Question

This data sufficiency problem consists of a question and two statements labelled (1) and (2), which contain certain data. Using these data and your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), decide whether the data given are sufficient for answering the question and then indicate one of the following answer choices:

Choose the most suitable option from the given alternatives pertaining to the sufficiency of the data provided.

What is $x$ ?
(1) $x=4y-4$
(2) $xy=8$

• A. Data in statement I alone is sufficient.
• B. Data in statement II alone is sufficient.
• C. Data in both statements together is sufficient.
• D. Data in both statements together is not sufficient.

Answer 1

The correct option is D Data in both statements together is not sufficient.

(D) Each statement alone is not enough information to solve for $x$. Using statements (1) and (2) combined, if you substitute the expression for $x$ in the first equation into the second, you get two different answers:

$x=4y-4$

$xy=(4y-4)y=8$

$4y^2-4y=8$

$y^2-y-2=0$

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

$y=\{-1,2\}$

$x=\{-8,4\}$