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

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Joined: 12 Sep 2015
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n and k are positive integers, and when n is divided by k²  [#permalink]

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01 Nov 2016, 11:30
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Question Stats:

65% (01:50) correct 35% (01:47) wrong based on 243 sessions

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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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01 Nov 2016, 12:37
2
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

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

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02 Nov 2016, 08:38
1
[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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Joined: 12 Sep 2015
Posts: 4003
Re: n and k are positive integers, and when n is divided by k²  [#permalink]

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02 Nov 2016, 10:10
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Top Contributor
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

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

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02 Nov 2016, 12:12
1
[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

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

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19 Jan 2019, 06:02
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Re: n and k are positive integers, and when n is divided by k²   [#permalink] 19 Jan 2019, 06:02
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