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:

If $x$ and $y$ are integers, what is the value of $x^2+2xy+y^2$?
(1) $x+y=7$
(2) $2x=\frac{28-4y}{2}$

• 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.
• E. Either of the statement I or II is sufficient.

Answer 1

The correct option is E Either of the statement I or II is sufficient.

The question stem specifies that $x$ and $y$ are integers and asks for the value of $x^2+2xy+y^2$. Since the expression is one of the common quadratic identities, write down its order form as well: ${(x+y)}^2$

(1) SUFFICIENT: The work is made much easier if you recognised the quadratic identity and wrote down both forms. Knowing the value of $x+y$ is enough to find the value of ${(x+y)}^2$.

(2) SUFFICIENT:

$2x=\frac{28-4y}{2}$

$4x=28-4y$

$4x+4y=28$

$x+y=7$