Does ab = a^2
(1) a^2 = b ^2
(2) a^3 = b ^3
1) a = + or - b. If a = +b. Answer is yes. If a = -b. Answer is no. Insufficient.
2)a = b. Sufficient.
Answer is B.
thanks for the reply, could you please elaborate more on the algebra use to solve?
(1) and why if a= + or -b or if a = +b stmt 1 suff, and if a = -b then insuff
did you pick numbers to test stmt 1 and 2?
1. We do not need to pick numbers.
1) \(a^2 = b^2\)
This means + or - a = + or - b. So we are basically given that a can be equal to b or a can be equal to -b.
If a = b, LHS of given equation becomes a^2 and hence is equal to RHS
If a = -b, LHS of given equation becomes -a^2 and hence may not be equal to RHS.
Since we are getting two different answers, this statement is insufficient.
2) \(a^3 = b^3\)
This means a = b and nothing else.
So, LHS of given equation can only be a^2 and hence is equal to RHS. Sufficient.
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