OG2016 PS If x = -1,

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lionsshare: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Wed Aug 09, 2017 3:54 pm

by lionsshare » Mon Aug 28, 2017 1:28 pm

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If x = -1, then (x^4 - x^3 + x^2)/(x - 1) =

(A) -3/2
(B) -1/2
(C) 0
(D) 1/2
(E) 3/2

OA: A

Anyone can please explain how to solve the problem. Thanks.

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OG2016 PS If x = -1,

by Brent@GMATPrepNow » Mon Aug 28, 2017 1:38 pm

lionsshare wrote:If x = -1, then (xâ�´ - xÂ³ + xÂ²)/(x - 1) =

(A) -3/2
(B) -1/2
(C) 0
(D) 1/2
(E) 3/2

Algebraic expressions (like the one above) can have many values, depending on the value of the variables that make up the expression.

Take for example the expression 2x + 1
If x = 3, then 2x + 1 = 2(3) + 1 = 6 + 1 = 7
If x = 6.5, then 2x + 1 = 2(6.5) + 1 = 13 + 1 = 14
If x = -5, then 2x + 1 = 2(-5) + 1 = -10 + 1 = -9
etc

Now let's work with the given expression (xâ�´ - xÂ³ + xÂ²)/(x - 1)
x = -1, then (xâ�´ - xÂ³ + xÂ²)/(x - 1) = [(-1)â�´ - (-1)Â³ + (-1)Â²]/[(-1) - 1]
= [1 - (-1) + 1]/(-2)
= 3/(-2)
= -3/2

Answer: A

Cheers,
Brent

Last edited by Brent@GMATPrepNow on Wed Nov 08, 2017 6:41 am, edited 1 time in total.

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jbryant62: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Wed Nov 23, 2016 4:04 pm; Thanked: 1 times

by jbryant62 » Tue Aug 29, 2017 1:00 pm

@brent

you said (1-(-1)+1)=1. shouldn't that be 3?

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by [email protected] » Tue Aug 29, 2017 1:59 pm

Hi AbeNeedsAnswers,

A couple of times on Test Day, the GMAT is going to 'test' your ability to subtract negatives. That type of math isn't too difficult, but it's likely that one of the wrong answers will be based on a little mistake that you MIGHT make, so you have to be real detail-oriented with your work.

Here, we're essentially asked to "plug in" -1 into four spots in the given equation and solve it.

(-1)^4 = +1
(-1)^3 = -1
(-2)^2 = +1
(-1 - 1) = -2

Thus, we have....
[(1) - (-1) + (1)]/-2 =
[3]/-2 =
-3/2

Final Answer: A

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Rich

Contact Rich at [email protected]

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Wed Aug 30, 2017 5:55 pm

lionsshare wrote:If x = -1, then (x^4 - x^3 + x^2)/(x - 1) =

(A) -3/2
(B) -1/2
(C) 0
(D) 1/2
(E) 3/2

OA: A

Anyone can please explain how to solve the problem. Thanks.

Replace every x in the equation with -1:

((-1)â�´ - (-1)Â³ + (-1)Â²)/(-1 -1)

From there it's pretty easy:

(1 - (-1) + 1)/(-2)

or

-3/2

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Mon Sep 04, 2017 10:14 am

lionsshare wrote:If x = -1, then (x^4 - x^3 + x^2)/(x - 1) =

(A) -3/2
(B) -1/2
(C) 0
(D) 1/2
(E) 3/2

OA: A

Let's substitute x = -1 for x in our expression:

(x^4 - x^3 + x^2)/(x - 1)

(1 - (-1) + 1)/(-1 - 1)

(1 + 1 + 1)/(-2) = -3/2

Answer: A

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Head of GMAT Instruction
[email protected]

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Admin1: Site Admin; Posts: 28; Joined: Wed Aug 30, 2017 10:11 pm

by Admin1 » Tue Sep 05, 2017 6:46 am

Solution:
Recall, that,
(-1)^p = -1 if p is odd
= +1 if p is even.
So, substituting the given value of x into the expression, we have
((+1) - (-1) + (+1)) / ((-1) - 1) = 3/(-2) = - 3/2.

Answer: A

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Admin1: Site Admin; Posts: 28; Joined: Wed Aug 30, 2017 10:11 pm

OG2016 PS If x = -1,

by Admin1 » Tue Sep 05, 2017 12:39 pm

If x = -1, then (x^4 - x^3 + x^2)/(x - 1) =?

((-1)^4 - (-1)^3 + (-1)^2)/((-1) - 1)
We know that any negative number raised to an odd power results into a negative number and any negative number raised to an even power results in to a positive number.
In other words,
x^n is a negative number if n is odd and
x^n is a positive number number if n is an even number.
Therefore,
((-1)^4 - (-1)^3 + (-1)^2)/((-1) - 1) = (1-(-1)+1)/(-1-1)
= (1 + 1 + 1)/(-2)
= 3/(-2)
= -3/2

Therefore, Option A is the correct answer.

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by Brent@GMATPrepNow » Wed Nov 08, 2017 6:41 am

jbryant62 wrote:@brent

you said (1-(-1)+1)=1. shouldn't that be 3?

Good catch!
I've edited my response accordingly.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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ca7ch22: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Sat Oct 27, 2018 10:35 am

reply

by ca7ch22 » Thu Nov 15, 2018 5:46 pm

This equation is solved by substituting -1 in for x. Also remember: a negative to an even power is positive; a negative to an odd power is negative.

$$\frac{x^4-x^3+x^2}{\left(x-1\right)}=\frac{\left(-1\right)^4-\left(-1\right)^3+\left(-1\right)^2}{\left(-1\right)-1}=\frac{1-\left(-1\right)+1}{-2}=-\frac{3}{2}$$

The answer is A.

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