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I could solve it by plugging numbers. But I am looking for the algebraic way to solve this equation.

Hi, and welcome to the Gmat Club. Below is algebraic solution for you question:

Guess the question must be \(\frac{p+5+p^3(-p-5)}{-p-5}=?\)

If yes than: \(\frac{p+5+p^3(-p-5)}{-p-5}=\frac{-(-p-5)+p^3(-p-5)}{-p-5}\) --> factor out \((-p-5)\) --> \(\frac{-(-p-5)+p^3(-p-5)}{-p-5}=\frac{(-p-5)(-1+p^3)}{-p-5}=-1+p^3=p^3-1\).

So we're looking for an answer that = 7 when P = 2

Answer A: 2 + 5 + 8 = 15 NOT a match Answer B: 8 + 5 = 13 NOT a match Answer C: 8 NOT a match Answer D: 8 - 1 = 7 This IS a MATCH Answer E: 8 - 5 = 3 NOT a match

You're going to face some GMAT questions on Test Day that 'test' you on concepts that you know, but in ways that you're probably not used to thinking about. If you choose to approach this question algebraically (which is an approach that you do not have to use), then you would find that factoring the given equation can help to simplify it. You probably already know how to factor...

For example: 2X + 4 can be factored down to 2(X +2).

In that same way, you can factor out other common 'pieces':

-2X - 10 can be factored down to -2(X + 5).

The concept of 'factoring out a negative' is what mcdude123 used:

-P + 5 can be factored down to -1(P+5). At that point, you can then factor out (P+5) out of the numerator of the fraction.

Hi, and welcome to the Gmat Club. Below is algebraic solution for you question:

Guess the question must be p+5+p3(−p−5)−p−5=?p+5+p3(−p−5)−p−5=?

If yes than: p+5+p3(−p−5)−p−5=−(−p−5)+p3(−p−5)−p−5p+5+p3(−p−5)−p−5=−(−p−5)+p3(−p−5)−p−5 --> factor out (−p−5)(−p−5) --> −(−p−5)+p3(−p−5)−p−5=(−p−5)(−1+p3)−p−5=−1+p3=p3−1−(−p−5)+p3(−p−5)−p−5=(−p−5)(−1+p3)−p−5=−1+p3=p3−1.

Answer: D.

Hope it helps.

Hi Brent,

Can you explain what you did after factoring (-p-5)?

Hi, and welcome to the Gmat Club. Below is algebraic solution for you question:

Guess the question must be p+5+p3(−p−5)−p−5=?p+5+p3(−p−5)−p−5=?

If yes than: p+5+p3(−p−5)−p−5=−(−p−5)+p3(−p−5)−p−5p+5+p3(−p−5)−p−5=−(−p−5)+p3(−p−5)−p−5 --> factor out (−p−5)(−p−5) --> −(−p−5)+p3(−p−5)−p−5=(−p−5)(−1+p3)−p−5=−1+p3=p3−1−(−p−5)+p3(−p−5)−p−5=(−p−5)(−1+p3)−p−5=−1+p3=p3−1.

Answer: D.

Hope it helps.

Hi Brent,

Can you explain what you did after factoring (-p-5)?

cancelled it from numerator and denominator to get -1+p^3. Maybe the absence of parenthesis in the denominator confused you? -p-5 in denominator is the same as (-p-5)

You're going to find that most GMAT questions can be approached in more than one way. As such, if you don't understand one particular approach to a question, then there's a pretty good chance that there will be another approach that you mind find easier to deal with. In my approach (above), I chose to TEST VALUES:

IF..... P = 2 Then the calculation becomes....

[2 + 5 + 8(-7)] / (-7)

[7 - 56]/(-7) [-49]/(-7) = 7

So we're looking for an answer that = 7 when P = 2

Answer A: 2 + 5 + 8 = 15 NOT a match Answer B: 8 + 5 = 13 NOT a match Answer C: 8 NOT a match Answer D: 8 - 1 = 7 This IS a MATCH Answer E: 8 - 5 = 3 NOT a match

A. p+5 + p^3 B. P^3 + 5 C. p^3 D. p^3 - 1 E. p^3 - 5

Let's just focus on the NUMERATOR for a second. Given: p + 5 + p³(-p - 5) Factor -1 from the first part to get: -1(-p - 5) + p³(-p - 5) So, we now have: -1(-p - 5) + p³(-p - 5) Combine terms to get: (-1 + p³)(-p - 5) Rearrange terms to get: (p³ - 1)(-p - 5)

Now replace ORIGINAL numerator with (p³ -1)(-p - 5) We get: (p³ - 1)(-p - 5)/(-p - 5) Simplify to get: (p³ - 1) Answer: D

We're looking for an expression that is equivalent to the original expression. So if we evaluate the original expression for a particular value of p, then the equivalent expression should also yield the same value when we plug in the same value of p. Let's test p = 1

Take: [p + 5 + p³(-p - 5)]/[-p - 5] Replace p with 1 to get: [1 + 5 + 1³(-1 - 5)]/[-1 - 5] Evaluate to get: 0/-6, which equals 0

So, when p = 1, the original express evaluates to be 0 Now let's plug p = 1 into the answer choices.... A. 1 + 5 + 1^3 = 7. No good, we want 0. ELIMINATE. B. 1^3 + 5 = 6. No good, we want 0. ELIMINATE. C. 1^3 = 1. No good, we want 0. ELIMINATE. D. 1^3 - 1 = 0. Great - KEEP E. 1^3 - 5 = -4. No good, we want 0. ELIMINATE.