Jakes regular hourly wage is twice of Kevins regular hourly wage, bu

Question

Jake’s regular hourly wage is twice of Kevin’s regular hourly wage, but Kevin gets paid at thrice his regular wage for any hours he works on weekends while Jake earned the same. Both men work an integer number of hours on any given day. If Jake and Kevin each worked for the same total non-zero number of hours last week, and earned the same total in wages, which of the following must be true?

I. Jake worked fewer hours Monday through Friday than did Kevin.
II. Kevin worked at least one hour on the weekend.
III. Kevin made more money on the weekend than Jake did.

A. I only
B. II only
C. I and II only
D. I and III only
E. II and III only

MMH91 · Answer

Jake’s regular hourly wage is twice of Kevin’s regular hourly wage, but Kevin gets paid at thrice his regular wage for any hours he works on weekends while Jake earned the same. Both men work an integer number of hours on any given day. If Jake and Kevin each worked for the same total non-zero number of hours last week, and earned the same total in wages, which of the following must be true?

I. Jake worked fewer hours Monday through Friday than did Kevin.
II. Kevin worked at least one hour on the weekend.
III. Kevin made more money on the weekend than Jake did.

A. I only
B. II only
C. I and II only
D. I and III only
E. II and III only

Hi,
please correct me if my solution is not correct:

Jake's total wage through a week
2x(t) for t hours of work

Kevin's total wage through a week
(x)(t1) for t1 hours of work from monday to friday
(3x)(t2) for t2 hours of work for saturday and sunday
we now that t1+t2=t

Because the total wages are the same for kevin and Jake
then we have:
(x)(t1)+(3x)(t2)=(2x)(t)
X(t1+3t2)=2X(t)
x(t1+t2+2t2)=2xt , t1+t2=t
x(t+2t2)=2xt
t2=t/2 , t1==t/2

so the answer is B

workingtowardit · Answer

Hi

My approach was this.

If Jake makes 10$ during the week and Kevin makes 5$, then Kevin makes 15$ at the weekend. If they both worked for 10 hours this week then:

S1: Jake worked 9 Hours during the week = 90$ and Kevin worked 8 hours so 40$. That means total earned during the week is 100$ Jake and 70$ Kevin. Untrue.
S2: Since Jake earns double during the week, Kevin has to work atleast an hour during the weekend to make up the same amount. So True.
S3: Using solve of S1 we can see that this statement can be true or untrue. Also we don't know how long Kevin worked for over the weekend although it doesn't really matter. Jake could work 10 hours and make 100$ throughout the week, but since we don't know the cut, we can't tell for sure.

I don't know if this approach is legit though.

Answer: B

Bunuel · Answer

Similar question to practice: https://gmatclub.com/forum/alan-s-regul ... 05600.html

mysterymanrog · Answer

We can solve using some nice numbers, as this is a MUST be true question:
Let Jake earn 2 dollars, and Kevin will thus earn 1 dollar on weekends and 3 dollars on weekends.

Roman Numeral 1)
->Jake worked fewer hours than Kevin did on the weekdays
We can see that it is false:
Suppose Jake worked 6 hours on the weekdays, 0 hours on the weekends, earning a total of 12 Dollars (6*2)
Kevin will then work 3 hours on the weekdays, and 3 hours on the weekends earning (3*1+3*3)=12, same as Jake

Eliminate answer choices A,C,D. 
Now we must only look at 3 (if 3 is true, it must be E, otherwise B)

Roman Numeral 3)
->Kevin made more money on the weekend than Jake did. 
We can actually use our previous example, and simply reverse it. Let Jake now work 6 hours on the weekends, and 0 hours on the weekdays, with the same calculations.

Therefore, 3 is not always true, and the answer must be B.

WiziusCareers1 · Answer

1. Set Up the Variables 
Let's define the hourly wages and the hours worked for both Jake and Kevin:
Kevin’s regular hourly wage: w
Jake’s regular hourly wage: 2w (since it is twice Kevin's)
Total hours worked by each: H (given as the same total non-zero number)
Kevin’s weekend hours: hkw
Jake’s weekend hours: hjw
​Kevin’s weekday hours (Mon-Fri): H − hkw
Jake’s weekday hours (Mon-Fri): H − hjw
​

2. Determine Hourly Rates 
Based on the prompt, the pay structures are as follows:
Jake: Earns 2w for both weekday and weekend hours.
Kevin: Earns w for weekday hours and 3w (thrice his regular wage) for weekend hours.

3. Equate Total Earnings 
The problem states they earned the same total amount last week. We set up an equation where Jake's total earnings equal Kevin's:

Jake’s Total = 2w(H)
Kevin’s Total = w(H − hkw) + 3w(hkw)
Since their earnings are equal:
2wH = w(H − hkw) + 3w(hkw)

Divide the entire equation by w (since w is a non-zero wage):
2H = H − hkw + 3hkw
2H = H + 2hkw
H = 2hkw
​ 
This tells us that Kevin’s weekend hours (hkw) must be exactly half of his total hours (H).

4. Evaluate the Statements

I. Jake worked fewer hours Monday through Friday than did Kevin. 
We know Kevin’s weekday hours are H − hkw = H − 0.5H = 0.5H.

We do not have any information about when Jake worked his hours. Jake earns 2w regardless of the day. He could have worked all his hours on Monday, or all on Sunday; it would not change his total earnings or the equality of the equation.

Therefore, this is not necessarily true.

II. Kevin worked at least one hour on the weekend. 
From our derived equation H = 2hkw, we can see that hkw = H/2.

The problem states they worked a "non-zero number of hours" (H>0).

If H is a positive integer, then hkw must be a positive value. Since they work an integer number of hours, Kevin must have worked at least some time on the weekend to reach that H/2 value.

Therefore, this must be true.

III. Kevin made more money on the weekend than Jake did.

Kevin’s weekend earnings = 3w × hkw = 3w(0.5H) = 1.5wH.

Jake’s weekend earnings = 2w × hjw.

Since we don't know how many hours Jake worked on the weekend (hjw), his weekend earnings could be anything from 0 (if he worked only weekdays) to 2wH (if he worked only weekends).

Therefore, this is not necessarily true.

Correct Answer: B. II only

Jakes regular hourly wage is twice of Kevins regular hourly wage, bu

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Jakes regular hourly wage is twice of Kevins regular hourly wage, bu

Prep Toolkit

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