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

[BTGModeratorVI]

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

Answer: B
Source: GMAT Prep Now

[Brent@GMATPrepNow]

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

Answer: B
Source: GMAT Prep Now

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

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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: B

Cheers,
Brent

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