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# At his regular hourly rate, Don had estimated the labour cos

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At his regular hourly rate, Don had estimated the labour cos [#permalink]  31 Jul 2012, 10:01
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63% (03:47) correct 36% (02:09) wrong based on 33 sessions
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
[Reveal] Spoiler: OA
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Re: At his regular hourly rate, Don had estimated the labour cos [#permalink]  31 Jul 2012, 10:21
5
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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

Say the regular hourly rate was r\$ and estimated time was t hours, then we would have:

rt=336 and (r-2)(t+4)=336;

So, (r-2)(t+4)=rt --> rt+4r-2t-8=rt --> t=2r-4.

Now, plug answer choices for t and get r. The pair which will give the product of 336 will be the correct answer.

Answer B fits: if t=24 then r=14 --> rt=14*24=336.

Hope it's clear.
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Re: At his regular hourly rate, Don had estimated the labour cos [#permalink]  01 Aug 2012, 10:39
2
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[336][/X] - [336][/(X+4)]= 2

Solve for X.

Ans= 24 since -28 is not a valid answer.
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Re: At his regular hourly rate, Don had estimated the labour cos [#permalink]  07 Dec 2012, 03:03
I have just worked on OG Math practice questions and hardly have I solved this question. That's why I have used Google and found you guys
sayak636 wrote:
[336][/X] - [336][/(X+4)]= 2
I have composed the same equation, however its solving has taken me for ages.

I like Bunuel's solution, but I has not guessed to do the same. I'd only slightly change the course of solving. When we get to t = 2r - 4, r easily seems to be replaced by 336/t. Now we have t = (2*336/t) - 4 and can plug answer choices to find out the correct option.
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Re: At his regular hourly rate, Don had estimated the labour cos [#permalink]  15 Jun 2013, 20:41
While substitution does tend to take long for this problem, before substitution you could
factorize 336 to its primes = 2*2*2*2*3*7

Now you can begin to substitute : Ans
Choice A = 28*12 (2*2*7*2*2*3) not equal to 32*10 (clearly its 320 and not 336)
Choice B = 24*14 (2*2*2*3*2*7) equals 28*12 (from prev choice)

thx
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Re: At his regular hourly rate, Don had estimated the labour cos [#permalink]  16 Jun 2013, 04:50
Shiv636 wrote:
[336][/X] - [336][/(X+4)]= 2

Solve for X.

Ans= 24 since -28 is not a valid answer.

Infact, one doesn't need to solve after this step too:

\frac{336}{x} - \frac{336}{(x+4)} = 2

336[(x+4)-x] = 2*x(x+4)

x(x+4) = 672

From the given options, we can straightaway eliminate A and C, as because the units digit after multiplication of 28*(28+4) and 16*(16+4) will never be 2.

We also know that 14*20 = 280 and 12*20 = 240. Thus, 14*18(D) or 12*16(E) can never equal 672.

By eliminaion, the answer is B.
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All that is equal and not --> inequalities-basics-154285.html

Re: At his regular hourly rate, Don had estimated the labour cos   [#permalink] 16 Jun 2013, 04:50
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