What is the value of x? (1) y² = x (2) x + 4 = 4(y + 1)
A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. Either statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.
(E) 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 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.The possible solutions for (x,y) are (0,0) and (16,4). Since we do not have sufficient information to determine the value of x, even after combining the statements, the correct answer is choice (E).
Couldnt you use form 2 to solve for y=x/4 and then plug that into formula 1 to get (x/4)²=x which then simplifies to x=16?
Post subject: Re: Math: question 32 (Data sufficiency / Algebra).
Posted: Tue Apr 13, 2010 10:10 am
Joined: Fri Apr 09, 2010 2:11 pm Posts: 403
No, we can't do that for the same reason as described above:
if we use statement (2) to solve for y = x/4 and then plug that into formula 1 to get (x/4)² = x, we can not simplify it to x=16, because we get x² = 16x and x can be zero as well. So we get the same two possible values for x: x = 0 and x = 16 and a corresponding values of y: y = 0, y = 4.
Please, remember to check if the variable can be 0 before dividing by it.
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