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Difficulty:
35%
(medium)
Question Stats:
77% (02:27) correct
23%
(02:34)
wrong
based on 3272
sessions
History
Date
Time
Result
Not Attempted Yet
A certain toll station on a highway has 7 tollbooths, and each tollbooth collects $0.75 from each vehicle that passes it. From 6 o'clock yesterday morning to 12 o'clock midnight, vehicles passed each of the tollbooths at the average rate of 4 vehicles per minute. Approximately how much money did the toll station collect during that time period?
A. $1,500
B. $3,000
C. $11,500
D. $23,000
E. $30,000
(PS01443)
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A. $1,500
B. $3,000
C. $11,500
D. $23,000
E. $30,000
(PS01443)
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Bunuel
4 Vehicle in 1 Minute
4 Vehicle*60 in 60 Minute(1 Hour) = 240 Vehicle in 1 Hour
Total time duration (6 o'clock yesterday morning to 12 o'clock midnight) = 18 hrs
Total tollbooths = 7
Cost of each vehicle passed = $0.75
Therefore,
Total cost collected = 240 * 18 * 7 * 0.75 = 22680 = 23000 (approx)
Hence, D.
General Discussion
From 6 am to 12 am - 18hrs
Vehicles per minute - 4
Vehicles per hour - 60×4 = 240
Therefore total number of vehicles passed - approx = 250×18 = 4500
Number of toll booths = 7
Money collected = 7×4500×0.75 = 23000$
Hence D (I've rounded up a few numbers above for easy calculation)
Posted from my mobile device
Vehicles per minute - 4
Vehicles per hour - 60×4 = 240
Therefore total number of vehicles passed - approx = 250×18 = 4500
Number of toll booths = 7
Money collected = 7×4500×0.75 = 23000$
Hence D (I've rounded up a few numbers above for easy calculation)
Posted from my mobile device
Bunuel
OA:D
Total hours: \(18 hours\)
Total Vehicles passed per toll booth per hour : \(4*60 =240\)
Toll collected per vehicle :\($0.75\)
Number of Toll booths:\(7\)
Total money collected = Total hours * Total Vehicles passed per toll booth per hour *Toll collected per vehicle *Number of Tollbooths
= \($18*240*0.75*7=$22680\)
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Expert reply
Posts: 22,738
Bunuel
We can create the expression:
7 tollbooths x $0.75 per vehicle x 4 vehicles per minute x 60 minutes x 18 hours = $22,680 ≈ $23,000
Answer: D
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Bunuel
6AM to 6PM = 12 hours then another 6 hours to midnight total 18 hours.
18 * 60 = 1,080 minutes * 4 cars = 4,320 cars passing.
Since the cost each car is 0.75 which equals 3/4
so 3/4 * 4,320 = 3 * 1,080 * 7(for the tollbooths) = 21 * 1,080
No need to go through tedious calculations 20 * 1,000 = 20,000 there is only one answer with such thousands digit.
Answer choice D
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Bunuel
18 hours = 18 * 60 minutes
4 vehicles per minute = 18 * 60 * 4
total 7 toolbooths = 18 * 60 * 4 * 7
0.75 = 3/4 $
Total collection = 18 * 60 * 7 * 3 = 1080 * 21 = 21600 + 1080 = 22680
D is the answer.
Bunuel
Remember you need to calculate approximate value:
From 6 o'clock yesterday morning to 12 o'clock midnight = 18 hours
m\frac{75}{100}m*18*60*4*7
=3*18*60*7
=3*20*60*7
=60*60*7
=3600*7
=25200 [value less than 25,200]
Ans. D; 23000
Hi Experts,
What is this question testing other than word translation skills? Is it testing how we can do tedious multiplication under 2 mins? Thanks!!
What is this question testing other than word translation skills? Is it testing how we can do tedious multiplication under 2 mins? Thanks!!
Bunuel
why is it 18 hours from 6 to 12, from 6 to 12 means 6 and 12 both are included so it should be 19 hours.
where am I wrong?
There is a similar question in one of the threads " tickets being sold to a group of 30 every 5 minutes FROM 9 am to 5:55 pm and there we have counted 9 and 5:55 both for calculating the 5 minute interval".
Bunuel please explain
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Products:
Convert 0.75 into 3/4.
7*18*60*4*3/4
Keeping Rounding off the answer as the answers have significant value differences.
7*20*60*4*3/4
7*20*60*3
21*20*60 = almost = 20*20*60 = 24000
We get our answer
7*18*60*4*3/4
Keeping Rounding off the answer as the answers have significant value differences.
7*20*60*4*3/4
7*20*60*3
21*20*60 = almost = 20*20*60 = 24000
We get our answer
Posts: 1,070
Mck2023
It's testing whether you can spot that you don't need to do the tedious multiplication at all, so it should take you less than ONE minute!!
Our total timespan is 18 hours and there are 60 minutes per hour. 18 and 60 are annoying. Ballpark!! Do ~20x50. That's ~1000 minutes.
Each toll booth averages 4 cars per minute at collects $0.75 per car. That's an average of $3/minute.
There are 7 toll booths.
~1000*3*7 = ~21000
Now look at the answer choices. Only one of them is close.
Answer choice D.
ThatDudeKnowsBallparking
GMATCoachBen
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GMAT Focus 1: 775 Q87 V90 DI88 (Online) 
GMAT 1: 760 Q50 V44
GMAT 2: 770 Q51 V44
GMAT 3: 770 Q50 V44
GMAT 4: 770 Q50 V45 (Online)
GMAT 5: 780 Q51 V48
Expert reply
daffy8
Let's look at a simpler example. How many hours are there between 3pm and 5pm?
5 - 3 = 2 hours
On this problem, midnight is the equivalent of 24:00.
So, we subtract: 24 - 6 = 18 hours.
Or, another way to look at it: it's a full 24-hour day, minus the 6 hours before 6am.
On the tickets problem you're referring to, it's counting the number of times we sell tickets, which are spaced out in 5 minute intervals. This is different, and invokes the +1 concept that you're thinking about, when we're counting the number of values in an evenly spaced set.
Suppose we are asked how much time passed between 9:00am and 9:10am: we simply subtract, and get 10 minutes.
However, if we're asked how many times we sell tickets, if they're sold every 5 minutes from 9:00am to 9:10am, inclusive, then there's still a 10-minute period, with TWO 5-minute breaks between sales, but we have sold tickets THREE times: 9:00, 9:05, and 9:10. The difference here is that we need to count the sales at each endpoint. Alternatively, if we are asked for a time interval, we can just subtract the start time from the end time.
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Expert reply
We can do this quickly if we notice a few things:
For the calculation, it's helpful to:
_________________
- "Approximately" is a signal to round; additionally, the answer choices have a wide spread
- "From 6 o'clock yesterday morning to 12 o'clock midnight" is 18 hours
- When we see "4 vehicles per minute", we need to convert hours to minutes, by multiplying by 60
- The question asks for units in $. If we multiply, all the other units cancel and we get $.
(7 tollbooths * 3/4 $/vehicle * 18 hours * 60 min/hour * 4 vehicles/min)
For the calculation, it's helpful to:
- cross off the 4 on the bottom and top right away
- 7*3 rounds to 20
- 18 rounds to 20
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Expert reply
Short video solution here (1:47):
Playlist with more "Quant Timesavers": https://www.youtube.com/playlist?list=PL2exXfCUscn-LGr7SGgyKmU4XwTmQmZFi
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