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

 It is currently 20 Nov 2019, 22:34

### 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:

45% (medium)

Question Stats:

72% (02:51) correct 28% (03:20) wrong based on 43 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

_________________
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3142

### Show Tags

21 Mar 2018, 23:14
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

R*T = 800
(R-10) * (T+4) = 800
if R = 50 then T = 16
Then R becomes 40 and T becomes 20

Hence D
examPAL Representative
Joined: 07 Dec 2017
Posts: 1155

### Show Tags

22 Mar 2018, 17:09
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

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.

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

$$\frac{800}{r-10} - \frac{800}{r} = 4$$

$$\frac{800r - 800(r-10)}{r(r-10)} = 4$$

$$800r - 800r + 8000 = 4* r(r-10)$$

$$8000 = 4 * r(r-10)$$

$$2000 = r^2 - 10r$$

$$r^2 - 10r - 2000 = 0$$

$$(r - 50)(r + 40) = 0$$

$$r = 50$$

_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.

Never doubt that a small group of thoughtful, committed citizens can change the world; indeed, it's the only thing that ever has -- Margaret Mead
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2812

### 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.