value of n

[alex.gellatly]

What is the value of the integer n?

1. n(n+2) = 15
2. (n+2)^n = 125

Thanks

[Anurag@Gurome]

What is the value of the integer n?

1. n(n+2) = 15
2. (n+2)^n = 125

Statement 1: n(n + 2) = 15
--> (n² + 2n - 15) = 0
--> (n - 3)(n + 5) = 0

Hence, n = 3 or n = -5

Not sufficient

Statement 2: (n + 2)^n = 125
Now, n (n + 2) both are integers.
And we can write 125 as an integer raised to the power of integer in only one way, 5^3.
Hence, n = 3.

Sufficient

The correct answer is B.

[tutorphd]

1) by plugging in, one of the roots is n = 3 because 3 x 5 = 15. Expanding the equation to n^2 + 2n -15=0 shows the other root has to be n=-5 (the product of the roots had to be -15).
Not sufficient.

2) (n+2)^n = 125 = 5^3 so n=3
Sufficient.