Hi AbeNeedsAnswers,

We're told that N is an integer. We are asked for the value of N.

1) (N)(N+1) = 6

Here, we can do a bit of algebra to create a Quadratic...

N^2 + N = 6
N^2 + N - 6 = 0
(N+3)(N-2) = 0
N = -3 or +2
With two different solutions...
Fact 1 is INSUFFICIENT

2) 2^(2N) = 16

The ONLY exponent that will fit here is 4.... 2^4 = 16.
2N = 4
N =2
Fact 2 is SUFFICIENT

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

AbeNeedsAnswers wrote:What is the value of integer n?

(1) n(n+1) = 6
(2) 2^(2n) = 16

We need to determine the value of integer n.

Statement One Alone:

n(n+1) = 6

Let's solve the equation:

n(n+1) = 6

n^2 + n = 6

n^2 + n - 6 = 0

(n+3)(n-2) = 0

n = -3 or n = 2

Since we have two values for n, statement one alone is not sufficient.

Statement Two Alone:

2^(2n) = 16

We express 16 as a power of 2, and then we equate the exponents; we can then determine a value for n.

2^(2n) = 2^4

2n = 4

n = 2

Statement two is sufficient to answer the question.

Answer: B

AbeNeedsAnswers wrote:What is the value of integer n?

(1) n(n+1) = 6
(2) 2^(2n) = 16

B

Question: What is the value of integer n?

Let's take each statement one by one.

(1) n(n+1) = 6

n*(n+1) means that it is a product of two consecutive integers. One can quickly think of 2 and 3. So, n = 2. However, you must not consider that the two consecutive integers cannot be negatives. So, the two consecutive negative integers, multiplying to 6, can be -3 and - 2. So, n can be -3 also.

So, n is either 2 or -3. No unique value. Insufficient.

(2) 2^(2n) = 16

=> 2^(2n) = 2^4; note that 16 ≠ 2^(-4)

=> 2n = 4 => n = 2. A unique value. Sufficient.

The correct answer: B

Hope this helps!

-Jay
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