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

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01 Nov 2016, 13:39

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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

Last edited by gracie on 01 Nov 2016, 13:53, edited 3 times in total.

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

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

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03 Nov 2016, 00:53

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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

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
_________________

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

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12 Apr 2017, 19:58

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

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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11 Aug 2017, 08:18

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?
_________________

Desperately need 'KUDOS' !!

gmatclubot

Re: n and k are positive integers. When n is divided by 23, the quotient i
[#permalink]
11 Aug 2017, 08:18