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At his regular hourly rate, Don had estimated the labor cos  [#permalink]

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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?

(A) 28
(B) 24
(C) 16
(D) 14
(E) 12
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Re: At his regular hourly rate, Don had estimated the labor cos  [#permalink]

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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 $$r=14$$ --> $$rt=14*24=336$$. Answer: B. Hope it's clear. _________________ Veritas Prep GMAT Instructor G Joined: 01 Jul 2017 Posts: 81 Location: United States Concentration: Leadership, Organizational Behavior At his regular hourly rate, Don had estimated the labor cos [#permalink] ### Show Tags 29 1 18 Let's talk strategy here. Many explanations of Quantitative questions focus blindly on the math, but remember: the GMAT is a critical-thinking test. For those of you studying for the GMAT, you will want to internalize strategies that actually minimize the amount of math that needs to be done, making it easier to manage your time. The tactics I will show you here will be useful for numerous questions, not just this one. My solution is going to walk through not just what the answer is, but how to strategically think about it. As a result, I might write out some steps that I would normally just do in my head on the GMAT, but I want to make sure everyone sees the complete approach. Ready? Here is the full "GMAT Jujitsu" for this question: First, the problem obviously gives us different rates and times. Since $$Amount = Rate * Time$$, the initial situation can be expressed as $$336 = R*T$$. The adjusted situation (using $$R$$ and $$T$$ to represent the initial amounts) would be $$336 = (R-2)(T+4)$$. Since this is a system of two equations, we can substitute chunks of one to eliminate what we don’t want to see in the other. There is a natural temptation to substitute the $$R*T$$ in the first equation for the $$336$$ in the other. However, this doesn’t get rid of either variable – in fact, it gets rid of a number. Substituting in this way would only get us down to a smaller equation, but still with two variables. Our “target” for this equation is $$T$$, so let’s eliminate $$R$$. If $$336 = R*T$$, then $$R = \frac{336}{T}$$ and $$336=(\frac{336}{T}-2)(T+4)$$ Multiplying both sides by $$T$$ gives us: $$336T=(336-2T)(T+4)$$ Foiling this out gives us: $$336T=336T+336(4)-2T^2-8T$$ This simplifies to: $$T^2+4T=2(336)$$ At this stage, there is another temptation to bring everything over to one side so we can have it in simplified quadratic form. However, factoring this quadratic might be a little messy. I like to call math like this “Mathugliness” in my classes. Whenever it looks like the math is getting ugly, try looking for other, more conceptual ways to approach the problems. After all, the GMAT is critical-thinking test, not a “let’s-see-if-you-can-solve-obnoxious-math-the-long-way-around” test. Incidentally, notice that I didn’t multiply large numbers out when I simplified the equations above. Multiplying just makes bigger numbers, so I avoid that until I have to. This not only saves time, it also allows me to more easily see factors. Now, one underutilized tool for many test takers is what I call “Look Out Below!” Use your answer choices as assets you can leverage to think about the question. With this problem, we have really pretty, integer answers that need to be plugged into otherwise messy math. And one of them is the right answer. You can use this to your advantage. Since our equation above simplifies down to $$T(T+4)=2(336)$$, we can plug in values into our equation, and see which ones work. In this case, it is really easy. Answer choice “C” is way too small, since $$(16)(16+4) = 16*20=320$$. “D” and “E” resolve to even small numbers. All three answers can be quickly eliminated. Answer choice "A" also fails, but for a different reason: The units digit if $$T=28$$ doesn’t even work out in our formula $$(T)(T+4) = 2(336)$$. (The units digit of 28*32 is "6", but the units digit of 2*336 is "2". You don't need to do any more math than that!) The only answer remaining is "B", which is the right answer. On the GMAT, I wouldn't even look any further. However, it might be useful here to prove why "B" works, from a critical-thinking perspective. If $$T=24$$, then $$24(28)$$ should be equal to $$2(336)$$. Instead of multiplying this out – which just makes bigger numbers and takes unnecessary time – it is easier to factor the numbers, trying to turn $$2(336)$$ into $$24(28)$$. Our goal, therefore, is to factor out a $$12$$ out of $$336$$. This is a piece of cake. After all, $$336=6(50+6)=6(2)(25+3) = 12*28$$. And $$24(28) = 2(12*28)$$. We are done without doing any messy multiplication. It matches perfectly. “B” is definitely our answer. Now, let’s look back at this problem from the perspective of strategy. This question can teach us several patterns seen throughout the GMAT. First, the GMAT tries to bait you into doing math the long way around. But if you use the answer choices as part of the analysis of the problem, look for common factors, and intelligently use math in a strategic way, you can avoid a lot of "Mathugliness!" That is how you think like the GMAT. _________________ Aaron Pond Veritas Prep Teacher of the Year Hit "+1 Kudos" if this post helped you understand the GMAT better. Visit me at https://www.veritasprep.com/gmat/aaron-pond/ if you would like to learn even more "GMAT Jujitsu"! ##### Most Helpful Community Reply Intern  Joined: 01 Jan 2011 Posts: 16 Location: Kansas, USA Schools: INSEAD, Wharton Re: At his regular hourly rate, Don had estimated the labor cos [#permalink] ### Show Tags 23 2 [/X] - [/(X+4)]= 2 Solve for X. Ans= 24 since -28 is not a valid answer. ##### General Discussion Intern  Joined: 26 Sep 2012 Posts: 14 Re: At his regular hourly rate, Don had estimated the labor cos [#permalink] ### Show Tags 3 1 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: [/X] - [/(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: 10 GMAT 1: 650 Q48 V32 GMAT 2: 730 Q49 V41 WE: Engineering (Other) Re: At his regular hourly rate, Don had estimated the labor cos [#permalink] ### Show Tags 3 3 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 B Joined: 10 Oct 2012 Posts: 583 Re: At his regular hourly rate, Don had estimated the labor cos [#permalink] ### Show Tags 7 6 Shiv636 wrote: [/X] - [/(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: 3 Re: At his regular hourly rate, Don had estimated the labor cos [#permalink] ### Show Tags 1 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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Re: At his regular hourly rate, Don had estimated the labor cos  [#permalink]

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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 labor cos  [#permalink]

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How do you go from

> 336[(x+4)-x] = 2*x(x+4)
to > x(x+4) = 672?
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Re: At his regular hourly rate, Don had estimated the labor cos  [#permalink]

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gciftci wrote:
How do you go from

> 336[(x+4)-x] = 2*x(x+4)
to > x(x+4) = 672?

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

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

x and -x get cancelled to give:

$$336 *  = 2 * x * (x+4)$$

Divide both sides by 2.
$$336 * 2 = x * (x+4)$$

$$672 = x * (x+4)$$
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Re: At his regular hourly rate, Don had estimated the labor cos  [#permalink]

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VeritasPrepKarishma wrote:

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?
[/quote]

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.[/quote]

Hi Karishma, Why do T and T+4 have to be factors of 336? Why cannot rate be a fraction and difference of two fractions can yield an integer in this case 2? What am I missing here? Thanks!
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Re: At his regular hourly rate, Don had estimated the labor cos  [#permalink]

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MensaNumber wrote:

Hi Karishma, Why do T and T+4 have to be factors of 336? Why cannot rate be a fraction and difference of two fractions can yield an integer in this case 2? What am I missing here? Thanks!

All the options are integers so value of T must be an integer. So T+4 must be an integer too. Therefore, T and T+4 must be factors of 336. Also, in GMAT, usually numbers are easy since you do not get calculators. So very rarely will you find that rate or time is a fraction. Even if it will be, it will be a simple fraction such as 1/2 etc.
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Re: At his regular hourly rate, Don had estimated the labor cos  [#permalink]

Let t be the hourly rate and p the price: t * p = $336 Additional 4 hours and$2 less per hour would yield: (t+4) * (p-2) = $336 Since both equations are equal: 336 : p = (336 : (p-2))-4 Solving for p yields 14 (the other solution is negative, so we do not consider it) At this point probably we are very pressed on time, so the shortcut is to find the answer the last digit of which multiplied by 4 yields 6. 14 squared is not 336 so by elimination it is 24 Answer: B Senior Manager  Status: Math is psycho-logical Joined: 07 Apr 2014 Posts: 402 Location: Netherlands GMAT Date: 02-11-2015 WE: Psychology and Counseling (Other) Re: At his regular hourly rate, Don had estimated the labor cos [#permalink] ### Show Tags 2 1 I back solved this one like this: I started with option A, but I will only show the correct option, which is B: I said that r*t=336, so the amount of hours he worked times the money he got for each hour should be his final salary. Then I substituted the proposed times for t: r*24=336 r=14 --> This is how much he should have got per hour worked. But he worked 4 hours more, so 24+2 = 28. Then he actually got 336/28 = 12, per hour. 12 is 2 less than 14, as it is supposed to, so the correct answer is ANS B. EMPOWERgmat Instructor V Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 15661 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: At his regular hourly rate, Don had estimated the labor cos [#permalink] ### Show Tags 7 Hi RussianDude, You're not expected to answer every question in the Quant section in under 2 minutes, so if you took a little longer than that on this question, then that's fine (as long as you were doing work and not staring at the screen). If you took more than 3 minutes to answer this question, then chances are that YOUR approach is the "long" approach and that you have to practice other tactics. Here, since the answer choices ARE numbers, we're really looking for an answer that divides into 336 AND when you add 4 to that answer, that sum ALSO divides evenly into 336. The difference between those two rates should be$2 (as the question states). In that way, you can answer this question with some basic division and note-taking (and likely save time and avoid a long-winded Algebra approach).

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GMAT 1: 630 Q49 V27 Re: At his regular hourly rate, Don had estimated the labor cos  [#permalink]

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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

$$\frac{336}{X} = \frac{336}{X+4}+2$$

X=24
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Re: At his regular hourly rate, Don had estimated the labor cos  [#permalink]

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t(t+4)=672
we can estimate here 20*30=600 --> 22*30=660 So we see that only A or B can be the answer here... 24*28 suits better (22*30)

A bit too large numbers to calculate, not really a GMAT Style, though it's an official GMAT Question.......
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Re: At his regular hourly rate, Don had estimated the labor cos  [#permalink]

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BrainLab wrote:
t(t+4)=672
we can estimate here 20*30=600 --> 22*30=660 So we see that only A or B can be the answer here... 24*28 suits better (22*30)

A bit too large numbers to calculate, not really a GMAT Style, though it's an official GMAT Question.......

An easier and more straightforward way to look at it will be:

Let T be the total hours initially calculated.

Thus per the question:

$$\frac{336}{T} - \frac{336}{T+4} = 2$$ (DO NOT solve the equation for T). Plug in the values from the options to arrive at the answer. Start with C (you can easily eliminate this as T+4 =20 and this will give a fractional value for 336/20). Then move onto B or D. If you choose D, the difference of the LHS = 7 (not equal to 2 ) and thus you can eliminate D,E as well. Finally, when you come to B, you will see that the equation is satisfied and is thus the answer.

In GMAT, if you end up calculating nasty numbers, then usually you missed out on a simple trick to reduce the effort.
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Re: At his regular hourly rate, Don had estimated the labor cos  [#permalink]

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Can someone correct me?

336=xh
h=336/x

(h+4)=336/2x
xh+4x=168
4x=168-336
x=42      Re: At his regular hourly rate, Don had estimated the labor cos   [#permalink] 08 Oct 2015, 00:02

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