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# Find a nonzero integer Q (1) Q is a prime root of Q^Q=Q^3

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Find a nonzero integer Q (1) Q is a prime root of Q^Q=Q^3 [#permalink]

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10 Jun 2003, 00:07
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Find a nonzero integer Q

(1) Q is a prime root of Q^Q=Q^3
(2) Q^2=3^2

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SVP
Joined: 03 Feb 2003
Posts: 1603

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12 Jun 2003, 00:28
(1) Q=1, -1, and 3; of which only 3 is prime. Thus, OK
(2) Q= 3 and -3, not enough

Thus, A.

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Intern
Joined: 04 Feb 2008
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21 Feb 2008, 12:37
In stolyar's answer. isn't -3 inadmissible in (ii). Resultantly, only 3 is the prime root in (ii).
so shouldn't the answer be D?

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Senior Manager
Joined: 15 Aug 2007
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Schools: Chicago Booth

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21 Feb 2008, 18:02
kanyshkae wrote:
In stolyar's answer. isn't -3 inadmissible in (ii). Resultantly, only 3 is the prime root in (ii).
so shouldn't the answer be D?

Keep in mind that -3 also an integer, negative though.

A is my pick

Q^Q=Q^3
Q^2(Q-1)=0
Q = 0 or 1
Since it's given that Q not= 0, Q=1

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Director
Joined: 30 Jun 2007
Posts: 781

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22 Feb 2008, 00:44

Even roots can have +/- numbers and second condition is not sufficient

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Senior Manager
Joined: 19 Nov 2007
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22 Feb 2008, 20:33
stolyar wrote:
(1) Q=1, -1, and 3; of which only 3 is prime. Thus, OK
(2) Q= 3 and -3, not enough

Thus, A.

how come 3 is a root of the equation Q^2=Q^3 ??
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Kudos [?]: 218 [0], given: 4

Senior Manager
Joined: 02 Aug 2007
Posts: 346

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Location: Greater New York City area
Schools: Tuck, Ross (R1), Duke, Tepper, ISB (R2), Kenan Flagler (R2)

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22 Feb 2008, 21:02
stolyar wrote:
Find a nonzero integer Q

(1) Q is a prime root of Q^Q=Q^3
(2) Q^2=3^2

I am not able to interpret the statement. "Q is a prime root of Q^Q = Q^3." What does it exactly mean ?

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Director
Joined: 14 Jan 2007
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23 Feb 2008, 06:40
vscid wrote:
stolyar wrote:
(1) Q=1, -1, and 3; of which only 3 is prime. Thus, OK
(2) Q= 3 and -3, not enough

Thus, A.

how come 3 is a root of the equation Q^2=Q^3 ??

The red text should be Q^Q = Q^3
Obviously, 3 is one of the roots of above equation.

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Director
Joined: 14 Jan 2007
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23 Feb 2008, 06:45
sreehari wrote:
kanyshkae wrote:
In stolyar's answer. isn't -3 inadmissible in (ii). Resultantly, only 3 is the prime root in (ii).
so shouldn't the answer be D?

Keep in mind that -3 also an integer, negative though.

A is my pick

Q^Q=Q^3
Q^2(Q-1)=0Q = 0 or 1
Since it's given that Q not= 0, Q=1

The equation in large text is wrong.
It should be Q^Q - Q^3 = 0
-1, 1 and 3 are the roots of the equation but only 3 is prime.
Stoylar's solution is perfect.

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Senior Manager
Joined: 19 Nov 2007
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23 Feb 2008, 09:03
vshaunak@gmail.com wrote:
sreehari wrote:
kanyshkae wrote:
In stolyar's answer. isn't -3 inadmissible in (ii). Resultantly, only 3 is the prime root in (ii).
so shouldn't the answer be D?

Keep in mind that -3 also an integer, negative though.

A is my pick

Q^Q=Q^3
Q^2(Q-1)=0Q = 0 or 1
Since it's given that Q not= 0, Q=1

The equation in large text is wrong.
It should be Q^Q - Q^3 = 0
-1, 1 and 3 are the roots of the equation but only 3 is prime.
Stoylar's solution is perfect.

yup. got it now!
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Re: DS: POWERS   [#permalink] 23 Feb 2008, 09:03
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