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

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

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New post 19 Jan 2018, 10:01
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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 ? [#permalink]

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New post 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

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

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New post 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
_________________

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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