What is the value of y – x^2 – x? (1) y = –3x (2) y = –4(x + 1)

(1) y=–3x insufic

\((-3x)-x^2-x…-x^2-4x;\)

(2) y=–4(x+1) insufic

\((-4x-4)-x^2-x…-x^2-5x-4;\)

(1&2) sufic

\(-3x=-4x-4…x=-4\)
\((-3x)-x^2-x…-x^2-4x;…-(-4)^2-4(-4)…-16+16=0\)

Ans (C)

What is the value of \(y–x^2–x\)?

(1) \(y = –3x\)
\(y – x^2 – x\)
--> \(-3x – x^2 – x\)
--> \(-4x - x^2\) --> Insufficient

(2) \(y = –4(x+1) = -4x - 4\)
\(y – x^2 – x\)
--> \(- 4x - 4 – x^2 – x\)
--> \(– x^2 – 5x - 4\) --> Insufficient

Combining (1) & (2),
--> \(- 3x = -4x - 4\)
--> \(4x - 3x = -4\)
--> \(x = -4\)
--> \(y = - 3x = -3*-4 = 12\)

So, value of \(y – x^2 – x\) can be calculated --> Sufficient

IMO Option C

We are to determine the value of y - x^2 - x

1. y=-3x
This is insufficient because there are infinite possibilities. We have an equation with two variables, so we cannot determine specific values of y and x.

2. y=-4(x+1)
This is also insufficient because there are infinite possibilities since we have an equation with two variables. We are therefore unable to determine unique values for y and x.

1+2
Sufficient because we are able to solve the equations
y=-3x and y=-4(x+1)
-3x=-4x-4
x=-4
and y=12
Hence y-x^2-x=12-(16)-(-4) = 12-12=0

Statements 1 and 2 taken together are sufficient.

The answer is option C.

eakabuah
My thought process was: We need to find the value of X, and if we find the value of X, We will automatically find the value of Y.
Now isn't it a possibility that in solving the quadratic equation the value of X is common?
Am I missing something? Because I had to solve the equation in order to understand and conform the point you made without solving.
Please help me in clearing the understanding.

Regards
Devesh

Hello deveshj21
Let me try to clear your doubts by further simplifying the problem.
The question is what is the value of y - x^2 - x?
One way you can look at this that will make you appreciate the task is to form an equation out of the question. All that you have to do to achieve it is to say if f(x,y)=y - x^2 - x, what is f(x,y)? From this point, you realize that the function f(x,y) depends on two variables. The question stem as it is without any clue can yield infinite solutions. Why? we are not restricted in any way to the values of x and y. So we can arbitrarily choose any value for x and y. x and y can be integers, fractions, irrational numbers, so obviously we need some clue to make sense out of f(x,y). With this reasoning, let's now re-evaluate the given statements (i.e. clues).

Statement 1: y=-3x.
What do we make of this statement? The idea is to find f(x,y)=y - x^2 - x.
Statement 1 says that replace y with -3x. In order words, find f(x,-3x), and this will yield f(x,-3x)=-3x - x^2 - x = -x^2 - 4x. I know you are tempted to solve at this point and say -[x(x+4)]=0, hence x=0 and x=-4 right? It doesn't work like that. x=0 and x=-4 are the values of x that make f(x,y)=0, but the question is not interested in making f(x,y)=0. What it is interested in is that you should find some numeric values for x and y, and plug it into the f(x,y) and what you get is the answer.

So let's relook at statement 1 again. Does the clue y=-3x lead us to get unique numeric values for x and y? How can I find specific values for x and y when all I have is one equation, meanwhile there are two variables? Clearly, statement 1 is insufficient. You need two equations in order to narrow down to unique values for x and y. Would statement 1 have been sufficient if we were given the value for one of the variables? Still no. Why? Because how would I determine the value of the other variable so I can plug them into f(x,y)? So even if were given one of the variables, we cannot determine f(x,y).

Statement 2: y=-4(x+1).
I'm sure you will agree with me that statement 2 is insufficient right, and that you cannot solve this equation to get unique values of x and y that you can plug into f(x,y)=y - x^2 - x to get a unique value. Hence let's move on.

1+2
y=-3x ......(1)
y=-4(x+1) ....(2)
Now you solve, but then and again, you actually don't need to sove these two equations. Why? All you need to ensure is that the two equations are not the same. Once you notice they are not the same, conclude that both statements are sufficient to determine the value of f(x,y). This mindset will hopefully save you time on the GMAT, mind you, I am no expert, I am yet to take my first GMAT exam.

The main point of ensuring that both statements are not identical is that you cannot solve two identical equations in two variables and get unique values for the two variables. So sometimes, they know most people won't bother to solve the equations and just say that the two statements when taken together are sufficient hence C is the answer. Hence in your bid to save time, ensure you double-check that the two equations are not identical or that you can actually solve them before concluding.

I hope this helps to clear your doubts.

eakabuah
I really appreciate you for writing such a long yet crisp post to clear my doubt, now I know the concept.
About the two equations being same. Yes, I fell into the trap once and now I double check it every time.

Kudos to you:)

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