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Intern  Joined: 27 Jan 2010
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Question Stats: 73% (01:23) correct 27% (01:45) wrong based on 431 sessions

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$$\frac{p+5+p^3(-p-5)}{-p-5}=$$

A. p+5+p^3
B. P^3+5
C. p^3
D. p^3-1
E. p^3-5
Math Expert V
Joined: 02 Sep 2009
Posts: 65828
Re: Princeton Review Test problem : ID4019  [#permalink]

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5
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undernet wrote:
$$p+5+p^3(-p-5)/-p-5$$=

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

OA

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 $$(-p-5)$$ --> $$\frac{-(-p-5)+p^3(-p-5)}{-p-5}=\frac{(-p-5)(-1+p^3)}{-p-5}=-1+p^3=p^3-1$$.

Hope it helps.
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##### General Discussion
Intern  Joined: 27 Jan 2010
Posts: 4
Re: Princeton Review Test problem : ID4019  [#permalink]

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Thank you Bunnel... negating the first term didn't struck me....
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Hi All,

This question can be solved by TESTing 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

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1
$$\frac{p+5+p^3(-p-5)}{-p-5}=$$

Multiply numerator/ denominator by -1

$$\frac{p^3(p+5) - 1(p+5)}{p+5} = p^3 - 1$$

Intern  Joined: 02 Aug 2016
Posts: 3

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i think its easier to work without negatives, so i just did the following:

[p+5 + p^3(-p-5)] / (-p-5) => [(p+5)(1-p^3)/-1(p+5)] => (1-p^3)/-1 => p^3 -1
Intern  Joined: 30 Sep 2016
Posts: 7

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Would you mind explaining the negative sign part? Is this a rule that I am missing?
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Hi Nasahtahir,

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.

GMAT assassins aren't born, they're made,
Rich
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Intern  B
Joined: 17 Nov 2016
Posts: 24

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Quote:
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.

Hope it helps.

Hi Brent,

Can you explain what you did after factoring (-p-5)?
Intern  B
Joined: 21 May 2017
Posts: 24

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Zoser wrote:
Quote:
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.

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)
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Sorry guy bust I still dont get it. Anyone can put a video for it?
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Hi Zoser,

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

GMAT assassins aren't born, they're made,
Rich
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Manager  G
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p+5+p^3(−p−5)/−p−5
=(p+5) -p^3(p+5)/ (-1)*(p+5)
Divide Numerator and Denominator by (p+5)
=1-p^3/-1
=p^3-1

Kudos if it helps.
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Top Contributor
undernet wrote:
$$\frac{p+5+p^3(-p-5)}{-p-5}=$$

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)
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If you enjoy my solutions, you'll love my GMAT prep course. Originally posted by BrentGMATPrepNow on 30 Nov 2017, 10:10.
Last edited by BrentGMATPrepNow on 01 Jun 2020, 08:33, edited 1 time in total.
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Top Contributor
undernet wrote:
$$\frac{p+5+p^3(-p-5)}{-p-5}=$$

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

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.

Cheers,
Brent
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undernet wrote:
$$\frac{p+5+p^3(-p-5)}{-p-5}=$$

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

Let’s use the distributive property over division:

(p + 5)/(-p - 5) + p^3(-p - 5)/(-p - 5)

(p + 5)/-(p + 5) + p^3

-1 + p^3

p^3 - 1

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I think people are are confused with the format as it's a bit foreign and people are wrongly eliminating the −p−5 from both the top and bottom.

Essentially the question is $$\frac{1+2+3(x)}{x}$$ in which simplified would be $$\frac{1}{x}$$+ $$\frac{2}{x}$$+ $$\frac{3}{1}$$ (cancelling the x's in 3x/x.

And not $$\frac{(1+2+3)x}{x}$$ Here, you can eliminate the x's and get 1+2+3
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There are a few ways to do this question. I chose the simplification/elimination (however you call it) method since I could see some symmetry in the question. Else I would have also gone for value substitution.

$$\frac{(p+5+p^3(-p-5))}{-p-5} = \frac{p+5}{-p-5} + \frac{p^3(-p-5)}{-p-5} = \frac{p+5}{-(p+5)}+ p^3 = -1 + p^3$$

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undernet wrote:
$$\frac{p+5+p^3(-p-5)}{-p-5}=$$

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

$$\frac{p+5+p^3(-p-5)}{-p-5}$$

Or, $$\frac{-1 (- p - 5 ) +p^3 ( -p - 5 )}{(-p -5 )}$$

Or, $$\frac{(- p - 5 )( p^3 - 1)}{(-p -5 )}$$

Or, $$( p^3 - 1)$$ , Answer must be (D)
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# (p+5+p^3(-p-5))/(-p-5)=  