At his regular hourly rate, Ed had estimated the cost of a research ta

Question

At his regular hourly rate, Ed had estimated the cost of a research task as $528 and he was paid that amount. However, the job took 8 hours less time than he had estimated and, consequently, he earned $11 per hour more than his regular hourly rate. What was the time Ed took to complete the task, in hours?

A. 36
B. 25
C. 16
D. 8
E. 4

Bunuel Why can't we set it up as r*t=528 and (r+11)(t-8)=528 like you did with the OG question with Don.

A. 36
B. 25
C. 16
D. 8
E. 4

Bunuel · Answer

Similar question to practice from OG: https://gmatclub.com/forum/at-his-regul ... 36642.html

Sokrat · Answer

I found the answer 16 by plugging in the answers. I got lucky on the first try because I started with C. There must be a faster way that avoids plugging in. I took 2min7 sec to solve it. If I would start with B(25) t-8 would be too large and then I would have guessed C, but the probability would be 1/3 for the right answer (risky).

=>
Let's say t is the time Ed calculated in the beginning. Then, t-8 is the time he actually took to finish the research. 
Let's say x $ is the price calculated by Ed in the beginning and (x+11)$ is the price he calculated after finishing the research.

We know that 528=t*x. Now (plugg in C) if t-8=16, then t =24 => 528=24*x => x=528/24=22
Now, x+11=22+11=33. Therefore (t-8)*33=528 => t-8=528/33=16. Matches the answer!

TestPrepUnlimited · Answer

Set the actual time he used to complete the task as x, then his expected time to complete the task would be x + 8. The two pay rates would be 528/x and 528/(x + 8), and the difference between them is 11. So we would have the equation 528/x = 528/(x + 8) + 11 (since 528/(x+8) is smaller the +11 is always on that side). Solving this seems insufficient so we can try plugging in numbers.

Prime factorizing 528 will help us do the division when we plug in for x,  528 = 480 + 48 = 11 * 48 = 11 * 3 * 2^4 . 
We can see 36 and 25 aren't factors of 528, so A and B cannot be the answer (left side won't be an integer while the right side is an integer, they cannot be equal). Plugging in C we get left side = 11 * 3, right side = 11 * 2 + 11. Therefore C is the correct answer.

Regor60 · Answer

Plugging in is fine but don't know what "insufficient" means, since you've set it up to be readily solved:

Clearing the numerators gives:

528(X+8)= 11(X^2+8X)+528X or

11X^2+88X-(8*528)=0

11 divides nicely:

X^2+8X-(8*48)=0

8*48=16*24 which gives the desired difference of 8:

(X+24)(X-16)=0 so

X=16

Posted from my mobile device

mikeyv31 · Answer

Bunuel  Why can't we set it up as r*t=528 and (r+11)(t-8)=528 like you did with the OG question with Don.

Bunuel · Answer

We  can  set it up this way. Solving r * t = 528 and (r + 11) * (t - 8) = 528 gives t = 24 hours. However, the question asks for the time Ed  actually  took, which is t - 8 = 16 hours.

Answer: C.

At his regular hourly rate, Ed had estimated the cost of a research ta

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At his regular hourly rate, Ed had estimated the cost of a research ta

Prep Toolkit

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