Vincen wrote:Is m^2n + mn^2 = 0 ?
(1) m + n = 1
(2) mn = 1
The OA is B.
I don't have this question clear. Why is the statement (2) sufficient? Experts, may you clarify this for me?
m^2n + mn^2 = 0 => mn(m + n) = 0
If either m = 0, or n = 0 or (m + n) = 0, the answer is Yes, else no.
(1) m + n = 1
Case 1: If m = 0 and n = 1, then mn(m + n) = 0. The answer is Yes.
Case 2: If say m = 1/2 and n = 1/2, then mn(m + n) = 1/4 ≠0. The answer is No. No unique answer. Insufficient.
(2) mn = 1
If (m + n) ≠0, then the answer is No; however, if (m + n) = 0, the answer is Yes.
Since mn = 1, we see that neither m nor n is 0 and m and n have the same sign. For (m + n) to be equal to 0, the absolute values of m and n must be equal and of opposite signs, which is not possible. Thus, (m + n) ≠0. This implies that mn(m + n) ≠0. The answer is No. A unique answer. Sufficient.
The correct answer:
B
Hope this helps!
-Jay
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