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 mileOn the first day, Kelly traveled 2/5 of the distance from City A to City B2/5 of

1 = (2/5)(

1) =

2/5So, on Day 1, she traveled

2/5 miles

This also means, the distance REMAINING =

1 -

2/5On the second day, Kelly traveled 2/3 of the REMAINING distance.On Day 2, the REMAINING distance =

1 -

2/5So, 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 mileWe 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)]

Answer: D

Cheers,

Brent

_________________

Brent Hanneson – Creator of greenlighttestprep.com

Sign up for my free GRE Question of the Day emails