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

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

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.

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.

(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)

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

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

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!

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.

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