[email protected] wrote:Alan's regular hourly wage is 1.5 times Barney's regular hourly wage, but Barney gets paid at twice his regular wage for any hours he works on Saturday. Both men work an integer number of hours on any given day. If Alan and Barney 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. Alan worked fewer hours Monday through Friday than did Barney.
II. Barney worked at least one hour on Saturday.
III. Barney made more money on Saturday than did Alan.
I only
II only
I and II only
I and III only
II and III only
Let Barney's wage Monday through Friday = $2 per hour.
Barney's Saturday wage = 2*2 = $4 per hour.
Alan's wage = (1.5)*2 = $3 per hour.
Alan's wage is HALFWAY between Barney's two wages.
Thus, for Barney to work the same amount of time as Alan and to earn the same AVERAGE wage as Alan, Barney MUST work for HALF his time at $2 per hour (Monday through Friday) and for HALF his time at $4 per hour (on Saturday), so that his AVERAGE wage = $3 per hour.
Thus, II must be true: Barney must work at least 1 hour on Saturday.
Eliminate any answer choice that does not include II.
Eliminate A and D.
To evaluate I and III, plug in for the number of hours worked.
Try to show that I and III do NOT have to be true.
Let the time worked = 2 hours.
Amount earned by Alan = 2*3 = $6.
Barney works for 1 hour Monday through Friday and for 1 hour on Saturday -- for a total of 2 hours -- earning 2+4 = $6.
Same number of hours for each, same total earnings for each.
I. Alan worked fewer hours Monday through Friday than did Barney.
Since it's possible that Alan worked for 2 hours Monday through Friday while Barney worked for only 1 hour Monday through Friday, eliminate any answer choice that includes I.
Eliminate C.
III. Barney made more money on Saturday than did Alan.
Since it's possible that Alan worked for 2 hours on Saturday -- earning $6 -- while Barney worked for only 1 hour on Saturday -- earning $4 -- eliminate any answer choice that includes III.
Eliminate E.
The correct answer is
B.
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