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# Jake’s regular hourly wage is twice of Kevin’s regular hourly wage, bu

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Manager
Joined: 31 Oct 2018
Posts: 77
Location: India
Jake’s regular hourly wage is twice of Kevin’s regular hourly wage, bu  [#permalink]

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25 Apr 2019, 07:00
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Difficulty:

95% (hard)

Question Stats:

18% (02:52) correct 82% (02:27) wrong based on 44 sessions

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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 & II only
D. I & III only
E. II & III only
Intern
Joined: 16 Nov 2015
Posts: 36
Location: United Kingdom
Concentration: Social Entrepreneurship, Other
GMAT 1: 670 Q44 V38
Re: Jake’s regular hourly wage is twice of Kevin’s regular hourly wage, bu  [#permalink]

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28 Apr 2019, 15:24
Answer B but not sure if my my method is ideal.

"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."

Let's calculate the maximum amount they will make in a week if they work 24 hours a day.

Kevin - (\$1/hour)
Jake - (\$2/hour)

Kevin - Monday to Friday (\$1 *120 (120 hours represents 24 hours a day for 5 days, so basically how much he makes from Monday to Friday)) . On Saturday, he earns 3 times his hourly wage. So if he works maximum hours on Saturday and Sunday, that is \$3 * 48 = *144.
So in a week, Kevin makes \$264.

Jake -Same method, however on Saturday and Sunday, he earns the same salary unlike Kevin. Monday to Friday (\$2 * 120 = \$240). Saturday and Sunday (\$2 * 48= \$96) . Total in a week is \$336

So now let's answer the questions.
Based on my above calculation, 'Statement I' is out as it's clear Jake earns more.
'Statement II' is true because in order for Kevin to begin to make as much as Jake, he has to work on weekends because even if he worked a maximum between Monday to Friday, if Jake worked the same amount, their salary will not be equal.

Now it's between statement answer choice B and E.

Statement III is wrong only because Kevin could've worked less on the weekend and Jake could have worked more hours and thus, made more money than Kevin. And Jake could've worked significantly less than Kevin during the week, and weighing the amount the work in the week and weekend, would equal the same pay.
Manager
Joined: 09 Nov 2015
Posts: 154
Jake’s regular hourly wage is twice of Kevin’s regular hourly wage, bu  [#permalink]

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01 May 2019, 08:24
Let \$1/hr be Kevin's regular wage. Then his weekend wage is \$3/hr and Jake's wage is \$2/hr (both on weekdays and weekends).
Let's assume Kevin worked 'x' hours Monday through Friday and 'y' hours in the weekend which means he worked for a total of (x+y) hrs last week. So Kevin's earning is \$x+\$3y.
Since Jake worked the same number of hours as Kevin he earned \$2(x+y) last week. Since their total earnings for the week were the same:
\$x+\$3y=\$2(x+y)---> x=y. That is, Kevin worked the same number of days during the weekend and the weekdays. So if Kevin worked 'h' hrs on the weekend he also worked 'h' hours Monday thru Friday and earned \$1*h+\$3*h= \$4h in the whole week working 2h hrs in total. Since it is given that Jake worked the same number of hours as Kevin, he too worked 2h hrs earning \$2*2h= \$4h. So we see that, since Jake earns a flat rate, he can distribute his total workload of 2h hrs between the weekdays and the weekend any way he wants and still earn the same amount of money as Kevin.

I. JAKE WORKED FEWER HOURS MONDAY THROUGH FRIDAY THAN DID KEVIN
Let's say Kevin worked a total of 10 hours during the weekdays which means he worked a 20 hours during the entire week. In that case, Jake also worked 20 hours of which he could have worked 12 hours during the weekdays and 8 hours during the weekend. So (I) is not necessarily true.

II. KEVIN WORKED AT LEAST ONE HOUR ON THE WEEKEND
This is obviously true - otherwise he wouldn't have worked at all or he would have worked a fraction of an hour, neither of which is possible because it is stipulated that (a) they worked for a "non-zero" number of hours; and (b) both men work an "integer number of hours on any given day".

III. KEVIN MADE MORE MONEY ON THE WEEKEND THAN JAKE DID
As before, let's assume that Kevin worked 10 hours on the weekend which means he earned \$30. Since Kevin worked the same number of hours on the weekend and the weekdays he worked for a total of 20 hours during the whole week which means Jake also worked 20 hours. Of this 20 hours Jake could have worked for 16 hours on the weekend and 4 hours on the weekdays. So he would have earned \$32 on the weekend which is more than the \$30 that Kevin earned. So (III) is not necessarily true.

Jake’s regular hourly wage is twice of Kevin’s regular hourly wage, bu   [#permalink] 01 May 2019, 08:24
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