AS # 47

[oquiella]

47. Is p = m, given that p and m are real numbers.

(1) p2 = m2
.
(2) p3 = m3


iS THERE A BASIC RULE?
.

[Brent@GMATPrepNow]

47. Is p = m, given that p and m are real numbers.

(1) p² = m²

(2) p³ = m³

The basic concept here is that EVEN powers result in outcomes that are positive (or zero)
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

[oquiella]

47. Is p = m, given that p and m are real numbers.

(1) p² = m²

(2) p³ = m³

The basic concept here is that EVEN powers result in outcomes that are positive (or zero)
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

Hello,

why wouldnt using different numbers be allowed in this case? Is it because I can only use the equation p=q and both numbers must be the same even when tested within the statements?

[MartyMurray]

why wouldnt using different numbers be allowed in this case? Is it because I can only use the equation p=q and both numbers must be the same even when tested within the statements?

Think about what you are asking. The question is asking whether p = m. So there's no reason to pick only numbers that fit that. In fact, in working on this question, part of what you might seek to do is find numbers that do not fit that equation.

The reason Brent picked the same number for p as he did for m, or at least picked for p and m negative and positive numbers with the same absolute value, was because he was constrained not by the question but by the statements.

For instance, Statement 2 says that p³ = m³. The only way that holds is if p = m. So of course any numbers that you pick to fit that equation have to be the same for both p and m.