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OG What is the value of integer n

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Source: — Data Sufficiency |

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by [email protected] » Mon Aug 21, 2017 1:32 pm
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

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by Scott@TargetTestPrep » Sun Nov 04, 2018 5:06 pm
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

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by Jay@ManhattanReview » Sun Nov 04, 2018 11:25 pm
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!

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by fskilnik@GMATH » Mon Nov 05, 2018 3:43 am
AbeNeedsAnswers wrote:What is the value of integer n?

(1) n(n+1) = 6
(2) 2^(2n) = 16
$$? = n\,\,\,\,\left( {n\,\,{\mathop{\rm int}} } \right)$$
$$\left( 1 \right)\,\,\,n\left( {n + 1} \right)\, = 6\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\left\{ \matrix{
\,n = 2\,\,\,\,\,\,\,\left[ {\,2 \cdot 3 = 6\,} \right] \hfill \cr
\,\,\,{\rm{or}} \hfill \cr
n = - 3\,\,\,\,\,\left[ {\,\left( { - 3} \right)\left( { - 2} \right) = 6\,} \right] \hfill \cr} \right.\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{INSUFF}}.$$
$$\left( 2 \right)\,\,{2^{2n}} = 16\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,2n\,\,{\rm{unique}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,n\,\,{\rm{unique}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{SUFF}}.$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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