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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?(1)Hergrossweeklypayiscurrently225.00.
(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.
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B
Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
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C
Both statements together are sufficient, but neither statement alone is sufficient.
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D
Each statement alone is sufficient.
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E
Statements (1) and (2) together are not sufficient.
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Solution

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=(30n)(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.

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