The basic concept here is that EVEN powers result in outcomes that are positive (or zero)oquiella wrote:47. Is p = m, given that p and m are real numbers.
(1) p² = m²
(2) p³ = m³
For example, 5² = 25 and (-5)² = 25
Conversely ODD powers preserve the sign of the base. That is (negative)^odd = negative, (positive)^odd = positive. For example, 5³ = 125 and (-5)³ = -125
We cover this concept at the 5:55 mark in this free video - https://www.gmatprepnow.com/module/gmat- ... video/1021
Now onto the question:
Target question: Is p = m?
Statement 1: p² = m²
There are several values of p and m that satisfy statement 1. Here are two:
Case a: p = 3 and m = 3. Notice that 3² = 3². In this case, p = m
Case b: p = 3 and m = -3. Notice that 3² = (-3)². In this case, p ≠m
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values
Statement 2: p³ = m³
So, p³ and m³ are either BOTH positive or BOTH negative.
By the above rule (since 3 is an odd power), we know that p and m are either BOTH positive or BOTH negative.
Also, since both p and q are raised to the same power, they must have the same magnitude.
From this, can can be certain that p = m
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer = B
Cheers,
Brent
