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

Question

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

BassanioGratiano · Answer

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?

kinghyts · Answer

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

anupamadw · Answer

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

aswaniwait4u · Answer

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.

Madhavi1990 · Answer

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  =  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!

ccooley · Answer

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.

exc4libur · Answer

(1)  y = x (x - 3) (x + 3)… y=x(x^2-3^2)… y=x^3-9x…substitute:(x^3-9x)+x^3 + x… =-8x  insufic.
(2)  y = -5x…substitute:(-5x)+x^3 + x… =x^3-4x  we dont know  x  insufic.

(1&2) 
 equate(y): -5x=x(x^2-3^2)…-5x=x^3-9x…x^3-4x=0…x(x^2-4)=0…x(x-2)(x+2)=0…x={0,2,-2} ; try these values of into the original equation, the answer will always equal to 0, sufficient.

Answer (C)

Shantanupandey · Answer

Please correct me if i'm wrong-
Eq1
y=x(x-3)(x+3)
y=(x^2-3x)(x+3)
y=x^3-9x

Putting this back in major eq
x^3-9x+x^3+x
2x^3-8x
2x(x^2-4)
2x(x+2)(x-2)
Eq1 is sufficient

Eq2 y=-5x
Putting this in major eq
-5x+x^3+x
x^3-4x
x(x^2-4)
x(x+2)(x-2)
So eq2 is sufficient as well

Ans (d) both sufficient

Posted from my mobile device

IreneDSosa · Answer

Inverse Relation of y = x3 + x is

First of all I know that y = x3 + x has an inverse since it is an increasing function. I know this because the sign of the derivative is positive for every real number x. My guess is that this comes from a calculus problem here you are to find the derivative of the inverse at some point. If so then you don't need an explicit expression for the inverse. If you really want to find the inverse interchange the roles of x and y and write x = y3 + y . Rewrite this expression as

y3 + y - x = 0

CrackverbalGMAT · Answer

In a DS question where a value is required as an answer, sometimes, one may have to go till the very end to find an actual answer, and that’s where it can go either ways. You may end up learning a lot from the question, but you may also take some extra time in solving the question.

This is one such question. To find the value of the expression, we will have to use Algebra to solve the resulting equations and find values for the variables, which will give us our answer.

Clearly, the individual statements, I and II, when taken alone are insufficient. This is because they end up expressing the variable y in terms of x, but this doesn’t give us an equation to solve. 
Answer options A, B and D can be eliminated. Possible answer options at this stage are C or E.

When we combine the statements I and II, we can say,

x (x-3) (x+3) = -5x. Simplifying this, we have,  x^3  -4x = 0, which gives us x (x-2) (x+2) = 0.

Substituting the value of y from statement I in the question stem and simplifying, we get, 
2 x (x-2) (x+2). Since x (x-2) (x+2) = 0, the value of the expression = 0.

Substituting the value of y from statement II in the question stem and simplifying, we get, 
 x^3  – 4x = 0. Clearly, we have already seen that this expression gives us 0.

This means, regardless of which statement we use, we get a unique value for the expression i.e. 0. 
The correct answer option is C.

Hope this helps!

Aishyk97 · Answer

Hi,

This is how I solved the question. Please let me know if my reasoning is correct.

(1) y = x (x - 3) (x + 3) 
Simplify to:
y = x(x^2 - 9)
y = x^3 - 9x

NS.

(2) y = -5x

NS.

Combine:

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

Plug in y = -5x in the question. So the question is asking x^3 - 4x. Which is equal to zero.

I did not try to find the individual values of x.

Kratosgmat · Answer

First off, brilliant question

stmt1,2 are obviously insufficient individually
lets combine

y=x^3-9x
y=-5x

X^3-9x = 5x (Do not cancel x on either side here as x could be 3)
x^3=4x

now sub. in equation y + x^3 + x= -5x+4x+x = 0

Hence option C

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards