BTGmoderatorDC wrote: ↑Fri Nov 12, 2021 7:37 pm
The toll for crossing a certain bridge is $0.75 each crossing. Drivers who frequently use the bridge may instead purchase a sticker each month for $13.00 and then pay only $0.30 each crossing during that month. If a particular driver will cross the bridge twice on each of x days next month and will not cross the bridge on any other day, what is the least value of x for which this driver can save money by using the sticker?
A. 14
B. 15
C. 16
D. 28
E. 29
OA
B
Source: GMAT Prep
In other words, we want to find the value of x such that: (
total payments WITH sticker) < (
total payments WITHOUT sticker)
total payments WITHOUT sticker
If the driver crosses the bridge
twice on x days, but then the total number of crossings = 2x
Since each crossing will cost $0.75, the total payments for the month = (2x)($0.75) =
1.5x
Total payments WITH sticker
The sticker costs $13.00
If the driver crosses the bridge
twice on x days, but then the total number of crossings = 2x
Since each crossing will cost $0.30, the total payments for the month = $13.00 + (2x)($0.30) =
13.00 + 0.6x
So, our inequality becomes:
13.00 + 0.6x <
1.5x
Subtract 0.6x from both sides: 13 < 0.9x
Divide both sides by 0.9 to get approximately: 14.44 < x
Since x must be a positive
integer, the smallest value of x is 15
Answer: B
Brent Hanneson - Creator of GMATPrepNow.com
