Data Sufficiency Value Questions

A Value question asks for a numerical value (e.g., What is the value of x?). For information to be considered sufficient, that information must allow us to deduce only one value for x.

When a question states "What is the value of x?" take the words "the value" literally. A statement will only be sufficient only if it allows you to find one, and only one, value for x.

Question:

If x and y are integers, what is the sum of x2 + y?

1- x = 4

2- y²= 16

Explanation:

The Correct Answer: E

• In order for a statement to be sufficient, the data from the statement must ensure that there is one-and-only-one value for the expression x² + y. If there are multiple possible values for this expression, then the statement is not sufficient.
• Evaluating Statement (1), we can substitute and write the equation: 4² + y. However, this is not sufficient because if y = 0, x² + y = 4² + 0 = 16 but if y = 1, x² + y = 4² + 1 = 17. Since there are two possible legitimate values for the expression given the information from Statement (1), Statement (1) is NOT SUFFICIENT.
• Evaluating Statement (2), we know that y is 4 or -4. We know now that the equation is x² + 4 or x² - 4. However, this statement is not sufficient because if x = 0, the equation could evaluate to 0² + 4 = 4 or 0² - 4 = -4. Since the information from Statement (2) does not allow us to determine one value for the expression, Statement (2) is NOT SUFFICIENT.
• When examining Statement (1) and (2) together, we know that the x = 4 and y = 4 or -4. However, these two statements are not sufficient because the expression could evaluate to 4² + 4 = 20 or 4² - 4 = 12. Statements (1) and (2), even when taken together, are NOT SUFFICIENT.