Question

Carmen currently works 30 hours per week at her part-time job. If her gross hourly wage were to increase by $1.50,howmanyfewerhourscouldsheworkperweekandstillearnthesamegrossweeklypayasbeforetheincrease?\left(1\right)Hergrossweeklypayiscurrently$225.00.
(2) An increase of $1.50 would represent an increase of 20 percent of her current gross hourly wage.

• 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 D Each statement alone is sufficient.

• Let $w$ be Carmen’s gross hourly wage and let n be the number of hours fewer Carmen will need to work. We have to find a unique value for n such that $30w=(30-n)(w+1.50)$.
• Considering statement 1, since Carmen’s gross weekly pay is currently $\$225.00$, then $30w=225$ and $w=7.50$. Substituting $7.50$ for $w$ in the equation we can get a unique value for $n$.
• Similarly from statement 2, since $1.50$ is $20$ percent of Carmen’s current gross hourly pay, $1.50=0.20w$ and $w=7.50$ will lead to the same result as statement 1. Thus, each statement alone is sufficient.