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Value of integer

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by Sak32 » Mon Nov 18, 2013 7:53 am
What is the value of integer n?

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

What is baffling me is that in 2) the answer should be Not Sufficient because logically it could be either 2 or -2. Why didnt we consider the -2 as well?? Both powers yield 16 since they are even. The answer was deemed sufficient with 2 only.

Its an OG question.
Last edited by Sak32 on Mon Nov 18, 2013 8:08 am, edited 1 time in total.
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Mon Nov 18, 2013 8:03 am
Sak32 wrote:What is the value of integer n?

1) n(n+1) = 6
2) 2^(2n) = 16
NOTE: When posting questions, please use the spoiler function to hide the correct answer. This will allow others to attempt the question without seeing the final answer. Please edit your post accordingly.


Target question: What is the value of integer n?

Statement 1: n(n+1) = 6
Expand to get: n² + n = 6
Set equal to zero: n² + n - 6 = 0
Factor: (n + 3)(n - 2) = 0
So, n = -3 or n = 2
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 2^(2n) = 16
2^(2n) = 16
Rewrite 16 as 2^4 to get: 2^(2n) = 2^4
So, we can conclude that (2n) = 4, in which case n must equal 2
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent
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by Brent@GMATPrepNow » Mon Nov 18, 2013 8:12 am
Sak32 wrote: What is baffling me is that in 2) the answer should be Not Sufficient because logically it could be either 2 or -2. Why didnt we consider the -2 as well?? Both powers yield 16 since they are even. The answer was deemed sufficient with 2 only.
Let's try n = 2 and n = -2

n = 2: 2^(2n) = 2^(4) = 16 PERFECT
n = -2: 2^(2n) = 2^(-4) = 1/16 nope

I believe that you're thinking of a different rule that refers to situations in which the BASE (not the exponent) is negative.

So for example, 4^2 = 16 and (-4)^2 = 16

Cheers,
Brent
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by Sak32 » Mon Nov 18, 2013 8:13 am
Thanxx
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by Mathsbuddy » Fri Nov 22, 2013 9:22 am
16 = 2^4
So 2n = 4 and n = 2

Check with 1) 2(2+1) = 6 OK

Answer: n=2

If n = -2, them 2^(2 * -2) = 2^-4 = 1/16 NOT RIGHT

Statement 1 ALONE: n^2 + n - 6 = (n + 3)(n - 2) = 0
so n = 2, -3

Answer: n=2
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