If x = y^2, what is the value of y x? (1) x = 4 (2) x + y = 2

VERITAS PREP OFFICIAL SOLUTION:

Question Type: What Is the value? This question asks for the value of y – x.

Given information from the question stem: x = y^2. While it may not be important for this question, you should train yourself to notice things like “x cannot be negative” here, as y^2 has to be > 0.

Statement 1: x = 4. This is not sufficient because even taken with the fact above it still results in two answers. Substitute x in the equation from the facts and you get 4 = y^2. So y can equal 2 or – 2. These two values for y will give you different answers for “y – x” and are therefore not specific enough. You need a single value in order to be sufficient and you do not have one. The answer will either be B, C, or E.

Statement 2: x + y = 2. This is not sufficient even if taken together with the information from the question stem. A quick example using Play Devil’s Advocate might be the simplest way to show that this is not sufficient. “x = 1 and y = 1”is compatible with the given information and with Statement 2. However, so is one of our examples from statement 1 “x = 4 and y = -2.” After all 4 + -2 = 2. These different values for x and y will result in different answers to “y – x = ?” This statement is also not sufficient. The answer is either C or E.

Together: Taken together the statements are sufficient. Only one set of values will work with the two statements and the fact. “x = 4 and y = -2.” The correct answer is C. One important takeaway from this question: Do not assume that a variable is positive! When people answer this question incorrectly it’s usually because they only considered 2 as a value (and not -2) for y when they saw Statement 1. When a statement gives you a solution for y^2, remember that y could be either positive or negative. “Forgetting about negatives” is one of the easiest (and most common) mistakes to make on Data Sufficiency problems.

(1) x=4, y=+/-2 Not Suff
(2) x+y=2 -> y^2+y-2=0 than y=-2,1 Not Suff
(1+2) E

ST 1. x = 4 i.e. 4 = y^2 , but y can be -2 not sufficient


ST 2 x + y = 2 i.e x = y^2 then it means x =1 ; y =1 Sufficient


IMO: B

hopefully I am correct ­

tricky.

\(x =y^2\)

y - x

\(y - y^2\)

Statement 1: x = 4. \(y^2 = 4\). y = +2 or - 2 .Not sufficient.

Statement 2:

x + y =2

\(y^2 + y = 2.\)


\(y^2 + y -2 = 0\)

( y + 2 ) ( y - 1) = 0

y + 2 = 0

y = -2

or

y -1 = 0

y = 1.

Not sufficient.


Combining : common value is - 2. Sufficient. ­

Given: \(x = y^2\)

Stmt 1: x = 4, hence \(4 = y^2\) or y = +2 or -2, which will give different values for y - x, hence insufficient. Eliminate A, D

Stmt 2: x + y = 2 or y^2 + y - 2 = 0 which gives:
(y+2)*(y-1) = 0 which gives, y = 1 or y = -2. Again, 2 values for y gives 2 values for y - x, hence insufficient. Eliminate B.

Combined: if x = 4, then substitute in x + y = 2 to get, y = -2, hence y - x = -2-4 = -6, hence sufficient. Eliminate E

Hence Option C

Question: \(y-x = ?\)

Given: \(x = y^2\)

Statement 1: \(x = 4\)
i.e. \(y^2 = 4\)
i.e. \(y = +2\)
i.e. \(y-x = -2-4 or 2-4\)
NOT SUFFICIENT

Statement 2: \(x + y = 2\)
i.e. \(y^2 + y = 2\)
i.e. \(y(y-1) = 2\)
i.e. \(y = 2\) OR \(y = -1\)
NOT SIFFICIENT

Combining the two statements
\(x + y = 2\) and \(x=4\)
i.e. \(y = -2\)
SUFFICIENT

Answer: Option C

Stmnt 1: we get y=+/-2
not sufficient
stmtnt 2: we y(y+1)=2
y=2 and y=1
not sufficient

combining two stmnts:
we get y=-2 , sufficient C­

Given: x = y²

Target question: What is the value of y – x?

Statement 1: x = 4
Plug this value into our given equation, x = y², to get: 4 = y², which means EITHER y = 2 OR y = -2
Let's examine both cases:
Case a: If y = 2 and x = 4, then the answer to the target question is y - x = 2 - 4 = -2
Case b: If y = -2 and x = 4, then the answer to the target question is y - x = (-2) - 4 = -6
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x + y = 2
Subtract with y from both sides of the equation to get: x = 2 - y
Now take x = y² and replace x with 2 - y to get: 2 - y = y²
Set this equation to zero to get: y² + y - 2 = 0
Factor: (y + 2)(y - 1) = 0
So, EITHER y = 2 OR y = 1
Case a: If y = 2, then x = 4 (since it's given that x = y²). So, the answer to the target question is y - x = 2 - 4 = -2
Case b: If y = 1, then x = 1 (since it's given that x = y²). So, the answer to the target question is y - x = 1 - 1 = 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT


Statements 1 and 2 combined
Statement 1 tells us that EITHER y = 2 OR y = -2
Statement 2 tells us that EITHER y = 2 OR y = 1
When we combine the statements, we can see that it MUST be the case that y = 2
If y = 2, then x = 4 (since it's given that x = y²). So, the answer to the target question is y - x = 2 - 4 = -2
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

(1) \(x = 4\) means \(y^2 = 4\) means \(y = ±2\) means \(y - x = -2\) or \(y - x = -6\) Insufficient.

(2) \(x + y = 2\) means \(y^2 + y - 2 = 0\) means \((y + 2)(y - 1) = 0\) means \(y = 1\) or \(y = -2\). If \(y = 1\) then \(x = 1\) (and \(y - x = 0\)). If \(y = -2\) then \(x = 4\) (and \(y - x = -6\)). Insufficient.

Combining the two we get:
\(x = 4\) and \(y = -2\) therefore, \(y - x = -6\)

Hence, C.­

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.