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

Question

If x = y^2, what is the value of y – x?

(1) x = 4
(2) x + y = 2

TheKingInTheNorth · Accepted Answer

If x = y^2, what is the value of y – x?

(1) x = 4
(2) x + y = 2

Kudos for a correct solution.

st 1 --- x = 4 , given that x = y^2 
hence y^2 = 4 , y can be 2 or -2

Hence not sufficient as we are two values of y .

st 2

x + y =2 
but given that x = y^2

y^2 + y = 2

y(y + 1) = 2

here also we are getting two different value of y .hence not sufficent

together 
x=4 
x+y =2

solving them we y = -2

also the value of x =4 and y = -2 --- satisfy x = y^2

hence ans is C

BrainLab · Answer

(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

Bunuel · Answer

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.

dave13 · Answer

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

KSBGC · Answer

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.

adkikani · Answer

y^2  = 4
Take square root on both side:
|y| = 2
y = 2, -2

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

Combining both, y = -2. 
 OA:C

nkin · Answer

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

GMATinsight · Answer

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

Archit3110 · Answer

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

BrentGMATPrepNow · Answer

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

kungfury42 · Answer

(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.

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

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

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