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

Question

Find a nonzero integer Q

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

Nsentra · Answer

Is it A?

1. Q^Q=Q^3 so Q=3? How does prime root information change things?
2. Q^2 = 3^2. Q = +-3 NOT SUFF.

ivymba · Answer

Based on the question asked , looks like D to me.

cicerone · Answer

Statement 1: Q^Q=Q^3
 so Q could be-1, 1 and 3. But since it is given that Q is prime root of the above equation, it must be 3

So 1 is sufficient

Statement 2: Q^2 = 3^2
i.e Q=3 or Q=-3

So 2 is not sufficient 

So A

sujayb · Answer

It says Q is a non-zero integer, so could be -ve. Hence, I think it's D. - what say

cicerone · Answer

Fine I agree Q is a non-zero integer, and it is because of this From the second statment Q does not have a unique value.

It could be 3 or -3
So statment 2 is not sufficient

HEnce A

Matrix02 · Answer

I think it is A. Q is supposed to be a Prime root ...I don't think Prime numbers/root can be negative?

Rayn · Answer

I agree with A, what would be an example of a prime root anyway? :roll:

cicerone · Answer

Hey rayn, in the first statement we have an equation .
So it is going to have certain number of roots.
One of the roots must be prime...........

Matrix02 · Answer

OK - so I dug around to see if prime numbers can be negative and there are two answers to this question: basically in lower level math (high school etc... prime numbers cannot be negative but in highler level complex math they can be. I think GMAT assumes PRIME numbers not to be negative no?

asaf · Answer

Find a nonzero integer Q 

(1) Q is a prime root of Q^Q=Q^3 
(2) Q^2=3^2

1) Q=3 Sufficient.
2) Q = 3, -3. Can not determine which one. Hence Insufficient.

A.

anandsebastin · Answer

There seems to be a question out here:
Can negative numbers be considered prime numbers  in GMAT ?

mst · Answer

Manhattan GMAT defines prime numbers as: Prime number is an integer (greater than 1) with exactly 2 factors : 1 and itself.

I would think that negative numbers should not be considered as prime. They are referred to as the associates of the positive prime numbers.

Rayn · Answer

What is the value of the prime number?

1) 13<x<19
2) x^2/17 = 17

After I give you the OA, we'll decide whether negative primes are welcomed on the GMAT.

Fig · Answer

(D) for me. A prime number is always positive and superior to 1

londonluddite · Answer

I'd say D too (but i'm guessing its not right :-D

)

Fig · Answer

It has to be right

OG 11, page 108, paragraph 5 : A prime number is a positive integer that has exactly 2 different positive divisors, 1 and itself

Rayn · Answer

OA is A.

We must consider -17 as a possible prime. (But I guess they are mistaken, since OG clearly wants us to consider solely +'ve integers)

Source: McGrawHill Test Prep.

Fig · Answer

Yes... The most important is the OG view so the GMAT rules to know and apply

Rayn · Answer

Could someone who understands differential speeds look at my last post under Beginners Forum (Re-worked questions), Page 5 and explain the guys reasoning to me?

https://www.gmatclub.com/phpbb/viewtopic ... 0&start=80

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

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