Carmen currently works 30 hours per week at her part-time

Hi,

I have a query with this question.

From option 1, after solving, we get that the new number of hours is 25 i.e, 5 hours less.

Option 2 states, that there was a 20% inc in the per hour wage. Can we use the concept of ratios here.
To keep total wage constant, if we increase per hour wage by 20%, we need to decrease the number of hours worked by 20% too.
=> New No. of Hours worked = 30-20%(30)= 24
This option does not provide the same answer as 1. Can you please explain the reason why ?
The relation used : Total Wage/month = No. of Hours worked * Wage/Hour

Thanks,
Sahil

We are initally given the equation x*30 = Total Salary, and then the question is if we can solve (x + 1.5) * 30 = Total Salary, so we have two unknown values we need to solve for

1) Solves total salary, so now we have one equation and one unknown, which means 1 is sufficient.
2) Gives us the ability to solve for x, so now we have one equation and one variable (Total salary), this is also sufficient.

So, D.

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)?

The video below has tips on rephrasing the target question

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

RELATED VIDEO

Rate and time have a RECIPROCAL relationship.
If the hourly rate DOUBLES, then the same income will be yielded in 1/2 the total time.

Statement 1:
Actual hourly rate \(= \frac{225}{30} =\) $7.50, implying that an additional $1.50 per hour will increase the hourly rate to $9.
\(\frac{increased-hourly-rate}{actual-hourly-rate} = \frac{9}{7.5} = \frac{18}{15} = \frac{6}{5}\)
Implication:
The same income will be yielded in \(\frac{5}{6}\) of the actual time -- a decrease of \(\frac{1}{6}\):
\(\frac{1}{6} * 30 = 5\) fewer hours.
SUFFICIENT.

Statement 2:
Since $1.50 increases the hourly rate by 20%, we get:
\(\frac{increased-hourly-rate}{actual-hourly-rate} = \frac{120}{100} = \frac{6}{5}\)
Implication:
The same income will be yielded in \(\frac{5}{6}\) of the actual time -- a decrease of \(\frac{1}{6}\):
\(\frac{1}{6} * 30 = 5\) fewer hours.
SUFFICIENT.

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