For real numbers a and b, is it true that a = b?
(1) a^4 = b^4
(2) a^5 = b^5
OA:B
Please explain
(1) a^4 = b^4
(2) a^5 = b^5
OA:B
Please explain
First consider statement (1).
It can be true even if a and b are of opposite signs. For example:
a = 2 and b = -2 gives a^4 = b^4
a = 2 and b = 2. gives a^4 = b^4
You cannot be sure whether or not a and b have equal signs because raising to an even power will always be positive. Hence (1) is not sufficient.
Consider statement (2).
If true, then a and b must have equal signs because any real number raised to an odd number will maintain its sign. For example:
(-2)^5 = -32. So in the case that a or b are negative then raising them to an odd number (5) will maintain their sign.
(2) is sufficient and the answer is B.
Feel free to ask again if not clear.
