A service provider charges c dollars for the first 50 hours of service

Question

A service provider charges c dollars for the first 50 hours of service used per month and 40 cents for each 30 minutes in excess of 50 hours used during the month. If x is an integer greater than 50, which of the following expressions gives this service provider's charge, in dollars, for a month in which x hours of service were used?

A. c + 0.40x
B. c + 0.80x
C. c + 0.40(x - 50)
D. c + 0.80(x - 50)
E. c + 0.40(2x - 50)

PS99551.02

A. c + 0.40x
B. c + 0.80x
C. c + 0.40(x - 50)
D. c + 0.80(x - 50)
E. c + 0.40(2x - 50)

PS99551.02

nick1816 · Answer

Amount charged for the first 50 hours = c Dollars

Amount charged for 1 hour service that is excess of first 50 hours = 0.40*2 = 0.80 Dollars

Hours of service that is taken excess of first 50 hours = x-50 hours

Amount charged for these x-50 hours = 0.80 * (x-50) Dollars

expressions gives this service provider's charge, in dollars, for a month in which x hours of service were used = c+ 0.80 * (x-50) Dollars

sujoykrdatta · Answer

Charge for the first 50 hours = $c
Charge for every extra 30 min = $0.40
=> Charge for every extra 1 hour = $0.80

Since x is an integer greater than 50, number of hours in addition to 50 hours = (x - 50) hours
=> Additional charge = $0.8(x-50)

=> Total charge = $

Alternatively:

All the options have $c present. Thus, we need to verify the additional change. The hourly charge additional change is $0.80 for every additional hour, i.e. the extra charge is $(0.80 x Extra time) = $

Answer D

Archit3110 · Answer

for first 50 hours the charge - $c
and for next hour >50 ; per $ charge ; 40 cents for 30 mins or say 80 cents for 1 hr
1 cents =$100 ; so 1 hr charge ; $.8
charges for x hours will be c+.8(x-50)
OPTION D

chetan2u · Answer

Substitution is another simple way..
Take simple values of c as 1 and x as 51....
so 1$+2*0.4=1.80$

Look at the choices...

A. c + 0.40x....1+0.4*51...NO
B. c + 0.80x ....1+0.8*51...NO
C. c + 0.40(x - 50)....1+0.4*(51-50)=1.4...NO
D. c + 0.80(x - 50)....1+0.8*(51-50)=1.8.....Yes
E. c + 0.40(2x - 50)....1+0.4*(2*51-50)=1+0.4*52....NO

D

Algebraic..

c $ for first 50 hrs
0.40 cents for 30 minutes or 0.80 cents for each additional hour.

If x>50, additional hours = x-50, and charges for this = 0.80(x-50)

Total = c+0.80(x-50)

D

gurmukh · Answer

Take x =51 hrs
Total cost = x + 0.8
Only option D gives the answer

Posted from my mobile device

perfectreview · Answer

Total no.of hours = x  (>50)

Amount paid for the first 50 hours = $c

After spending the first 50 hours, remaining hours = x - 50

Amount charged for each excess 30 min = $0.4
Therefore amount charged for each excess 1 hour = 2*(0.4) = $0.8

So total amount earned = c + 0.8(x - 50)

Therefore answer is  Option D

MHIKER · Answer

40 CENT 30 MINUTES 80 OR .80 DOLLAR CENTS FOR 1 HOUR
TOTAL:
C+ 0.80(X-50)
ANS. D

CrackverbalGMAT · Answer

SOLUTION:
A NEW OG 2021 QUESTION

The question here tests on skills in Unitary Methods.

"c" is the FIXED Charge to be paid and hence PRESENT IN ALL OPTIONS.

Beyond "50" hrs, the x-50 hrs (as we know that x is beyond 50 and hence greater than 50) are the VARIABLE cost.

40 cents is the VARIABLE CHARGE per 30 min =>80 cents/$0.80 is the VARIABLE charge every hour

=> $0.8 (x-50) is the VARIABLE charge for the excess of (x-50) hours.

Hence total cost = Fixed +Variable charge for x hours
= c + 0.8(x-50) OPTION (D)

Hope this helps

GMATinsight · Answer

Answer: Option D

Video solution by  GMATinsight

https://www.youtube.com/watch?v=HChyi5NN3Yg

Kimberly77 · Answer

Hi  BrentGMATPrepNow , given 40 cents for each 30 minutes in excess of 50 hours rather than 40 cents for each additional 30 minutes.....Therefore wondering why is not answer B but D? How to differentitate between "each" and "additional" terms and when to use (x-50) format ? Thanks Brent

ScottTargetTestPrep · Answer

First, c dollars was charged for the first 50 hours of service.

Next, we see that the excess hours was x - 50, since x hours of service were used. Also, the cost per hour, for the excess hours is 40/100 x 2 or 0.4 x 2 = 0.8.

Thus, the cost of the excess hours, in dollars, is 0.8(x - 50).

So, the total charge was c + 0.8(x - 50).

Answer: D

harshittahuja · Answer

A service provider charges c dollars for the first 50 hours of service used per month and 40 cents for each 30 minutes in excess of 50 hours used during the month. If x is an integer greater than 50, which of the following expressions gives this service provider's charge, in dollars, for a month in which x hours of service were used?
Solution:-

For first 50 hours= c
and addition 1 hours = 80 cents.
so for x hours 
=c+(x-50)*80
=c+(x-50)*80

Kimberly77 · Answer

Great thanks  ScottTargetTestPrep  for the great explanation. To clarify this is due to x is an unknown integer greater than 50 right? If it had been given as 51 hrs then it'd have been B? Is my understanding correct? Thanks Scott.

ScottTargetTestPrep · Answer

Exactly.

KDM91 · Answer

Amount for first 50 hrs = C dollars
hourly charges greater than 50 hrs = 0.4 * 2 = 0.8
Service Hours greater than 50 hrs= x-50

Service provider's charges for the month = c + 0.8 (x-50)

Option D.

A service provider charges c dollars for the first 50 hours of service

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GMAT Problem Solving (PS) Questions

A service provider charges c dollars for the first 50 hours of service

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