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# Kelly took three days to travel from City A to City B by aut

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Kelly took three days to travel from City A to City B by aut [#permalink]  05 Mar 2017, 09:05
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Question Stats:

71% (01:36) correct 28% (02:11) wrong based on 97 sessions

Kelly took three days to travel from City A to City B by automobile. On the first day, Kelly traveled $$\frac{2}{5}$$ of the distance from City A to City B and on the second day, she traveled $$\frac{2}{3}$$ of the remaining distance. Which of the following is equivalent to the fraction of the distance from City A to City B that Kelly traveled on the third day.

A) $$1 - \frac{2}{5} - \frac{2}{3}$$

B) $$1 - \frac{2}{5} - \frac{2}{3}(\frac{2}{5})$$

C) $$1 - \frac{2}{5} - \frac{2}{5}(1 - \frac{2}{3})$$

D) $$1 - \frac{2}{5} - \frac{2}{3}(1 - \frac{2}{5})$$

E) $$1 - \frac{2}{5} - \frac{2}{3}(1 - \frac{2}{5} - \frac{2}{3})$$
[Reveal] Spoiler: OA

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Re: Kelly took three days to travel from City A to City B by aut [#permalink]  11 Mar 2017, 17:32
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Explanation

Day 1: Kelly traveled $$\frac{2}{5}$$ of the distance, so her remaining distance is $$1 - \frac{2}{5}$$.

Day 2: Kelly traveled 2/3 of the remaining distance, or $$\frac{2}{3} \times (1 - \frac{2}{5})$$.

Day 3: Kelly traveled the rest of the way. $$1 - \frac{2}{5} - \frac{2}{3} \times (1 - \frac{2}{5})$$.

Hence option D is correct.
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Re: Kelly took three days to travel from City A to City B by aut [#permalink]  22 Sep 2017, 07:44
There are some missing information in the question as in " On the first day, Kelly traveled of the distance from City A to City B", where I think there is a missing fraction
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Re: Kelly took three days to travel from City A to City B by aut [#permalink]  22 Sep 2017, 09:40
IlCreatore wrote:
There are some missing information in the question as in " On the first day, Kelly traveled of the distance from City A to City B", where I think there is a missing fraction

Here is the question

Kelly took three days to travel from City A to City B by automobile. On the first day, Kelly traveled 2/5 of the distance from City A to City B and on the second day, she traveled 2/3 of the remaining distance. Which of the following is equivalent to the fraction of the distance from City A to City B that Kelly traveled on the third day.

Hope that helps
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Re: Kelly took three days to travel from City A to City B by aut [#permalink]  07 Aug 2019, 09:43
Expert's post
Carcass wrote:

Kelly took three days to travel from City A to City B by automobile. On the first day, Kelly traveled $$\frac{2}{5}$$ of the distance from City A to City B and on the second day, she traveled $$\frac{2}{3}$$ of the remaining distance. Which of the following is equivalent to the fraction of the distance from City A to City B that Kelly traveled on the third day.

A) $$1 - \frac{2}{5} - \frac{2}{3}$$

B) $$1 - \frac{2}{5} - \frac{2}{3}(\frac{2}{5})$$

C) $$1 - \frac{2}{5} - \frac{2}{5}(1 - \frac{2}{3})$$

D) $$1 - \frac{2}{5} - \frac{2}{3}(1 - \frac{2}{5})$$

E) $$1 - \frac{2}{5} - \frac{2}{3}(1 - \frac{2}{5} - \frac{2}{3})$$

Let's take this one step at a time....

Since all of the answer choices begin with 1, let's say that the distance between City A and City B is 1 mile

On the first day, Kelly traveled 2/5 of the distance from City A to City B
2/5 of 1 = (2/5)(1) = 2/5
So, on Day 1, she traveled 2/5 miles

This also means, the distance REMAINING = 1 - 2/5

On the second day, Kelly traveled 2/3 of the REMAINING distance.
On Day 2, the REMAINING distance = 1 - 2/5
So, on day 2, Kelly's travel distance = 2/3 of (1 - 2/5) miles
In other words, on day 2, Kelly's travel distance = 2/3(1 - 2/5) miles

Summary:
(distance traveled on Day 1) + (distance traveled on Day 2) + (distance traveled on Day 3) = 1 mile
We can rearrange this to get: (distance traveled on Day 3) = 1 mile - (distance traveled on Day 1) - (distance traveled on Day 2)
Plug in our above values to get: distance traveled on Day 3 = 1 - (2/5) - [2/3(1 - 2/5)]

Cheers,
Brent
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Re: Kelly took three days to travel from City A to City B by aut   [#permalink] 07 Aug 2019, 09:43
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