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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, 09:01
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Difficulty:

45% (medium)

Question Stats:

57% (03:21) correct 42% (02:56) wrong based on 108 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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Kudos [?]: 17628 [9] , given: 2232

Re: At his regular hourly rate, Don had estimated the labour cos [#permalink]  31 Jul 2012, 09:21
9
KUDOS
Expert's post
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. Answer: B. Hope it's clear. _________________ Intern Joined: 01 Jan 2011 Posts: 22 Location: Kansas, USA Schools: INSEAD, Wharton Followers: 2 Kudos [?]: 5 [3] , given: 9 Re: At his regular hourly rate, Don had estimated the labour cos [#permalink] 01 Aug 2012, 09:39 3 This post received KUDOS [336][/X] - [336][/(X+4)]= 2 Solve for X. Ans= 24 since -28 is not a valid answer. Intern Joined: 26 Sep 2012 Posts: 17 Followers: 0 Kudos [?]: 6 [0], given: 1 Re: At his regular hourly rate, Don had estimated the labour cos [#permalink] 07 Dec 2012, 02:03 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. Intern Joined: 07 Feb 2013 Posts: 13 Schools: Darden GMAT Date: 03-10-2014 Followers: 0 Kudos [?]: 5 [1] , given: 9 Re: At his regular hourly rate, Don had estimated the labour cos [#permalink] 15 Jun 2013, 19:41 1 This post received KUDOS 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 Verbal Forum Moderator Joined: 10 Oct 2012 Posts: 619 Followers: 33 Kudos [?]: 468 [0], given: 133 Re: At his regular hourly rate, Don had estimated the labour cos [#permalink] 16 Jun 2013, 03:50 Expert's post 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. _________________ Intern Joined: 16 Oct 2013 Posts: 4 Followers: 0 Kudos [?]: 0 [0], given: 0 Re: At his regular hourly rate, Don had estimated the labour cos [#permalink] 07 Jan 2014, 07:41 Bunuel wrote: 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.

On my own I got to the step where I need to utilize the answer choices. I didn't know what to do at that point because it never crosses my mind to use the answer choices and backwards solve like this.

I've only ever seen this kind of method recommended when the problem involves second degree equations. Is that a fair statement? You only backwards solve like this when dealing with second degree equations?
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Kudos [?]: 3616 [0], given: 144

Re: At his regular hourly rate, Don had estimated the labour cos [#permalink]  07 Jan 2014, 21:38
Expert's post
Rdotyung wrote:
Bunuel wrote:
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

On my own I got to the step where I need to utilize the answer choices. I didn't know what to do at that point because it never crosses my mind to use the answer choices and backwards solve like this.

I've only ever seen this kind of method recommended when the problem involves second degree equations. Is that a fair statement? You only backwards solve like this when dealing with second degree equations?

You utilize the answer choices whenever you CAN. Here I would keep an eye on the choices right from the start. I would say
R*T = 336 (his regular hourly rate * time he estimated)
The options give us the value of T which is an integer.

336 = 2^4*3*7

So R*T = 336
(R-2)*(T + 4) = 336
So T as well as T+4 should be factors of 336.
If T is 28, T+4 is 32 which is not a factor of 336 so ignore it.
If T is 24, T+4 is 28. Both are factors of 336. Keep it. If T is 24, R is 14. So (R - 2) is 12. 12*28 does gives us 336 so T = 24 must be the correct answer.

But note that if you want to reduce your mechanical work, you need to be fast in your calculations. You cannot spend a minute working on every option or making calculation mistakes.
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Re: At his regular hourly rate, Don had estimated the labour cos   [#permalink] 07 Jan 2014, 21:38
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