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

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For each trip, a taxicab company charges $4.25 for the first mile and [#permalink]

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New post 23 Jul 2017, 12:19
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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

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Re: For each trip, a taxicab company charges $4.25 for the first mile and [#permalink]

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New post 23 Jul 2017, 15:16
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carcass wrote:
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


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.
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Re: For each trip, a taxicab company charges $4.25 for the first mile and [#permalink]

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New post 23 Jul 2017, 15:58
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carcass wrote:
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


I. Total = 4.25+2.65(x-1), 62.55 = 4.25+2.65(x-1), 58.30 = 2.65(x-1), 58.30/2.65 = x -1,
II. Simplify 58.30/2.65 dividing by 5 = 11.66/0.53 = x-1, 22 = x-1, x = 23
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Re: For each trip, a taxicab company charges $4.25 for the first mile and [#permalink]

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New post 23 Jul 2017, 19:21
1
carcass wrote:
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



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
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Re: For each trip, a taxicab company charges $4.25 for the first mile and [#permalink]

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New post 24 Jul 2017, 01:06
ccooley wrote:
carcass wrote:
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


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.


I did forget the first mile and picked 22 for my answer. 1 Kudo for great remind. Thank you.
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Re: For each trip, a taxicab company charges $4.25 for the first mile and [#permalink]

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New post 24 Jul 2017, 08:42
carcass wrote:
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


\(\frac{62.25 - 4.25}{2.65} + 1\)

Or, 21.89 + 1

Or, 22.89 ~ 23

Thus, answer must be (C) 23
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For each trip, a taxicab company charges $4.25 for the first [#permalink]

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New post 25 Jul 2017, 17:39
$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.
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For each trip, a taxicab company charges $4.25 for the first [#permalink]

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New post 25 Jul 2017, 18:48
alexjst wrote:
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


OG:2018


Charge for first mile \(= $4.25\)

Charge for each additional mile \(= $2.65\)

Let the additional miles be \(= x\)

Total charge for the trip \(= $62.55\)

\(4.25 + 2.65x = 62.55\)

\(2.65x = 62.55 - 4.25 = 58.30\)

\(x = \frac{58.30}{2.65} = 22\)

Total miles of the trip \(= 1 + 22 = 23\) miles

Answer (C)...

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Re: For each trip, a taxicab company charges $4.25 for the first mile and [#permalink]

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New post 26 Jul 2017, 16:40
carcass wrote:
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



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
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Re: For each trip, a taxicab company charges $4.25 for the first mile and [#permalink]

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New post 10 Sep 2017, 03:40
carcass wrote:
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



Total fare = 62.55

62.55 = (4.25) + (2.65 x m)
22 = m

But, this is not the answer since it only accounts for the number of miles with the lower rate.
4.25 = 1 mile
therefore, the total miles is 22 + 1 = 23 miles

Answer (C)
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Re: For each trip, a taxicab company charges $4.25 for the first mile and [#permalink]

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New post 02 Nov 2017, 18:49
I get the reasoning behind the calculations, but how are you guys able to quickly do the math of 58.3/2.65?
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Re: For each trip, a taxicab company charges $4.25 for the first mile and [#permalink]

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New post 02 Nov 2017, 19:31
haxxx043 wrote:
I get the reasoning behind the calculations, but how are you guys able to quickly do the math of 58.3/2.65?


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
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Re: For each trip, a taxicab company charges $4.25 for the first mile and [#permalink]

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New post 07 Dec 2017, 20:20
haxxx043 wrote:
I get the reasoning behind the calculations, but how are you guys able to quickly do the math of 58.3/2.65?


I found it easier to multiply the numerator and denominator by 100 so the expression becomes 5830/265.
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Re: For each trip, a taxicab company charges $4.25 for the first mile and [#permalink]

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New post 01 Jun 2018, 22:22
Hi ScottTargetTestPrep niks18 gmatbusters VeritasPrepKarishma

Any ways to simplify (6095/265) or (5830/265) ?
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Re: For each trip, a taxicab company charges $4.25 for the first mile and [#permalink]

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New post 01 Jun 2018, 22:37
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Hii

Try to cancel the conspicuous common factors, convert the bigger number to product of factors. these will help in cancellation of terms.
See
Attachment:
WhatsApp Image 2018-06-02 at 11.03.51.jpeg
WhatsApp Image 2018-06-02 at 11.03.51.jpeg [ 26.52 KiB | Viewed 543 times ]


adkikani wrote:
Hi ScottTargetTestPrep niks18 gmatbusters VeritasPrepKarishma

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

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Re: For each trip, a taxicab company charges $4.25 for the first mile and [#permalink]

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New post 05 Jun 2018, 10:27
gmatbusters wrote:
Hii

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


adkikani wrote:
Hi ScottTargetTestPrep niks18 gmatbusters VeritasPrepKarishma

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



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.
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Re: For each trip, a taxicab company charges $4.25 for the first mile and   [#permalink] 05 Jun 2018, 10:27
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