macjas wrote:
At his regular hourly rate, Don had estimated the labour 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?
(A) 28
(B) 24
(C) 16
(D) 14
(E) 12
STRATEGY: Upon reading any GMAT Problem Solving question, we should always ask, Can I use the answer choices to my advantage?
In this case, we can easily test the answer choices.
Now let's give ourselves up to 20 seconds to identify a faster approach.
In this case, we can also follow the conventional algebraic approach, but I think testing answer choices will be faster (and less prone to algebraic errors)GMAT-specific approach: Testing the answer choices
Let’s start by testing answer choice C, the middle value. . .
(C) 16. This tells us that Don originally estimated the job would take 16 hours.
Hourly rate = (total labor cost)/(number of hours worked) = $336/16 =
$21/hourIf the job took
4 extra hours, then Don worked 20 hours, which means his actual hourly rate = $336/20 = 84/5 =
$16.80/hour (check out the video below on dividing numbers by 5 in your head)
$21/hour -
$16.80/hour ≈
$4 per hour So, testing choice C resulted in a rate difference of approximately
$4 per hour, whereas the question tells us the rate difference is only $2 per hour.
This bigger-than-needed difference tells us that Don’s estimated work time must have been
more than 16 hours, since this would reduce the effect of the 4 extra hours (and thus a smaller difference).
Since we need Don's estimated work time to be
more than 16 hours, we can eliminate answer choices C, D, and E.
Now let’s test choice B. . . .
(B) 24. This tells us that Don originally estimated the job would take 24 hours.
Estimated hourly rate = $336/24 =
$14/hourIf the job took 4 extra hours, then Don worked 28 hours, which means his actual hourly rate = $336/28 =
$12/hourSo, the difference in hourly rates =
$14/hour -
$12/hour =
$2/hour. Perfect!!
Answer: B.
Conventional approach: Assign variables, create equation, solve equation
Let
h = # of hours that Don ESTIMATED for the job.
So,
h + 4 = ACTUAL # of hours it took Don to complete the job.
Hourly rate = (total labor cost)/(number of hours worked)So, IF Don, had completed the job in h hours, his RATE would have been
$336/hHowever, 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, we can substitute values to get:
$336/h - 2 = $336/(h + 4)IMPORTANT: Since the above equation will be a pain to solve, you might consider plugging in the answer choices to see which one works. Okay, let's solve this thing:
$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) = 336hExpand:
336h + 1344 - 2h² - 8h = 336hSimplify:
-2h² - 8h + 1344 = 0Multiply both sides by -1 to get:
2h² + 8h - 1344 = 0Divide both sides by 2 to get:
h² + 4h - 672 = 0Factor (yeeesh!) to get:
(h - 24)(h + 28) = 0Solve to get:
h = 24 or h = -28Since h cannot be negative (in the real world), h must equal 24.
Answer: B
RELATED VIDEO - Shortcut for Dividing by 5