riding in the carpool lane

[sanju09]

The fine for a driver riding in the carpool lane without any passengers is $133. A driver is issued a bench warrant for $2,294.25, which includes a 15% fee for late charges and court costs. How many tickets has the driver not paid?
A. 10
B. 12
C. 13
D. 14
E. 15



OA E

[truplayer256]

The $2294.25 that the driver is charged for fines also includes the 15% late charge. So, in order to find out how much the driver was actually charged for ticket fines, we can do the following:
x=Amount driver was charged for ticket fines.
1.15x=2294.25
x=1995

1995/133= The total amount of tickets received= 15

[Stuart@KaplanGMAT]

The fine for a driver riding in the carpool lane without any passengers is $133. A driver is issued a bench warrant for $2,294.25, which includes a 15% fee for late charges and court costs. How many tickets has the driver not paid?
A. 10
B. 12
C. 13
D. 14
E. 15

Very ambiguously worded question (how do we know that the bench warrant is only for this specific type of ticket?), but let's ignore that for the moment.

We could do some wild and wacky calculations to solve, but backsolving is going to be MUCH faster (if we work forwards, we're going to have to do some ugly division, whereas if we work backwards we'll do multiplication, which most people find a lot simpler).

When we backsolve, we generally start with (B) or (D). Just estimating, 12*133 seems way too small, so let's try (D) first.

If we got 14 tickets, then our cost would be 14*133*1.15

14*133 = 1862. 15% of 1862 is certainly less than 400, so there's no way that 14 tickets are going to give us a total cost of 2294.25.

Since 14 tickets was below what we want, we can eliminate 10, 12, 13 and 14, leaving us with only (e) 15.

[sanju09]

Thanks for blotching and ignoring the bench warrant, Stuart! Yours have been a wonderful and always working approach. Pay heed to this aspirants, please!

[Goal to 800]

The fine for a driver riding in the carpool lane without any passengers is $133. A driver is issued a bench warrant for $2,294.25, which includes a 15% fee for late charges and court costs. How many tickets has the driver not paid?
A. 10
B. 12
C. 13
D. 14
E. 15

Very ambiguously worded question (how do we know that the bench warrant is only for this specific type of ticket?), but let's ignore that for the moment.

We could do some wild and wacky calculations to solve, but backsolving is going to be MUCH faster (if we work forwards, we're going to have to do some ugly division, whereas if we work backwards we'll do multiplication, which most people find a lot simpler).

When we backsolve, we generally start with (B) or (D). Just estimating, 12*133 seems way too small, so let's try (D) first.

If we got 14 tickets, then our cost would be 14*133*1.15

14*133 = 1862. 15% of 1862 is certainly less than 400, so there's no way that 14 tickets are going to give us a total cost of 2294.25.

Since 14 tickets was below what we want, we can eliminate 10, 12, 13 and 14, leaving us with only (e) 15.

Agreed. Achieved the answer by plugging in 15 to begin. Luckily, it worked because 15 is a great number to work with.

Great method for this type of complicated division.

Thanks for all your solutions. You are a tremendous asset to the GMAT/MBA Community.

[m&m]

Numbers worked out quite nicely working backwards.

2294 ~ 2300 and 1.15 = 115/100 = 23/20 so

2300 * 20/23 = 100 * 20 = 2000 and 133*10 is 1330 and 50% of that is 665. Adding the 2 (10+5 = 15) is close enough to 2000. So must be E

[brianwalter]

Thanks for this post. HOV lanes, or carpool lanes, allow automobiles with more than one occupant to skirt busy traffic. It is a benefit for saving fuel and polluting less. A new program in California permits motorists of so-called green cars the same opportunity, even if they are driving alone. I hope that there's big possibility that this program will be passed into law.

[Scott@TargetTestPrep]

The fine for a driver riding in the carpool lane without any passengers is $133. A driver is issued a bench warrant for $2,294.25, which includes a 15% fee for late charges and court costs. How many tickets has the driver not paid?
A. 10
B. 12
C. 13
D. 14
E. 15

OA E

If x is the total charge of all the tickets without any fees, we can create the equation:

1.15x = 2,294.25

x = 2,294.25/1.15 = 1995

So the driver was charged $1995 without any fees, and therefore,the driver was issued 1995 / 133 = 15 tickets.

Answer: E