The toll for crossing a certain bridge is $0.75...

[BTGmoderatorLU]

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

The OA is B.

I'm really confused with this PS question. Experts, any suggestion about how to solve it? Thanks in advance.

[DavidG@VeritasPrep]

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

The OA is B.

I'm really confused with this PS question. Experts, any suggestion about how to solve it? Thanks in advance.

Cost not using the sticker: number of crossings = 2x. Cost per crossing: $.75. Total cost = 2x * .75 = 1.50x

Cost using the sticker: Cost per crossing: $.30. Number of crossings: 2x. Cost for crossings: .30*2x = .60x. But there's a $13 fee, so the total cost for this option is 13 + .60x.

Break-even point: 1.50x = 13 + .60x
.90x = 13
x = 13/.9 = 130/9 = 14 4/9.

If the break-even point is a little greater than 14, then the sticker begins saving the user money at 15 days. The answer is B

[DavidG@VeritasPrep]

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

The OA is B.

I'm really confused with this PS question. Experts, any suggestion about how to solve it? Thanks in advance.

Alternative approach. If you see that the driver will spend $1.50 on crossing days without the sticker and $.60 on crossing days with the sticker, then we see that she's saving $.90 on each crossing day. So the question becomes: For how many days must she save $.90 until she's made up for that $13 fee.

Now back solve.
A: If she save $.90 on each of 14 days, she'll save .9*14 = $12.60. Not enough to offset the $13 fee.

But we know we'll save an additional $.90 on the 15th day, bringing the total savings to 12.60 + .90 --> clearly more than 13. So the answer is B

[Jeff@TargetTestPrep]

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

We can create the following inequality:

0.75(2x) > 13 + 0.3(2x)

1.5x > 13 + 0.6x

0.9x > 13

x > 13/0.9

x > 130/9

x > 14 4/9

So the minimum value of x is 15.

Answer: B

[Brent@GMATPrepNow]

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

The OA is B.

I'm really confused with this PS question. Experts, any suggestion about how to solve it? Thanks in advance.

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