Hello Bunuel, here is my solution

let total number of hours be y
let hourly rate be x
Total amount payed x*y= 360 ---> Hourly rate x= y/336
to complete job it took 4 hours longer --> y+4
hourly rate reduced by 2 USD ---> x-2

(y+4)(x-2) = 336
plug in into above equation x= y/336

(y+4)(y/336 - 2)

336y/y - 2y+1344/y - 8 = 336
336 -2y+1344/y-8=336
-2y+1344/y= 336+8-336
-2y+1344/y =8
ok after this I got stuck and confused, where am I going what I am solving

can you please explain what have I done wrong ? I decoded the info correctly I mean expressed initially in numbers.

thanks for your help.

Bunuel - Many thanks ! Just two more question

could you show in detail how you got this \(y^2 + 4y - 672 = 0\); and another question what is the point of factoring ? \(y(y + 4) = 672\) I remember when we see such equation\(y^2 + 4y - 672 = 0\); we need to find discriminant ? like D = B^2-4AC

Thank you Bunuel. When you reduce by 2, why didn't you reduce fraction by 2 as well 336/y Normally when we reduce and or multiply numbers in equation all numbers are subject to be changed accordingly - No ? please correct me if I am wrong.

Bunuel - But isn't 336/y a separate number ? Shouldn't we have done so 1/2 *4 and 1/2 * 336/y ?

@Bunuel- thanks for asking me this question I think if we reduce 4*6 by 2 the answer will be 12 because 4*6 is one number. I have brushed up fundamentals but sometimes in some PS questions i encounter some technical details i have a vague idea about or simply cant use theory in practice. Thanks a lot for explanation

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.

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.

Great question, Saiganesh999! I am so glad that the Veritas Prep solutions resonate with you. Most people end up spinning their wheels trying to do the math the long way around because they don't realize how conceptually-oriented many Quantitative GMAT questions really are. Conceptually looking at a question can sometimes turn a mean, 5-minute problem into a quick, 20-second solution. However, it is important to note that not every question can be solved solely by waving a conceptual wand and having the answer fall into your lap. I would even argue that most GMAT Quantitative questions are a combination of both conceptual and mathematical approaches. (And many conceptual approaches only become visible once you get a couple of steps into the math!)

This problem is no exception. If you look at my solution (https://gmatclub.com/forum/at-his-regul ... l#p2143221), you can see that once we distill the equation down to one variable, then we can look at it conceptually -- or more specifically, we can use our answer choices as leverage to think about the question. (I call this strategy "Look Out Below!" in my classes.) We can quickly eliminate answer choices C, D, and E because they are too small. Answer choice A can be eliminated because it fails the unit's digit test. Approximation, unit's digit math, and plugging in answer choices are all part of a comprehensive, balanced strategy you will want to use on the GMAT.

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