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

Question

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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damybox · Answer

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

sobby · Answer

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.

BrentGMATPrepNow · Answer

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:  D

Cheers,
Brent

abhi4212 · Answer

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

Apeksha2101 · Answer

How are you taking 5k^2+5k  =====>  n+k= 5k^2+6k ? Shoudln;t it be 
k^2 = 5k + 5n ??

Bunuel · Answer

The condition "when n is divided by k², the quotient is 5 and the remainder is 5k" implies  n= 5k^2+5k .

The question asks to find the value of n + k. Add k to both sides of that equation to get:  n + k= 5k^2+6k .

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

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