Data Sufficiency

BTGmoderatorDC wrote:Carmen currently works 30 hours per week at her part-time job. If her gross hourly wage were to increase by $1.50, how many fewer hours could she work per week and still earn the same gross weekly pay as before the increase?

(1) Her gross weekly pay is currently $225.00.
(2) An increase of $1.50 would represent an increase of 20 percent of her current gross hourly wage.

OA D

Source: Official Guide

Say Carmen currently earns $x per hour; thus, she earns $30x per week. Now her per hour wage increased to $(x + 1.50). Thus, to earn the same gross weekly wages, she must work 30x / (x + 1.50) hours.

We have to get the value of x.

Let's take each statement one by one.

(1) Her gross weekly pay is currently $225.00.

=> 30x = 225 => x = $7.5. Sufficient

(2) An increase of $1.50 would represent an increase of 20 percent of her current gross hourly wage.

=> 30x + 20% of 30x = 30(x + 1.50)

1.2x = x + 1.50

=> x = $7.5. Sufficient

The correct answer: D

Hope this helps!

-Jay
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BTGmoderatorDC wrote:Carmen currently works 30 hours per week at her part-time job. If her gross hourly wage were to increase by $1.50, how many fewer hours could she work per week and still earn the same gross weekly pay as before the increase?

(1) Her gross weekly pay is currently $225.00.
(2) An increase of $1.50 would represent an increase of 20 percent of her current gross hourly wage.

Given: Carmen currently works 30 hours per week

Target question: If Carmen's gross hourly wage were to increase by $1.50, how many fewer hours could she work per week and still earn the same gross weekly pay as before the increase?

This is a good candidate for rephrasing the target question

Let H = Carmen's CURRENT hourly pay rate
So, 30H = Carmen's CURRENT weekly salary (since she works 30 hours each week)

H + 1.5 = Carmen's HYPOTHETICAL hourly pay rate
Let x = the number of FEWER hours Carmen can work.

Aside: our goal is to determine the value of x

So, (30 - x) = the number of hours Carmen would HYPOTHETICALLY works
So, (30 - x)(H + 1.5) = Carmen's HYPOTHETICAL weekly salary

We want the two salaries (current and hypothetical) to be equal
So, we can write: 30H = (30 - x)(H + 1.5)
Expand right side: 30H = 30H + 45 - xH - 1.5x
Subtract 30H from both sides: 0 = 45 - xH - 1.5x
Add xH and 1.5x to both sides to get: xH + 1.5x = 45
Factor left side: x(H + 1.5) = 45
Divide both sides by (H + 1.5) to get x = 45/(H + 1.5)

IMPORTANT: Our goal is to find the value of x (the number of FEWER hours Carmen can work).
Now that we know that x = 45/(H + 1.5), we can see that, in order to find the value of x, we need only find the value of H.

So, we can REPHRASE our target question to get....
REPHRASED target question: What is the value of H (Carmen's CURRENT hourly wage)?

Aside: Here's a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

Statement 1: Her gross weekly pay is currently $225.00.
So, Carmen presently earns $225 per week (after working for 30 hours)
We can write: 30H = $225
Solve: H = 225/30 = 7.5
The answer to the REPHRASED target question is H = 7.5
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Aside: For more on this idea of testing values when a statement doesn't feel sufficient, read my article: https://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: An increase of $1.50 would represent an increase of 20 percent of her current gross hourly wage.
We can write: $1.50 = 20% of Carmen's CURRENT hourly wage
In other words: $1.50 = 20% of H
Or: $1.50 = 0.20H
Solve: H = 1.5/0.2 = 15/2 = 7.5
The answer to the REPHRASED target question is H = 7.5
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent