For each trip, a taxicab company charges $4.25 for the first mile and

Question

For each trip, a taxicab company charges $4.25 for the first mile and $2.65 for each additional mile or fraction thereof. If the total charge for a certain trip was $62.55, how many miles at most was the trip?

A. 21

B. 22

C. 23

D. 24

E. 25

A. 21 
B. 22
C. 23
D. 24
E. 25

ccooley · Accepted Answer

Interesting. The 'at most' phrasing tells me that I need to be very careful. It would be quite easy to accidentally pick an answer that's 1 bigger or 1 smaller than the right answer. The problem asks for the  largest  number of miles, so I'm looking for the absolute maximum number of miles that could work. That makes sense with what the problem says; since the $2.65 charge applies to any mile 'or fraction thereof', a trip of 9.01 miles will cost the same as a trip of 10 miles exactly. In that scenario, I'd want to pick the answer 10.

Now let's do the math. The total cost of a trip is $4.25 + $2.65 per mile * (number of extra miles). That's equal to $62.55 for this trip.

$4.25 + $2.65 * (extra miles) = $62.55

$2.65 * (extra miles) = $58.30

Extra miles = 22

It was very deliberate on my part to use the term 'extra miles'! In problems like this, the easiest mistake is to forget to count the very  first  mile. We'll have to add it back in to find that the trip is at most 23 miles.

john80rivera · Answer

$62.55 total for the trip.

Total - First Mile
$62.55 - $4.25 = $58.30

$58.30 is the total for miles after the first mile. Just did quick numbers in my head:
$2.65 x 10 = 26.50, 26.50 x 2 = $53.00 (20 miles)

58.30 - 53.00 = 5.30 =2 extra miles

Total Miles is 23.

rohit8865 · Answer

First mile  charges = $4.25

Charges for  remaining miles  = 62.55-4.25=58.3

remaining distance travelled = 58.3 / 2.65 = 22 miles

total distance =  first mile + remaining miles  = 1+22 =23 miles

Ans C

nimapi · Answer

I did forget the first mile and picked 22 for my answer. 1 Kudo for great remind. Thank you.

ScottTargetTestPrep · Answer

We can let the maximum number of miles = m and create the following equation:

62.55 = 4.25 + 2.65(m - 1)

58.3 = 2.65m - 2.65

60.95 = 2.65m

23 = m

Answer: C

haxxx043 · Answer

I get the reasoning behind the calculations, but how are you guys able to quickly do the math of 58.3/2.65?

chetan2u · Answer

Hi..
If you are having problems in such numbers, take help of choices..

Choices are 21,22,23,24,25.....
The first mile is subtracted from price, so choices become 20,21,22,23,24..
Now 58.3/2.65 ... When you are multiplying 2.65 with correct choice, it gives you 58.3 or 3 as last digit...
20 will give 20*2.65....5 in the end
21 and 23 will keep the two decimals but 58.3 has only one decimal..
22 will give 22*2.65.... just Multiply with units digit of 22 so 2*2.65=5.3
So 3 in the end, suits are logic
24...4*2.65=10.6.... NO
So 22 is our answer, add 1 to it=22+1=23

adkikani · Answer

Hi  ScottTargetTestPrep   niks18   gmatbusters   VeritasPrepKarishma

Any ways to simplify (6095/265) or (5830/265) ?

GMATBusters · Answer

Hii Try to cancel the conspicuous common factors, convert the bigger number to product of factors. these will help in cancellation of terms. See WhatsApp Image 2018-06-02 at 11.03.51.jpeg

ScottTargetTestPrep · Answer

Just divide the numerator by denominator, 6095/265 = 23 and 5830/265 = 22. Alternatively, you can first cancel the factors of 5 from the numerator and the denominator to obtain 6095/265 = 1219/53 and 5830/265 = 1166/53 and then perform the division. That will make the division somewhat easier.

BrentGMATPrepNow · Answer

STRATEGY : Upon reading any GMAT Problem Solving question, we should always ask,   Can I use the answer choices to my advantage?   
In this case, we can easily test the answer choices until we find the one that yields a trip cost of $62.55. 
Now let's give ourselves up to 20 seconds to identify a faster approach. 
In this case, we can use algebra (let x = the total trip distance, etc...).
It's a close call, but I'll go with testing the answer choice...
We'll begin with answer choice C, the middlemost answer choice, because we can often eliminated answer choices based on the results of testing choice C.

C. 23  This means the entire trip was 23 miles. 
The passenger is charged   $4.25   for the first mile
And then   $2.65   for each of the remaining   22   miles
So, the total cost of the trip =   $4.25   + (  22  )(  $2.65  )  = $4.25 + $58.3 = $62.55

Perfect!
 Answer: C

Ophelia__ · Answer

Found an error so removed my post

nguyenpham1309 · Answer

My way is not the fastest one, but it might be suitable for people who don't work well with decimal and work better with fraction. Besides that, my principle is to reduce the workload at the final step of calculation to avoid unnecessary mistakes. I don't want to lose this type of question after spending over 2 mins to read the question, have a plan and solve the equation

1. They ask "at most", so to avoid forgetting +1 at the last step, assign x as the total miles at most. Thus, the extra miles are demonstrated as x-1 (miles)

2. Change all the decimal numbers to the fractions:
4.25 = 41/4 = 17/4
2.65 = 2 65/100 = 2 13/20 = 53/20
62.55 = 62 11/20 = 1251/20

3. Combine the above information to have your completed equation:
17/4 + 53/20 (x-1) = 1251/20 ---> At this time, you can see that by multiplying "20" to both sides of the equation, you will simplify the calculation
17*5 + 53x - 53 = 1251 ---> Now you only work with the integer number
53x +85 - 53 = 1251
53x = 1219

To this point, you have two ways: either you are confident with your division skill and have x =23, or if faster, recognize the last digit of the calculation: 3*x = 9 -> the answer must be 23

bumpbot · Answer

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For each trip, a taxicab company charges $4.25 for the first mile and

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