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 < DFor 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 = 5case b: j = 2: Since k = 4j, this tells us that k = 8, which means
j + k = 2 + 8 = 10Since 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 = 5Since 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