Question

On a certain date, Hannah invested $5,000atxpercentsimpleannualinterestandadifferentamountatypercentsimpleannualinterest.WhatamountdidHannahinvestatypercentsimpleannualinterest?\left(1\right)ThetotalamountofinterestearnedbyHanna{h}^{\prime }stwoinvestmentsinoneyearwas$900.
(2) Hannah invested the $5,000 at 6 percent simple annual interest.

• 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 E Statements (1) and (2) together are not sufficient.

Let $A be the amount that Hannah invested at y percent. From statement 1, given that the sum of and is $\$900$, or , it is clear that more than one value of A is possible. Thus, statement 1 is insufficient. From statement 2, given that $x=6$, it is clear that more than one value of A is possible. Thus, statement 2 is also insufficient. We get multiple vales of A even after combining both the statements.