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OG16 - PS 162
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amina.shaikh309
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Brent@GMATPrepNow
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Here's an algebraic solution:At his regular hourly rate, Don had estimated the labor cost of a repair job as $336 and he was paid that amount. However, the job took 4 hours longer than he had estimated and, consequently, he earned 2$ per hour less than his regular hourly rate. What was the time Don had ESTIMATED for the job, in hours?
28
24
16
14
12
Let h = # of hours that Don ESTIMATED for the job.
So, h + 4 = ACTUAL # of hours it took Don to complete the job.
So, IF Don, had completed the job in h hours, his RATE would have = $336/h
However, since Don completed the job in h+4 hours, his RATE was actually = $336/(h + 4)
...consequently, he earned 2$ per hour less than his regular hourly rate.
In other words, (John's estimated rate) - 2 = (John's actual rate)
So, $336/h - 2 = $336/(h + 4)
ASIDE: since the above equation is a bit of a pain to solve, you might consider plugging in the answer choices to see which one works.
Okay, let's solve this: $336/h - 2 = $336/(h + 4)
To eliminate the fractions, multiply both sides by (h)(h+4) to get: 336(h+4) - 2(h)(h+4) = 336h
Expand: 336h + 1344 - 2h² - 8h = 336h
Simplify: -2h² - 8h + 1344 = 0
Multiply both sides by -1 to get: 2h² + 8h - 1344 = 0
Divide both sides by 2 to get: h² + 4h - 672 = 0
Factor (yeeesh!) to get: (h - 24)(h + 28) = 0
Solve to get: h = 24 or h = -28
Since h cannot be negative (in the real world), h must equal 24.
Answer: B
Cheers,
Brent
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We can PLUG IN THE ANSWERS, which represent the estimated time: 28, 24, 16, 14, or 12.At his regular hourly rate, Don had estimated the labor cost of a repair job as $336 and he was paid that amount. However, the job took 4 hours longer than he had estimated and, consequently, he earned 2$ per hour less than his regular hourly rate. What was the time Don had estimated for the job, in hours?
28
24
16
14
12
The actual time was 4 hours longer: 32, 28, 20, 18, or 16.
Both the estimated time and the actual time must divide evenly into 336 (the labor cost).
Since 336 is not a multiple of 32, eliminate A.
Since 336 is not a multiple of 20, eliminate C.
336 is not a multiple of 9, since the sum of its digits is not a multiple of 9.
Thus, 336 is not a multiple of 18; eliminate D.
The correct answer must be B or E.
Answer choice B: estimated time = 24, actual time = 28
Estimated payrate = 336/24 = 14.
Actual payrate = 336/28 = 12.
Difference = 14-12 = 2.
Success!
The correct answer is B.
Note that we had to try only ONE answer choice -- a very efficient way to solve the problem.
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If we've got
336 = x * y
and
336 = (x + 4) * (y - 2)
We could factor 336 to look for solutions. Since the answers are likely to have both the time and the hourly rate (in an attempt to trap us if we're not careful), we might cheat with them and assume that they multiply to our number ... which, of course, they do!
336 = 28 * 12
336 = 24 * 14
Since Don's estimate had a lower time and a higher hourly rate, his estimate must've been 24 * 14. We want the time, which must be LOWER than the time in the other equation, so our answer is 24.
336 = x * y
and
336 = (x + 4) * (y - 2)
We could factor 336 to look for solutions. Since the answers are likely to have both the time and the hourly rate (in an attempt to trap us if we're not careful), we might cheat with them and assume that they multiply to our number ... which, of course, they do!
336 = 28 * 12
336 = 24 * 14
Since Don's estimate had a lower time and a higher hourly rate, his estimate must've been 24 * 14. We want the time, which must be LOWER than the time in the other equation, so our answer is 24.
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Hi All,
We’re told that Don was paid $336 for an hourly-rate for a job that he estimated would take a certainly number of hours. However, the job took 4 hours LONGER than estimated, which means he was actually paid $2/hour LESS than his normal hourly-rate for the job. We’re asked for the original number of hours that Don estimated the job would take. This question can be approached in a couple of different ways, including by TESTing THE ANSWERS.
Since the extra 4 hours spent working only decreased his normal hourly-rate by $2/hour for the job, we should start by TESTing one of the larger numbers (since the smaller the ratio of 4 hours to the original estimated time, the less impact that 4 hours would have on the average). Let’s TEST Answer B…
Answer B: 24 hours.
IF… the original estimate was 24 hours to complete the job, then Don’s hourly pay would have been $336/24 = 14 dollars/hour.
The extra 4 hours would increase the total time to 24+4 = 28 hours. In this situation, Don’s hourly pay would have been $336/28 = 12 dollars/hour. This is an exact MATCH for what we were told, so this MUST be the answer.
Final Answer: B
GMAT Assassins aren’t born, they’re made,
Rich
We’re told that Don was paid $336 for an hourly-rate for a job that he estimated would take a certainly number of hours. However, the job took 4 hours LONGER than estimated, which means he was actually paid $2/hour LESS than his normal hourly-rate for the job. We’re asked for the original number of hours that Don estimated the job would take. This question can be approached in a couple of different ways, including by TESTing THE ANSWERS.
Since the extra 4 hours spent working only decreased his normal hourly-rate by $2/hour for the job, we should start by TESTing one of the larger numbers (since the smaller the ratio of 4 hours to the original estimated time, the less impact that 4 hours would have on the average). Let’s TEST Answer B…
Answer B: 24 hours.
IF… the original estimate was 24 hours to complete the job, then Don’s hourly pay would have been $336/24 = 14 dollars/hour.
The extra 4 hours would increase the total time to 24+4 = 28 hours. In this situation, Don’s hourly pay would have been $336/28 = 12 dollars/hour. This is an exact MATCH for what we were told, so this MUST be the answer.
Final Answer: B
GMAT Assassins aren’t born, they’re made,
Rich
