Hi All,
This question is more of a logic question than anything else (although you can TEST VALUES to prove what MUST be true)
We're given the hourly pay rates for Alan and Barney:
Alan = 1.5X
Barney = X
Barney (on Saturday) = 2X
We're told that each person work an integer number of hours on any given day and that each work the SAME NUMBER OF HOURS and earned the SAME TOTAL PAY. We're asked which of the 3 Roman Numeral MUST be true (which really means "which of the following is ALWAYS TRUE no matter how many examples you come up with?")
Before we look at the Roman Numerals though, we should take a moment to review the situation. What would have to happen for the two people to work the SAME NUMBER OF HOURS and earn the SAME TOTAL PAY? Alan makes more money per hour than Barney EXCEPT on Saturdays, so Barney MUST have worked some Saturday hours (otherwise the total pay for each would have been different. Keep THAT in mind when working through the 3 Roman Numerals.
I. Alan worked fewer hours Monday-Friday than did Barney.
We know that Barney worked some hours on Saturday, but Alan COULD have worked on ANY day. Thus, this statement isn't necessarily true.
We can prove it by TESTing VALUES
Alan: works 2 hours on Friday = 2(1.5X) = 3X in pay
Barney: works 1 hour on Friday and 1 hour on Saturday = 1(X) + 2(X) = 3X in pay
Same total hours, same total pay
Alan did NOT worker fewer hours Monday-Friday than Barney
#1 is NOT necessarily true.
II. Barney worked at least one hour on Saturday.
We determined this already; this MUST be true.
III. Barney made more money on Saturday than did Alan.
If we use the example from Roman Numeral 1 and shift Alan's work to Saturday, then we can prove that this statement is NOT necessarily true.
Alan: works 2 hours on Saturday = 2(1.5X) = 3X in pay
Barney: works 1 hour on Friday and 1 hour on Saturday = 1(X) + 2(X) = 3X in pay
Alan on Saturday = 3X
Barney on Saturday = 2X
#3 is NOT necessarily true.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
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