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.
OG2016 PS If x = 1,
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 lionsshare
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Algebraic expressions (like the one above) can have many values, depending on the value of the variables that make up the expression.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
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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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 detailoriented 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
GMAT assassins aren't born, they're made,
Rich
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 detailoriented 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
GMAT assassins aren't born, they're made,
Rich

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Replace every x in the equation with 1: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.
((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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Let's substitute x = 1 for x in our expression: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
(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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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)/(11)
= (1 + 1 + 1)/(2)
= 3/(2)
= 3/2
Therefore, Option A is the correct answer.
((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)/(11)
= (1 + 1 + 1)/(2)
= 3/(2)
= 3/2
Therefore, Option A is the correct answer.
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 Brent@GMATPrepNow
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Good catch!jbryant62 wrote:@brent
you said (1(1)+1)=1. shouldn't that be 3?
I've edited my response accordingly.
Cheers,
Brent
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.
$$\frac{x^4x^3+x^2}{\left(x1\right)}=\frac{\left(1\right)^4\left(1\right)^3+\left(1\right)^2}{\left(1\right)1}=\frac{1\left(1\right)+1}{2}=\frac{3}{2}$$
The answer is A.
$$\frac{x^4x^3+x^2}{\left(x1\right)}=\frac{\left(1\right)^4\left(1\right)^3+\left(1\right)^2}{\left(1\right)1}=\frac{1\left(1\right)+1}{2}=\frac{3}{2}$$
The answer is A.