Hi All,
This prompt gives us a changing pay rate depending on the total number of hours that John works in a given day:
1) For the first 8 hours, he earns X dollars per hour
2) For the next 4 hours after that, he earns 1.5X dollars per hour
3) For any time over 12 hours, he earns 2X dollars per hour
We're told that X is an integer. We're asked for the number of hours that John worked on Monday. TESTing VALUES will help to define the possibilities here....
1) John was paid a total of $280 for his work on Monday.
This information allows for a number of different possibilities....
IF...
X = $35
Then (8 hours)($35/hour) = $280 and the answer to the question is 8
IF...
X = $20
Then (8 hours)($20/hour) + (4 hours)($30/hour) = $280 and the answer to the question is 12
IF...
X = $14
Then (8 hours)($14/hour) + (4 hours)($21/hour) + (3 hours)($28/hour) = $280 and the answer to the question is 15
Fact 1 is INSUFFICIENT
2) If John had worked 2 additional hours, then he would have made an additional 80 dollars.
IF...
X = $40
Then any 2 additional hours (up to 8 hours) would have gained him (2 hours)($40/hour) = $80; the answer to the question is any integer 3 through 8 inclusive.
IF....
X = $20
Then (8 hours)($20/hour) + (4 hours)($30/hour) = $280 and an extra 2 hours would have gained him (2 hours)($40/hour); the answer to the question is 12
Fact 2 is INSUFFICIENT
Combined, we know...
John was paid a total of $280 for his work on Monday.
If John had worked 2 additional hours, then he would have made an additional 80 dollars.
Since John earns $X/hour for the first 8 hours, the extra two hours CANNOT have been paid at $40/hour. 7 hours at $40/hour would = $280, but working past 8 hours would have made the second 'extra' hour 1.5X (or $60/hour at that rate), which does NOT match up with the increase of $80. This means that John MUST have worked some total over 8 hours (and at a rate that was LESS than $40/hour). Based on the restriction that X is an INTEGER, the only option that 'fits' is when X = 20.
At X = 20, the John would have worked 12 hours to earn $280 (8 hours at $20/hour + 4 hours at $30/hour). The extra two hours would have been at 2X dollars/hour (or $40/hour), so the extra two hours would equal $80 total.
Combined, SUFFICIENT
Final Answer:
GMAT assassins aren't born, they're made,
Rich
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