 5j
From rule #1, we can write: n = (9)(5k) + 5j
Simplify: n = 45k + 5j
Since we also know that n = 46k + j, we can write: 46k + j = 45k + 5j
Simplify to get: k = 4j

NOTE: From rule #2, we know that the remainder must be LESS THAN 9
Since we're told that j is a positive integer, this means 5j MUST equal either 5 (when j = 1)
So, we KNOW that j = 1
We also know that k = 4j, which means k = 4
So, we can be CERTAIN that j + k = 1 + 4 = 5
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer:

Cheers,
Brent
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Originally posted by GMATPrepNow on 02 Nov 2016, 08:22.
Last edited by GMATPrepNow on 03 May 2018, 07:22, edited 1 time in total.
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n and k are positive integers. When n is divided by 23, the quotient i [#permalink]

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New post Updated on: 01 Nov 2016, 14:53
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n and k are positive integers. When n is divided by 23, the quotient is 2k and the remainder is j. What is the value of j + k?

(1) When n is divided by 15, the quotient is 3k and the remainder is 5j
(2) When n is divided by 9, the quotient is 5k and the remainder is 5j

n/23=2k+j
equation 1: n=46k+j
n/15=3k+5j
equation 2: n=45k+5j
subtracting e1 from e2,
k=4j
insufficient
n/9=5k+5j
remainder 5j must be less than divisor 9
if j is less than 2, then j=1
k=4j=4
j+k=5
sufficient

Originally posted by gracie on 01 Nov 2016, 14:39.
Last edited by gracie on 01 Nov 2016, 14:53, edited 3 times in total.
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Re: n and k are positive integers. When n is divided by 23, the quotient i [#permalink]

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New post 01 Nov 2016, 14:42
1
n=46k+j

j+k=n-45k??

Statement 1:

n=45k+5j

Substitute in question stem

k=4j

Insufficient

Statement 2:

n=45k+5j

Again gives k=4j

Insufficient

Statement 1&2:

Together also insufficient

E


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Re: n and k are positive integers. When n is divided by 23, the quotient i [#permalink]

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New post 01 Nov 2016, 14:54
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acegmat123 wrote:
n=46k+j

j+k=n-45k??

Statement 1:

n=45k+5j

Substitute in question stem

k=4j

Insufficient

Statement 2:

n=45k+5j

Again gives k=4j

Insufficient

Statement 1&2:

Together also insufficient

E


Sent from my iPhone using GMAT Club Forum mobile app


Sorry, but the answer isn't E.
You're missing an important feature related to remainders.
Hint: watch the video :-D
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Re: n and k are positive integers. When n is divided by 23, the quotient i [#permalink]

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New post 01 Nov 2016, 14:58
1
GMATPrepNow wrote:
acegmat123 wrote:
n=46k+j

j+k=n-45k??

Statement 1:

n=45k+5j

Substitute in question stem

k=4j

Insufficient

Statement 2:

n=45k+5j

Again gives k=4j

Insufficient

Statement 1&2:

Together also insufficient

E


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Sorry, but the answer isn't E.
You're missing an important feature related to remainders.
Hint: watch the video :-D


Yeah. Reminder should be less than Divisor.

Answer should be B.


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Re: n and k are positive integers. When n is divided by 23, the quotient i [#permalink]

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New post 01 Nov 2016, 15:50
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acegmat123 wrote:

Yeah. Reminder should be less than Divisor.

Answer should be B.


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Exactly!
Nice work!

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n and k are positive integers. When n is divided by 23, the quotient i [#permalink]

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New post 03 Nov 2016, 01:53
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GMATPrepNow wrote:
GMATPrepNow wrote:
n and k are positive integers. When n is divided by 23, the quotient is 2k and the remainder is j. What is the value of j + k?

(1) When n is divided by 15, the quotient is 3k and the remainder is 5j
(2) When n is divided by 9, the quotient is 5k and the remainder is 5j



There are two important rules regarding remainders:

Rule #1: "If N divided by D equals Q with remainder R, then N = DQ + R"
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2

Rule #2: When positive integer N is divided by positive integer D, the remainder R is such that 0 < R < D
For example, if we divide some positive integer by 7, the remainder will be 6, 5, 4, 3, 2, 1, or 0

---------------------------

Target question: What is the value of j + k?

Given: When n is divided by 23, the quotient is 2k and the remainder is j
From Rule #1, we can write: n = (23)(2k) + j
Simplify: n = 46k + j

Statement 1: When n is divided by 15, the quotient is 3k and the remainder is 5j
From rule #1, we can write: n = (15)(3k) + 5j
Simplify: n = 45k + 5j
Since we also know that n = 46k + j, we can write: 46k + j = 45k + 5j
Simplify to get: k = 4j

NOTE: From rule #2, we know that the remainder must be LESS THAN 15
Since we're told that j is a positive integer, this means 5j can equal either 5 (if j = 1) or 10 (if j = 2).
This means there are two possible cases:
case a: j = 1: Since k = 4j, this tells us that k = 4, which means j + k = 1 + 4 = 5
case b: j = 2: Since k = 4j, this tells us that k = 8, which means j + k = 2 + 8 = 10
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: When n is divided by 9, the quotient is 5k and the remainder is 5j
From rule #1, we can write: n = (9)(35) + 5j
Simplify: n = 45k + 5j
Since we also know that n = 46k + j, we can write: 46k + j = 45k + 5j
Simplify to get: k = 4j

NOTE: From rule #2, we know that the remainder must be LESS THAN 9
Since we're told that j is a positive integer, this means 5j MUST equal either 5 (when j = 1)
So, we KNOW that j = 1
We also know that k = 4j, which means k = 4
So, we can be CERTAIN that j + k = 1 + 4 = 5
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer:

Cheers,
Brent


Such an annoying question. The moment you realise you did all the hard part but forgot one simple step of 'application of concepts'. Alas! But should agree that it got me wrong footed :shock: :oops:
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Re: n and k are positive integers. When n is divided by 23, the quotient i [#permalink]

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New post 12 Apr 2017, 20:58
GMATPrepNow wrote:
GMATPrepNow wrote:
n and k are positive integers. When n is divided by 23, the quotient is 2k and the remainder is j. What is the value of j + k?

(1) When n is divided by 15, the quotient is 3k and the remainder is 5j
(2) When n is divided by 9, the quotient is 5k and the remainder is 5j



There are two important rules regarding remainders:

Rule #1: "If N divided by D equals Q with remainder R, then N = DQ + R"
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2

Rule #2: When positive integer N is divided by positive integer D, the remainder R is such that 0 < R < D
For example, if we divide some positive integer by 7, the remainder will be 6, 5, 4, 3, 2, 1, or 0

---------------------------

Target question: What is the value of j + k?

Given: When n is divided by 23, the quotient is 2k and the remainder is j
From Rule #1, we can write: n = (23)(2k) + j
Simplify: n = 46k + j

Statement 1: When n is divided by 15, the quotient is 3k and the remainder is 5j
From rule #1, we can write: n = (15)(3k) + 5j
Simplify: n = 45k + 5j
Since we also know that n = 46k + j, we can write: 46k + j = 45k + 5j
Simplify to get: k = 4j

NOTE: From rule #2, we know that the remainder must be LESS THAN 15
Since we're told that j is a positive integer, this means 5j can equal either 5 (if j = 1) or 10 (if j = 2).
This means there are two possible cases:
case a: j = 1: Since k = 4j, this tells us that k = 4, which means j + k = 1 + 4 = 5
case b: j = 2: Since k = 4j, this tells us that k = 8, which means j + k = 2 + 8 = 10
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: When n is divided by 9, the quotient is 5k and the remainder is 5j
From rule #1, we can write: n = (9)(35) + 5j
Simplify: n = 45k + 5j
Since we also know that n = 46k + j, we can write: 46k + j = 45k + 5j
Simplify to get: k = 4j

NOTE: From rule #2, we know that the remainder must be LESS THAN 9
Since we're told that j is a positive integer, this means 5j MUST equal either 5 (when j = 1)
So, we KNOW that j = 1
We also know that k = 4j, which means k = 4
So, we can be CERTAIN that j + k = 1 + 4 = 5
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer:

Cheers,
Brent


Hi bro!

I think that you are missing the case when remainder = 0 (divisible)!

both statement 1 and 2 said that the remainder is 5j ---> we can not infer that 5j <> 0.
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Re: n and k are positive integers. When n is divided by 23, the quotient i [#permalink]

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leanhdung wrote:
Hi bro!

I think that you are missing the case when remainder = 0 (divisible)!

both statement 1 and 2 said that the remainder is 5j ---> we can not infer that 5j <> 0.


5j may or may not equal zero.
However, it doesn't matter, because the target question asks us to find the value of j+k

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Re: n and k are positive integers. When n is divided by 23, the quotient i [#permalink]

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New post 13 Apr 2017, 06:41
But if it's 0 it changes the answer ? I'm not following

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Re: n and k are positive integers. When n is divided by 23, the quotient i [#permalink]

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gmathopeful19 wrote:
But if it's 0 it changes the answer ? I'm not following

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Can you give me an example please.

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Re: n and k are positive integers. When n is divided by 23, the quotient i [#permalink]

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New post 13 Apr 2017, 07:13
Oops nvmd I misread my work


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Re: n and k are positive integers. When n is divided by 23, the quotient i [#permalink]

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New post 13 Apr 2017, 07:14
GMATPrepNow wrote:
gmathopeful19 wrote:
But if it's 0 it changes the answer ? I'm not following

Posted from my mobile device


Can you give me an example please.

Cheers,
Brent

Let me give you an example!

From the stem, we have n = 23*2k +j = 46k+j

From statement 2, we have n = 45k +5j

---> 46k+j = 45k +5j ---> k = 4j

5j < 9 --> j can be 0 or 1.

IF j = 0 ---> k = 0 --- j+k = 0.

IF j = 1 ---> k = 4 --- j+k = 5.

Hence, insufficient!
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Re: n and k are positive integers. When n is divided by 23, the quotient i [#permalink]

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New post 13 Apr 2017, 07:24
So that's what I thought initially but that would mean that n is 0 and the problem states n is a positive integer

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Re: n and k are positive integers. When n is divided by 23, the quotient i [#permalink]

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leanhdung wrote:
GMATPrepNow wrote:
gmathopeful19 wrote:
But if it's 0 it changes the answer ? I'm not following

Posted from my mobile device


Can you give me an example please.

Cheers,
Brent

Let me give you an example!

From the stem, we have n = 23*2k +j = 46k+j

From statement 2, we have n = 45k +5j

---> 46k+j = 45k +5j ---> k = 4j

5j < 9 --> j can be 0 or 1.

IF j = 0 ---> k = 0 --- j+k = 0.

IF j = 1 ---> k = 4 --- j+k = 5.

Hence, insufficient!


The question states that k is a positive integer, and 0 is not positive.

Cheers,
Brent
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n and k are positive integers. When n is divided by 23, the quotient i [#permalink]

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New post 09 Aug 2017, 23:46
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Given quotient when divided by 23 is 2k and the remainder is j

We will have values 1,2,3,4 etc for k and find out.

Statement 1: We see at k=4, the numbers can range from 184 to 194. Remainder j and 5j means, the number is 185 and j=1 . But, when k =8, the numbers range from 368 to 374. Remainder j and 5j means the number is 370 and j =2. So info not sufficient to determine j and k exactly as there are 2 possible values of j and k.

Statement 2: when k=4, the numbers can range from 184 to 189. Remainder j and 5j means the number is 185.

In the second case we will have only one range of numbers that accommodate both j and 5j. Hence statement 2 is sufficient.

So what is tested is one's understanding that the remainder cannot be greater than 9 in the second case i.e., j being 2 which was possible in the case of 15.
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Re: n and k are positive integers. When n is divided by 23, the quotient i [#permalink]

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New post 11 Aug 2017, 09:18
gracie wrote:
n and k are positive integers. When n is divided by 23, the quotient is 2k and the remainder is j. What is the value of j + k?

(1) When n is divided by 15, the quotient is 3k and the remainder is 5j
(2) When n is divided by 9, the quotient is 5k and the remainder is 5j

n/23=2k+j
equation 1: n=46k+j
n/15=3k+5j
equation 2: n=45k+5j
subtracting e1 from e2,
k=4j
insufficient
n/9=5k+5j
remainder 5j must be less than divisor 9
if j is less than 2, then j=1
k=4j=4
j+k=5
sufficient


And where do you get the highlighted part from? You get it from statement 1 !! So it should be C, right? :)
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Re: n and k are positive integers. When n is divided by 23, the quotient i [#permalink]

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New post 03 May 2018, 07:24
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rekhabishop wrote:
gracie wrote:
n and k are positive integers. When n is divided by 23, the quotient is 2k and the remainder is j. What is the value of j + k?

(1) When n is divided by 15, the quotient is 3k and the remainder is 5j
(2) When n is divided by 9, the quotient is 5k and the remainder is 5j

n/23=2k+j
equation 1: n=46k+j
n/15=3k+5j
equation 2: n=45k+5j
subtracting e1 from e2,
k=4j
insufficient
n/9=5k+5j
remainder 5j must be less than divisor 9
if j is less than 2, then j=1
k=4j=4
j+k=5
sufficient


And where do you get the highlighted part from? You get it from statement 1 !! So it should be C, right? :)


We don't need statement 1 to conclude that k = 4j
Here's why:

Given: When n is divided by 23, the quotient is 2k and the remainder is j
We can write: n = (23)(2k) + j
Simplify: n = 46k + j

Statement 2: When n is divided by 9, the quotient is 5k and the remainder is 5j
We can write: n = (9)(5k) + 5j
Simplify: n = 45k + 5j
Since we also know that n = 46k + j, we can write: 46k + j = 45k + 5j
Simplify to get: k = 4j

Does that help?

Cheers,
Brent
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Re: n and k are positive integers. When n is divided by 23, the quotient i   [#permalink] 03 May 2018, 07:24
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