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from i, q= 1 and 3 but q is prime, so q=3. so suff. from ii, q=-3 or 3. so insuff.

This would be wrong, unless the definition is clear.

What is the meaning of "Q is a prime root of Q^Q=Q^3 "

There can be two meaning

1) Q is prime (which is used by MA)
2) Q is a "prime root", which imply square root (2 prime), cube root (3 prime), fifth root(5 prime) but NOT fourth root (4 not prime), not sixth root (6 not prime)

If second one is true then A is not sufficient.

Assuming the (2) to be true, then both 1 and 3 qualify. Since 1 is a "prime root" of itself.

Note that the condition does not say that "Q is a prime root only of "

from i, q= 1 and 3 but q is prime, so q=3. so suff. from ii, q=-3 or 3. so insuff.

This would be wrong, unless the definition is clear.

What is the meaning of "Q is a prime root of Q^Q=Q^3 " There can be two meaning 1) Q is prime (which is used by MA) 2) Q is a "prime root", which imply square root (2 prime), cube root (3 prime), fifth root(5 prime) but NOT fourth root (4 not prime), not sixth root (6 not prime) If second one is true then A is not sufficient. Assuming the (2) to be true, then both 1 and 3 qualify. Since 1 is a "prime root" of itself. Note that the condition does not say that "Q is a prime root only of "Ketan

I think u r wright. i was unclear and confused with prime root. but the safe side is that answer is A.

This is of the type a^b = 1 which has the following solutions a) a = 1, b = anything b) a = anything, b = 0 c) a = -1 and b = even

Yes, I suppose you are right. This can only be solved by treating it as a special case. If we have Q^(Q-3) = 2, then we'll have to go through the steps like what I had before. Just wonder if I would be missing any values by those steps ... (I certainly missed one when the equation is Q^(Q-3) = 1. )