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# What is the value of y + x^3 + x?

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Math Expert
Joined: 02 Sep 2009
Posts: 43335

Kudos [?]: 139528 [3], given: 12794

What is the value of y + x^3 + x? [#permalink]

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06 Nov 2014, 07:53
3
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Expert's post
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Difficulty:

75% (hard)

Question Stats:

56% (01:52) correct 44% (01:40) wrong based on 155 sessions

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Tough and Tricky questions: Algebra.

What is the value of y + x^3 + x?

(1) y = x (x - 3) (x + 3)
(2) y = -5x

Kudos for a correct solution.
[Reveal] Spoiler: OA

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Kudos [?]: 139528 [3], given: 12794

Manager
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Re: What is the value of y + x^3 + x? [#permalink]

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06 Nov 2014, 16:05
2
KUDOS
I got C.

1. y=x(x-3)(x+3)
y=x(x^2-9)
We can't do anything with this.

2. y=-5x
-5x=x(x^2-9) <-Pull this equation from 1.
-5=x^2-9
0=x^2-4
0=(x-2)(x+2)
x=2 or -2

Plug both y=-5x into the equation you need to solve
-5x+x^3+x Now solve with x = 2 or -2
-5(2)+(2)^3+(2) or -5(-2)+(-2)^3+(-2)
-10+8+2 or 10-8-2
0 or 0

y+x^3+x = 0

The answer is C. Or so I hope. OA?

Kudos [?]: 59 [2], given: 66

Manager
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Concentration: Strategy, Technology
WE: Information Technology (Computer Software)
Re: What is the value of y + x^3 + x? [#permalink]

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06 Nov 2014, 18:37
1
KUDOS
Statement 1: y = x (x - 3) (x + 3)

This is clearly insufficient

Statement 2: y = -5x
This is also insufficient

Combining 1 and 2

-5x = x^3 -9x
or, x^3-4x =0

Therefore x can have three different values of 0, +2 and -2
Hence insufficient. E) should be the answer

Kudos [?]: 77 [1], given: 49

Manager
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Re: What is the value of y + x^3 + x? [#permalink]

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06 Nov 2014, 23:10
2
KUDOS
Bunuel wrote:

Tough and Tricky questions: Algebra.

What is the value of y + x^3 + x?

(1) y = x (x - 3) (x + 3)
(2) y = -5x

Kudos for a correct solution.

What is the value of y + x^3 + x?

(1) y = x (x - 3) (x + 3)

y=x(x^2-9)
y=x^3-9x

so y + x^3 + x = x^3-9x +x^3 + x
Insuff as we are getting interms of x only

(2) y = -5x
Insuff

1+2

y =x^3-9x
-5x =x^3-9x (from 1 and 2)
x^3 = 4x

Finally,
y + x^3 + x
= -5x+ 4x +x
= 0

IMO C

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Intern
Joined: 20 Aug 2015
Posts: 13

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What is the value of y + x^3 + x? [#permalink]

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22 Apr 2016, 20:29
1
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1
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BOOKMARKED
BassanioGratiano wrote:
I got C.

1. y=x(x-3)(x+3)
y=x(x^2-9)
We can't do anything with this.

2. y=-5x
-5x=x(x^2-9) <-Pull this equation from 1.
-5=x^2-9

0=x^2-4
0=(x-2)(x+2)
x=2 or -2

Plug both y=-5x into the equation you need to solve
-5x+x^3+x Now solve with x = 2 or -2
-5(2)+(2)^3+(2) or -5(-2)+(-2)^3+(-2)
-10+8+2 or 10-8-2
0 or 0

y+x^3+x = 0

The answer is C. Or so I hope. OA?

You found the answer. However, your approach has a small mistake. I have marked the lines in red.
-5x=x(x^2-9)
After this you can not simply cancel x from both sides as you do not know the sign of x.
-5x=x(x^2-9)
=> -5x = x^3-9x
=> x^3-4x=0
=> x(x^2-4)=0
The above implies 3 solutions for x.
x = 0 OR x = -2 OR x = 2
If we plug in any of the above values in the simplified equation in terms of x i.e -5x+x^3+x, the result will be zero.
Hence (C) is the answer.

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Re: What is the value of y + x^3 + x? [#permalink]

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13 Dec 2017, 11:38
Okay, I am a little confused here.

St 1 also boils down to y = -5x
y = x(x^2 -9)
y = x cube - 9x
x cube = 9x + y

Substituting x cube in original equation we get --> y + 9x + y + x = 0 --> 10x + 2y = 0 so y = -5x

and again if I put -5x = x (x^2 - 9) we get x = 2 or -2, inturn making LHS = RHS = 0 [ (-5)(2)]= [2(4-9)]and we get 0 with positive two as well

St 2: y = -5x, same as above. So the LHS = RHS = 0.

Thus, as both statements give 0, Shouldn't the OA be D?

Please request an expert opinion on my answer. Thank you!

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Re: What is the value of y + x^3 + x? [#permalink]

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13 Dec 2017, 13:34
2
KUDOS
Expert's post
Okay, I am a little confused here.

St 1 also boils down to y = -5x
y = x(x^2 -9)
y = x cube - 9x
x cube = 9x + y

Substituting x cube in original equation we get --> y + 9x + y + x = 0 --> 10x + 2y = 0 so y = -5x

and again if I put -5x = x (x^2 - 9) we get x = 2 or -2, inturn making LHS = RHS = 0 [ (-5)(2)]= [2(4-9)]and we get 0 with positive two as well

St 2: y = -5x, same as above. So the LHS = RHS = 0.

Thus, as both statements give 0, Shouldn't the OA be D?

Please request an expert opinion on my answer. Thank you!

$$y + x^3 + x$$ is part of the question. You're being asked to find its value, given certain information. Instead, you're treating the problem as if you already know that its value is 0 (by substituting other equations into $$y + x^3 + x = 0$$). This is why it isn't coming out correctly. You're using information that you don't actually have, which will make you get DS problems wrong.

Instead, think to yourself: if the only information I have is that y = -5x, is that enough for me to figure out the value of $$y + x^3 + x$$? It isn't - you can't figure out what $$y + x^3 + x$$ is by using only that information. That's why the statement is insufficient.
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Re: What is the value of y + x^3 + x?   [#permalink] 13 Dec 2017, 13:34
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