Value of integer n

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ash4gmat: Senior | Next Rank: 100 Posts; Posts: 57; Joined: Thu Sep 17, 2015 2:57 am

by ash4gmat » Tue Apr 05, 2016 9:56 pm

Q 67.What is the value of integer n?
1) n(n+1) = 6
2) 2^2n = 16

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Source: Beat The GMAT — Data Sufficiency | Tue Apr 05, 2016 9:56 pm

MartyMurray: Legendary Member; Posts: 2135; Joined: Mon Feb 03, 2014 9:26 amFollowed by: 140 members; Location: https://martymurraycoaching.com/; Thanked: 955 times; GMAT Score:800

by MartyMurray » Wed Apr 06, 2016 1:24 am

What is the value of integer n?

Statement 1: n(n+1) = 6

n is an integer. So to assume that n = 2 and n + 1 = 3 is tempting, and will get you the wrong answer.

If we multiply out the left side and move the 6 over we get, nÂ² + n - 6 = 0

Given that -6 has to have one positive factor and one negative factor, the equation must have two roots, one positive and one negative. So there are two possible values of n.

If you want to go further and factor to be sure, you will get (n + 3)(n - 2) = 0

Insufficient.

Statement 2: 2Â²â�¿ = 16

16 = 2â�´ So n = 2

Sufficient.

The correct answer is B.

Marty Murray
Perfect Scoring Tutor With Over a Decade of Experience
MartyMurrayCoaching.com
Contact me at [email protected] for a free consultation.

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Wed Apr 06, 2016 9:16 am

Hi ash4gmat,

This DS question is built around a couple of math concepts; if you recognize those concepts, then you can actually avoid a lot of 'step-heavy' math and still get the correct answer.

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

1) N(N+1) = 6

Given that N is an integer, "N" and "N+1"are consecutive integers. Can you think of two consecutive integers that have a product of 6?

The obvious answer is 2 and 3, so the answer to the question would be 2.

HOWEVER... can you think of any OTHER consecutive integers that have a product of 6....?

There's also -3 and -2, so the answer to the question would be -3.
Fact 1 is INSUFFICIENT.

2) 2^(2N) = 16

The only "power of 2" that equals 16 is 4, since 2^4 = 16 (but 2^(-4) = 1/16, so there's no 'negative solution'). This means that 2N = 4, so N=2.
Fact 2 is SUFFICIENT

Final Answer: B

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

Contact Rich at [email protected]

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