What is the value of y-x^2-x?

What is the value of \(y-x^2-x\)?

(1) y = -3x --> the question becomes: what is the value of \(-3x-x^2-x\). We need the value of x to answer this question. Not sufficient.

(2) y = -4(x + 1) --> the question becomes: what is the value of \(-4(x + 1)-x^2-x\). We need the value of x to answer this question. Not sufficient.

(1)+(2) We have two distinct linear equations: \(y = -3x\) and \(y = -4(x + 1)\), thus we can solve for both variables and get the value of \(y-x^2-x\). Sufficient.

Answer: C.

Hope it's clear.

Awesome, thanks a lot Bunuel. You are, as they say, "The Man".

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The explanation about linear equation is not clear

If you have n distinct linear equations and n variables then you can solve for them. "Distinct linear equations" means that no equation can be derived with the help of others or by arithmetic operation (by multiplication, addition, ...).

We have two distinct linear equations: \(y = -3x\) and \(y = -4(x + 1)\). Solving gives: x=-4 and y=12.

Hope it's clear.

Hi All,

This DS question can be solved with a combination of TESTing VALUES and Algebra skills.

We're asked for the value of Y - X^2 - X.

Fact 1: Y = -3X

IF....
X = 0
Y = 0
The answer to the question is 0 - 0^2 - 0 = 0

IF...
X = 1
Y = -3
The answer to the question is -3 - 1^2 - 1 = -5
Fact 1 is INSUFFICIENT

Fact 2: Y = -4(X+1)

IF...
X = 0
Y = -4
The answer to the question is -4 - 0^2 - 0 = -4

IF...
X = 1
Y = -8
The answer to the question is -8 - 1^2 - 1 = -10
Fact 2 is INSUFFICIENT

Combined, we know...
Y = -3X
Y = -4(X+1)

Looking at this, you should recognize a "system" of equations - we can set the equations equal to one another...

-3X = -4X - 4
X = -4

With one fixed value for X, we can solve for Y:

Y = -3(-4) = 12

Thus, X = -4 and Y = 12, so we CAN answer the question.
Combined, SUFFICIENT

Final Answer:
GMAT assassins aren't born, they're made,
Rich

Does this question belongs to the 700 level category? Seems pretty straightforward for a 700 leveler...

The difficulty level is based on user attempts on this question. Check the stats in the original post.

Hi dhruvmadra,

As you study, you're going to find that what you think is "hard" is not necessarily what the Test Makers 'define' as "hard" (and vice-versa). It's not practical to spend time trying to assess the difficulty level of any individual question. Since your goal is almost certainly to increase your scores, you should look at the types of questions that you're getting wrong and WHY you're getting them wrong. If you get a question wrong that you SHOULD have gotten correct (but you made a silly/little mistake), then I don't care what 'level' of question it is - you've got to work to keep those mistakes from happening (since too many little mistakes will kill your scores).

GMAT assassins aren't born, they're made,
Rich

Hi Bunuel, love your answers on each thread! Could you please clarify how to easily spot "distinct" linear equations? Does that mean essentially that you can add them or subtract them (or solve one and substitute in another) and in doing so eliminate one of the two variables? Just trying to figure out how to quickly understand if equations are distinct.

For example:
x + y = 100
x - y = 100

These are distinct, correct? y = 0 and x = 100. However, is there a trick for spotting that, or do you just have to quickly mentally almost "solve" them and see?

x + y = 100
2x + 2y = 200

not distinct because one equation is just a multiple of another. Is the trick to try to spot multiples of equations or are there even more advanced traps used by GMAT?

Hi pranskius,

To start, nothing about a GMAT question is ever "random" - every word (and in the case of most Quant questions, every number) is specifically chosen to 'test' you on one or more concepts. When you find yourself thinking... this piece of information is a bit 'weird' relative to the other pieces of information that I was given in the prompt, you should take a moment to think/work through the differences.

For example, if you're first given a straight-forward equation such as X + 2Y = 100.... but then the next equation you're given is 4Y = 200 - 2X... you should take a moment to think about WHY the author wrote the second equation in a different way... Maybe it's to 'test' your ability to simplify an equation and spot a pattern?

As a general rule, you should be doing all of your work on your notepad (and not doing any steps "in your head", since you're far more likely to make a silly mistake when you don't take notes). When you re-format that second equation, you might also recognize that all of the numbers are EVEN - meaning that you can divide the entire equation by 2... Doing so gives you X + 2Y = 100. Thus, we do NOT have 2 unique equations here - we have the SAME equation twice (and this is NOT a 'System' of equations).

Most Quant questions require that you work through 3-5 'steps' to get the correct answer. Most prompts are fairly "thin" when it comes to information though, so you should get in the habit of looking for simple steps that you can do to organize and simplify information that you've been given. Going through those steps can actually help save you time and make it easier to spot the built-in pattern(s) involved.

GMAT assassins aren't born, they're made,
Rich

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