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# If n is an integer, is the prime number y equal to 5 ?

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Math Expert
Joined: 02 Sep 2009
Posts: 43853
If n is an integer, is the prime number y equal to 5 ? [#permalink]

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19 Jan 2018, 10:01
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Question Stats:

69% (01:34) correct 31% (01:38) wrong based on 45 sessions

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If n is an integer, is the prime number y equal to 5 ?

(1) y = n^2 + 1
(2) y = n^3 - 3
[Reveal] Spoiler: OA

_________________
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Joined: 25 Feb 2013
Posts: 929
Location: India
GPA: 3.82
If n is an integer, is the prime number y equal to 5 ? [#permalink]

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19 Jan 2018, 19:20
Bunuel wrote:
If n is an integer, is the prime number y equal to 5 ?

(1) y = n^2 + 1
(2) y = n^3 - 3

Statement 1: if $$n=2$$ then $$y=5$$ but if $$n=1$$, then $$y=2$$. Insufficient

Statement 2: if $$n=2$$, then $$y=5$$ but if $$n=4$$, then $$y=61$$. Insufficient

Combining 1 & 2: we have $$n^2+1=n^3-3$$

$$=>n^3-n^2=4$$

$$=>n^2(n-1)=4 =>n^2(n-1)=2^2*1$$

therefore $$n=2$$, hence $$y=5$$. Sufficient

Option C
Math Expert
Joined: 02 Aug 2009
Posts: 5660
Re: If n is an integer, is the prime number y equal to 5 ? [#permalink]

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19 Jan 2018, 19:53
Bunuel wrote:
If n is an integer, is the prime number y equal to 5 ?

(1) y = n^2 + 1
(2) y = n^3 - 3
....

statements alone are clearly insuff..

(1) $$y = n^2 + 1$$
when n is 2, y is 5
n is 4, y is 17
n is 1, y is 2
insuff

(2) $$y = n^3 - 3$$
when n is 2, y is 5
n is 4, y is 61
insuff

combined..
$$n^2+1 = n^3 - 3........n^3-n^2=4$$
clearly n^3>n^2, so n has to be positive..
n>4 will make the difference much greater than 4. so try 1,2,3
$$n=1, n^3-n^2=0$$..
$$n=2, n^3-n^2=4$$..
$$n=3, n^3-n^2=23$$..
any number greater will further increase the difference
ans yes
sufficient

C
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Re: If n is an integer, is the prime number y equal to 5 ?   [#permalink] 19 Jan 2018, 19:53
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# If n is an integer, is the prime number y equal to 5 ?

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