What is the value of x?

Question

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

Kudos for a correct  solution .

GMATinsight · Answer

Question : What is the value of x?

Statement 1 : y^2 = x 
No other relation between x and y is known and y is unknown so x can't be calculated. hence
 NOT SUFFICIENT

Statement 2 : (x + 4)/4 = y + 1 
i.e. x = 4y
No other relation between x and y is known and y is unknown so x can't be calculated. hence
 NOT SUFFICIENT

Combining the two statements:  
x = 4y = y^2

i.e. y^2-4y = 0
i.e. y(y-4) = 0
i.e. y = 0 or 4
i.e. x = 0 or 16
 NOT SUFFICIENT

Answer: option E

ENGRTOMBA2018 · Answer

x=?

Clearly each statement alone is not sufficient.

Thus, combining the statements we get,

y^2 = 4y ---> either y=0 or y =4

Thus we get x = y^2 = 0 or 16. Thus we get 2 values of x and hence E is the correct answer.

cutegirlsimran · Answer

statement 1 y^2 = x Not Sufficient

Statement 2 (x+4)/4= y+1 or x = 4y Not sufficient

Together y^2 = 4y

y can be 1 and y can 4 so we get two values of x so not sufficient

Hence E is the correct Answer

GMATinsight · Answer

Hi  cutegirlsimran ,

y can't be 1

y can be either 0 or 4

KS15 · Answer

Statement 1: y^2=x. Insufficient
Statement 2:(x+4)/4=y+1. Gives us values only in 2 variables x and y. Insufficient.

Using both statements,

y^2+4=4y+4
y^2=y
y^2-y=0
y(y-1)=0
y=0 or 1
Answer E

GMATinsight · Answer

Highlighted 4 has gone missing from the explanation and hence the answer has changed a bit. y = 0 or 4 are the solutions for the equation. :wink:

However, The final Answer remains same. Beauty of DS

Bunuel · Answer

800score Official Solution:

Statement (1) is insufficient: we cannot determine the value of x without knowing the value of y.

If we multiply both sides of the equation in Statement (2) by 4, we get:
x + 4 = 4(y + 1), or 
x + 4 = 4y + 4.
Subtracting 4 from both sides gives us:
x = 4y. 
This statement is also insufficient.

Combined, both statements are still insufficient. When we substitute the second equation into the first, we get:
y² = 4y.

We cannot simply divide each side of the equation by y because this is a quadratic equation, and we do not know that y is not equal to 0.

We must set the equation equal to zero and factor it:
y² – 4y = 0
y(y – 4) = 0
y = 0 or 4.

Possible solutions for (x,y) are (0,0) and (16,4). But, we aren't looking for "possible" solutions, we are interested in THE solution. Since we do not have sufficient information to determine the value of x, even after combining the statements,  the correct answer is choice (E).

bumpbot · Answer

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What is the value of x?

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