GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Oct 2018, 01:15

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

### Show Tags

21 Mar 2018, 23:05
00:00

Difficulty:

35% (medium)

Question Stats:

74% (02:51) correct 26% (03:13) wrong based on 41 sessions

### HideShow timer Statistics

A painter was paid $800 as labor cost for painting the exterior of the front of a house. This amount was the painter’s estimated labor cost based on a regular rate of R, in dollars per hour, for an estimated time T, in hours. However, the actual time it took for the painter to do the job was 4 hours longer than the estimated time, thereby reducing the hourly rate for the job by$10 per hour. What is R, the painter’s regular rate, in dollars per hour?

(A) 20
(B) 30
(C) 40
(D) 50
(E) 60

_________________
Intern
Joined: 14 Mar 2018
Posts: 10

### Show Tags

22 Mar 2018, 01:21
Bunuel wrote:
A painter was paid $800 as labor cost for painting the exterior of the front of a house. This amount was the painter’s estimated labor cost based on a regular rate of R, in dollars per hour, for an estimated time T, in hours. However, the actual time it took for the painter to do the job was 4 hours longer than the estimated time, thereby reducing the hourly rate for the job by$10 per hour. What is R, the painter’s regular rate, in dollars per hour?

(A) 20
(B) 30
(C) 40
(D) 50
(E) 60

This is an Alternative approach and is especially useful if long word problems tend to confuse you.

Starting with the median - C.
If the regular rate is 40 then the regular time is 800/40 = 20. In this case the new rate was 40-10=30 and the new time was 800/30 = 80/3. Since 20 + 4 does not equal 80/3, this answer is incorrect.
Let's try the next largest answer, (D).
If the regular rate is 50 then the regular time is 800/50 = 16. In this case the new rate was 50-10=40 and the new time was 800/40 = 20. Since 16 + 4 = 20 then all our calculations work out and our answer is (D).

Note that you don't actually need to write down any equations with variables to use this approach.
_________________

Watch free GMAT tutorials in Math, Verbal, IR, and AWA.

GMAT test takers: Watch now the GMAC interview with the people who write the GMAT test!
We discussed the chances of improving a GMAT score; how important the first questions on the test are; what to do if you don’t have enough time to complete a whole section; and more.

You can watch all the action from the interview here.

Senior SC Moderator
Joined: 22 May 2016
Posts: 2040
Re: A painter was paid $800 as labor cost for painting the exterior of the [#permalink] ### Show Tags 22 Mar 2018, 17:09 1 Bunuel wrote: A painter was paid$800 as labor cost for painting the exterior of the front of a house. This amount was the painter’s estimated labor cost based on a regular rate of R, in dollars per hour, for an estimated time T, in hours. However, the actual time it took for the painter to do the job was 4 hours longer than the estimated time, thereby reducing the hourly rate for the job by $10 per hour. What is R, the painter’s regular rate, in dollars per hour? (A) 20 (B) 30 (C) 40 (D) 50 (E) 60 Answer choices For each answer's rate and decreased rate, find time taken. The difference in hours should be 4. Rate * Time = Pay, P Thus, Time, $$T = \frac{P}{R}$$ Start with C)$40 per hour (estimated). $30 per hour (actual) Time at$40: $$\frac{800}{40per.hr}= 20$$ hours
Time at $30: $$\frac{800}{30per.hr}=\frac{80}{3}= 26.xx$$ hours 800/30 is not an integer. I calculated to find out whether$40 per hour = too high or too low

6.xx extra hours. Too great. Needs to decrease.

R and T are inversely proportional
(one increases, the other decreases)
T needs to come down. R must go up.
$40 per hour is too low Try D)$50 per hour (estimated). $40 per hour (actual) Time at$50: $$\frac{800}{50} = 16$$ hours
Time at $40, from above = $$20$$ hours Difference? 4 hours. That's correct. Answer D Algebra (Hourly pay rate) * (# hours worked) = Total pay in dollars Same basis as $$RT = W$$ $$RT = W$$, so $$T = \frac{W}{R}$$ W = 800 Estimated rate = $$r$$ Actual rate = $$r-10$$ Estimated time = $$\frac{800}{r}$$ Actual time = $$\frac{800}{r-10}$$ To find rate, $$r$$, use time, which is defined in terms of $$r$$ (Actual time) - (estimated time) = $$4$$ hours $$\frac{800}{r-10} - \frac{800}{r} = 4$$ $$\frac{800r - 800(r-10)}{r(r-10)} = 4$$ $$800r - 800r + 8000 = 4* r(r-10)$$ $$8000 = 4 * r(r-10)$$ $$2000 = r^2 - 10r$$ $$r^2 - 10r - 2000 = 0$$ $$(r - 50)(r + 40) = 0$$ $$r = 50$$ Answer D _________________ ___________________________________________________________________ For what are we born if not to aid one another? -- Ernest Hemingway Target Test Prep Representative Status: Head GMAT Instructor Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 2830 Re: A painter was paid$800 as labor cost for painting the exterior of the  [#permalink]

### Show Tags

23 Mar 2018, 12:41
Bunuel wrote:
A painter was paid $800 as labor cost for painting the exterior of the front of a house. This amount was the painter’s estimated labor cost based on a regular rate of R, in dollars per hour, for an estimated time T, in hours. However, the actual time it took for the painter to do the job was 4 hours longer than the estimated time, thereby reducing the hourly rate for the job by$10 per hour. What is R, the painter’s regular rate, in dollars per hour?

(A) 20
(B) 30
(C) 40
(D) 50
(E) 60

We can create the equation:

RT = 800

T = 800/R

and

(T + 4)(R - 10) = 800

RT + 4R - 10T - 40 = 800

RT + 4R - 10T = 840

Substituting, we have:

R(800/R) + 4R - 10(800/R) = 840

800 + 4R - 8000/R = 840

4R - 8000/R = 40

Multiplying by R, we have:

4R^2 - 8000 = 40R

4R^2 - 40R - 8000 = 0

Dividing by 4, we have:

R^2 - 10R - 2000 = 0

(R - 50)(R + 40) = 0

R = 50 or R = -40

Since R can’t be negative, R = 50.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2069

### Show Tags

26 Mar 2018, 11:16
Wasted my time trying to go for an algebraic solution but such questions could best be solved using options.
We know that - R*T=800.
Let C be the correct answer.
Then, R=40; T=20.

Now, T is increased by 4 hours and R is reduced by $10. R(new) = 30; T(new) = 24. -> RT(New) = 720. So we know that R cannot be 20 and 30 either because the decrease in number is by 10 while the increase is by 4 only. Thus, the product will get smaller. Therefore, for easier calculations, let R=50, then T=16. When R is reduced by$10 and T is increased by 4 hours, then R=40 and T=20.

Thus, both remain the same.

So the correct answer is 50.
_________________

"Success is a lousy teacher. It seduces smart people to think they can't lose" - Bill Gates.