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n and k are positive integers, and when n is divided by k²

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n and k are positive integers, and when n is divided by k² [#permalink]

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n and k are positive integers, and when n is divided by k², the quotient is 5 and the remainder is 5k, What is the value of n + k?

(1) n = 550
(2) k = 10

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Re: n and k are positive integers, and when n is divided by k² [#permalink]

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GMATPrepNow wrote:
n and k are positive integers, and when n is divided by k², the quotient is 5 and the remainder is 5k, What is the value of n + k?

(1) n = 550
(2) k = 10

*Kudos for all correct solutions



\(n= 5k^2+5k\) =====> \(n+k= 5k^2+6k\) the real question is: what is \(k\)?

(1) n = 550 ====> \(5k^2+5k=550\)
solving the quadratic equation we find that \(k=-11\) or \(k=10\)
but n and k are positive integers ===> k=10 SUFFICIENT

(2) k = 10 answers directly the question SUFFICIENT

answer D
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Re: n and k are positive integers, and when n is divided by k² [#permalink]

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[quote="GMATPrepNow"]n and k are positive integers, and when n is divided by k², the quotient is 5 and the remainder is 5k, What is the value of n + k?

(1) n = 550
(2) k = 10

*Kudos for all correct solutions

D.

we can form equation -5k^2 + 5K = n
1.if n is provided we can solve for k = -11 or 10
we can neglect -11 as n and k are +ve integer
so suff.

2.
k is given , we can plugin and get n.
so suff.
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Re: n and k are positive integers, and when n is divided by k² [#permalink]

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GMATPrepNow wrote:
n and k are positive integers, and when n is divided by k², the quotient is 5 and the remainder is 5k. What is the value of n + k?

(1) n = 550
(2) k = 10


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

Given: when n is divided by k², the quotient is 5 and the remainder is 5k
There's a nice rule that say, "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
Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3
So, we can take the given information and write: n = 5k² + 5k

Statement 1: n = 550
Since we already know that n = 5k² + 5k, we can write: 550 = 5k² + 5k
Write as: 5k² + 5k - 550 = 0
Factor to get: 5(k² + k - 110) = 0
Factor again: 5(k + 11)(k - 10) = 0
This means that k = -11 or k = 10
We're told that k is POSITIVE, so it must be the case that k = 10
We can now conclude that n + k = 550 + 10 = 560
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: k = 10
Since we already know that n = 5k² + 5k, we can write: n = 5(10)² + 5(10) = 500 + 50 = 550
We can now conclude that n + k = 550 + 10 = 560
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer:
[Reveal] Spoiler:
D


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Brent
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Re: n and k are positive integers, and when n is divided by k² [#permalink]

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[quote="GMATPrepNow"]n and k are positive integers, and when n is divided by k², the quotient is 5 and the remainder is 5k, What is the value of n + k?

(1) n = 550
(2) k = 10




1. Put all the values in equation D=dQ+R, (D is dividend, d is divisor, Q is quotient & R is remainder)Where, D=n, d=K^2, Q=5 & R=5K
We will get the equation n=5K^2+5K
Now put n=110, by solving quadratic equation we will get K=10,-11
Since, n & K are +ve integers so K=10
SUFFICIENT

2. Put K=10 in above equation and we will directly get n=550
SUFFICIENT


ANSWER= D
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Re: n and k are positive integers, and when n is divided by k² [#permalink]

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Re: n and k are positive integers, and when n is divided by k²   [#permalink] 17 Dec 2017, 06:48
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