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3/5 of a certain class left on a field trip. 1/3 of the students who s

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Math Expert
Joined: 02 Sep 2009
Posts: 58381
3/5 of a certain class left on a field trip. 1/3 of the students who s  [#permalink]

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06 Oct 2014, 09:53
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Difficulty:

45% (medium)

Question Stats:

71% (02:08) correct 29% (02:18) wrong based on 417 sessions

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Tough and Tricky questions: Ratios

3/5 of a certain class left on a field trip. 1/3 of the students who stayed behind did not want to go on the field trip (all the others did want to go). When another vehicle was located, 1/2 of the students who did want to go on the field trip but had been left behind were able to join. What fraction of the class ended up going on the field trip?

A. 1/2
B. 2/3
C. 11/15
D. 23/30
E. 4/5

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Re: 3/5 of a certain class left on a field trip. 1/3 of the students who s  [#permalink]

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06 Oct 2014, 11:25
2
1
Bunuel wrote:

Tough and Tricky questions: Ratios

3/5 of a certain class left on a field trip. 1/3 of the students who stayed behind did not want to go on the field trip (all the others did want to go). When another vehicle was located, 1/2 of the students who did want to go on the field trip but had been left behind were able to join. What fraction of the class ended up going on the field trip?

A. 1/2
B. 2/3
C. 11/15
D. 23/30
E. 4/5

let total no. of students be 30
students left on a field trip = 3/5(30) =18
thus 12 students left behind
1/3(12)=4 students did not want to go. thus 8 students want to go on the trip
1/2(8)=4 were able to join the other students on the field trip.
thus total number of students that went on a field trip =18+4 =22
thus required fraction = 22/30 =11/15
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Re: 3/5 of a certain class left on a field trip. 1/3 of the students who s  [#permalink]

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06 Oct 2014, 13:05
3
$$\frac{3}{5}$$ left so $$\frac{2}{5}$$ stayed

$$\frac{1}{3}$$ didn't want to go so $$\frac{2}{3}$$ of those that stayed did want to go

$$\frac{1}{2}$$ of those that stayed and wanted to go could so $$\frac{2}{5} * \frac{2}{3} * \frac{1}{2} = \frac{2}{15}$$ that stayed and wanted to go could

$$\frac{3}{5} + \frac{2}{15} = \frac{11}{15}$$ got to go
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Re: 3/5 of a certain class left on a field trip. 1/3 of the students who s  [#permalink]

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06 Oct 2014, 19:35
2
Let the total students = x

Students went to trip = $$\frac{3x}{5}$$ ................. (1)

Students left behind = $$\frac{2x}{5}$$

$$\frac{1}{3}$$ rd of left behind students DO NOT want to go $$= \frac{2x}{5} * \frac{1}{3} = \frac{2x}{15}$$

So, students who are ready to go $$= \frac{2x}{5} - \frac{2x}{15} = \frac{4x}{15}$$

$$\frac{1}{2}$$ of students who are ready to go went in another vehicle $$= \frac{2x}{15}$$ ........... (2)

Total students gone to trip = (1) + (2)$$= \frac{3x}{5} + \frac{2x}{15} = \frac{11x}{15}$$

Required fraction$$= \frac{\frac{11x}{15}}{x} = \frac{11}{15}$$

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Re: 3/5 of a certain class left on a field trip. 1/3 of the students who s  [#permalink]

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02 Dec 2016, 09:12
Hey what difficulty would this question be 600?
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Re: 3/5 of a certain class left on a field trip. 1/3 of the students who s  [#permalink]

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02 Dec 2016, 09:21
seanf wrote:
Hey what difficulty would this question be 600?

You can check difficulty level, which is calculated based on the users attempts via the timer in the original post:
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Re: 3/5 of a certain class left on a field trip. 1/3 of the students who s  [#permalink]

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02 Dec 2016, 10:12
Question is simple. However, the language is little tricky if somebody reads it in hurry. Taken initial number of student as 300 and proceeded.

My answer is C i.e. 11/15.
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Re: 3/5 of a certain class left on a field trip. 1/3 of the students who s  [#permalink]

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30 May 2017, 23:23
Bunuel wrote:

Tough and Tricky questions: Ratios

3/5 of a certain class left on a field trip. 1/3 of the students who stayed behind did not want to go on the field trip (all the others did want to go). When another vehicle was located, 1/2 of the students who did want to go on the field trip but had been left behind were able to join. What fraction of the class ended up going on the field trip?

A. 1/2
B. 2/3
C. 11/15
D. 23/30
E. 4/5

Let total no of students=30 ( LCM of denominators)
Now, 3/5 of a class left on a field trip.
went for field trip=3/5x30 =3x6=18
Stayed=30-18 = 12
Then, 1/3 of student who stayed behind did not want to go to field trip. i.e. 1/3 x 12 = 4
All other ddid want to go i.e student's who want to go=12-4=8
Again, 1/2 of the students who did want to go joined i.e. 1/2 x 8=4
Students who ended up going to field trip = 18 + 4= 22
Fraction= 22/30 = 11/15
Hence, Ans is: C
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Re: 3/5 of a certain class left on a field trip. 1/3 of the students who s  [#permalink]

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31 May 2017, 19:30
Very Good Question, With One Minute Answer

Instead of Fractions take a common number in this case we can take the LCM of the deniominators(3,5,2) = 30

Total count of students = 30

3/5 left for the Trip
so left = 18, and remaining students stayed is 12

1/3 of the students who stayed behind did not want to go on the field trip
= 1/3 of 12 = 4
This gives students who did want to go is 12-4 = 8 and did not want to go =4

1/2 of the students who did want to go on the field trip but had been left behind were able to join.
= From the above 8/2 = 4

So total who went is 18(already left) +4(Joined later) = 22

and the Fraction is 22/30 = 11/15 Option C
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Re: 3/5 of a certain class left on a field trip. 1/3 of the students who s  [#permalink]

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01 Jun 2017, 21:01
- 2/5 of class remained.
- Of that 2/3 wanted to go
- Bus picked up half of those wanting to go. 1/2*2/3 = 1/3. 1/3*2/5 = 2/15.
- 2/15+3/5 = 11/15
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Re: 3/5 of a certain class left on a field trip. 1/3 of the students who s  [#permalink]

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05 Jun 2017, 15:52
1
Bunuel wrote:

Tough and Tricky questions: Ratios

3/5 of a certain class left on a field trip. 1/3 of the students who stayed behind did not want to go on the field trip (all the others did want to go). When another vehicle was located, 1/2 of the students who did want to go on the field trip but had been left behind were able to join. What fraction of the class ended up going on the field trip?

A. 1/2
B. 2/3
C. 11/15
D. 23/30
E. 4/5

We can let the original number of students = 300. Since 3/5 x 300 = 180 students went on the trip, 2/5 x 300 = 120 students stayed behind. Since 1/3 of the students who stayed behind did not want to go, 1/3 x 120 = 40 students did not want to to go. Thus, 120 - 40 = 80 students actually wanted to go but were left behind. Since 1/2 of the 80 students who stayed behind but wanted to go went in another vehicle, 1/2 x 80 = 40 students went on the field trip via the other vehicle.

Thus, (180 + 40)/300 = 220/300 = 22/30 = 11/15 of the students went on the trip.

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Re: 3/5 of a certain class left on a field trip. 1/3 of the students who s  [#permalink]

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31 Oct 2018, 01:50
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Re: 3/5 of a certain class left on a field trip. 1/3 of the students who s   [#permalink] 31 Oct 2018, 01:50
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