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# N is an integer such that N > 1.

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Joined: 18 Apr 2015
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N is an integer such that N > 1. [#permalink]  02 Dec 2018, 05:33
Expert's post
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Question Stats:

99% (00:19) correct 0% (00:00) wrong based on 7 sessions
N is an integer such that $$N > 1$$.

 Quantity A Quantity B $$(N+1)^2 -1$$ $$N^2$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given
[Reveal] Spoiler: OA

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Director
Joined: 20 Apr 2016
Posts: 762
Followers: 6

Kudos [?]: 522 [2] , given: 94

Re: N is an integer such that N > 1. [#permalink]  04 Dec 2018, 06:01
2
KUDOS
Carcass wrote:
N is an integer such that $$N > 1$$.

 Quantity A Quantity B $$(N+1)^2 -1$$ $$N^2$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given

Explanation::

Qty A = $$(N+1)^2 -1 = N^2 + 2N + 1 - 1 = N^2 + 2N$$

Therefore
$$N^2 + 2N > N^2$$

Hence Option A
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Kudos [?]: 1159 [1] , given: 7

Re: N is an integer such that N > 1. [#permalink]  04 Dec 2018, 10:01
1
KUDOS
Expert's post
Carcass wrote:
N is an integer such that $$N > 1$$.

 Quantity A Quantity B $$(N+1)^2 -1$$ $$N^2$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given

We can solve this question using matching operations

Given:
Quantity A: (N + 1)²
Quantity B: N²

Expand and simplify Quantity A to get:
Quantity A: N² + 2N + 1
Quantity B: N²

Subtract N² from both quantities to get:
Quantity A: 2N + 1
Quantity B: 0

Subtract 1 from both quantities to get:
Quantity A: 2N
Quantity B: -1

Since we're told that N > 1, we know that 2N must be POSITIVE.
So, we have:
Quantity A: some POSITIVE number
Quantity B: -1

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Re: N is an integer such that N > 1.   [#permalink] 04 Dec 2018, 10:01
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