Question

A total of $60,000wasinvestedforoneyear.Partofthisamountearnedsimpleannualinterestattherateofxpercentperyear,andtherestearnedsimpleannualinterestattherateofypercentperyear.Ifthetotalinterestearnedbythe$60,000 for that year was $4,080,whatisthevalueofx?\left(1\right)$x=\cfrac{3y}{4}$
(2) The ratio of the amount that earned interest at the rate of x percent per year to the amount that earned interest at the rate of y percent per year was 3 to 2.

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

The correct option is C Both statements together are sufficient, but neither statement alone is sufficient.

• Let X be the amount invested at x percent and let Y be the amount invested at y percent, where X + Y = 60000. If determine the value of x.

1. Given that , then . Since, X + Y = 60000, then Y = 60000 - X. By substitution, becomes . However, because the value of X is unknown, it is impossible to determine a unique value for x; NOT sufficient.
2. Given that ,then and , from which the values of Y and, in turn, X can be determined. However, since the value of y in the equation is still unknown, it is impossible to determine a unique value for x; NOT sufficient.

• Taking (1) and (2) together, from the stem becomes , using the information from (1). Then, using the values of X and Y obtained from the information in (2) leaves an equation with x as the only unknown. This equation can be solved for a unique value of x.
• The correct answer is C; both statements together are sufficient.