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# At Pedantic Publishing Corporation, 1/5 of the employees take the bus

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Math Expert
Joined: 02 Sep 2009
Posts: 58415
At Pedantic Publishing Corporation, 1/5 of the employees take the bus  [#permalink]

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05 Feb 2019, 04:42
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Difficulty:

45% (medium)

Question Stats:

65% (02:34) correct 35% (02:47) wrong based on 37 sessions

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At Pedantic Publishing Corporation, 1/5 of the employees take the bus to work and 1/3 drive to work. Of the employees who do not take the bus or drive to work, 1/4 take the subway and the rest either walk or ride a bicycle. If 1/7 of the remaining employees ride a bicycle to work, what fraction of the employees walks to work?

A. 1/10
B. 1/5
C. 3/10
D. 2/5
E. 1/2

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Posts: 995
Location: India
Re: At Pedantic Publishing Corporation, 1/5 of the employees take the bus  [#permalink]

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05 Feb 2019, 05:09
Bunuel wrote:
At Pedantic Publishing Corporation, 1/5 of the employees take the bus to work and 1/3 drive to work. Of the employees who do not take the bus or drive to work, 1/4 take the subway and the rest either walk or ride a bicycle. If 1/7 of the remaining employees ride a bicycle to work, what fraction of the employees walks to work?

A. 1/10
B. 1/5
C. 3/10
D. 2/5
E. 1/2

IMO C

Total employees at PPC = 3 * 5 * 4* 7 = 420

Take bus to work = 420/5 = 84
Drive to work = 420/3 = 140

Total employees who do not take the bus or drive to work = 420 - 224 = 196

employees who take subway = 196/4 = 49

employees who walk or ride a bicycle = 147

remaining employees ride a bicycle to work = 1/7 * 147 = 21

what fraction of the employees walks to work = 126/420 = 3/10
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Re: At Pedantic Publishing Corporation, 1/5 of the employees take the bus  [#permalink]

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05 Feb 2019, 05:53
Bunuel wrote:
At Pedantic Publishing Corporation, 1/5 of the employees take the bus to work and 1/3 drive to work. Of the employees who do not take the bus or drive to work, 1/4 take the subway and the rest either walk or ride a bicycle. If 1/7 of the remaining employees ride a bicycle to work, what fraction of the employees walks to work?

A. 1/10
B. 1/5
C. 3/10
D. 2/5
E. 1/2

total employees = 420
bus to work = 420* 1/5 = 84
drive to work = 420 * 1/3 = 140
left 196
.25 take subway = 196 * .25 = 49
left with 147 of whom 1/7 ride bicycle = 21
rest 126/420 = 0.3
IMO C
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Re: At Pedantic Publishing Corporation, 1/5 of the employees take the bus  [#permalink]

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08 Feb 2019, 08:13
Bunuel wrote:
At Pedantic Publishing Corporation, 1/5 of the employees take the bus to work and 1/3 drive to work. Of the employees who do not take the bus or drive to work, 1/4 take the subway and the rest either walk or ride a bicycle. If 1/7 of the remaining employees ride a bicycle to work, what fraction of the employees walks to work?

A. 1/10
B. 1/5
C. 3/10
D. 2/5
E. 1/2

Since 1/5 take the bus and 1/3 drive, 1/5 + 1/3 = 3/15 + 5/15 = 8/15, take the bus or drive. Thus 1/4 x 7/15 = 7/60 take the subway and 3/4 x 7/15 = 21/60 = 7/20 walk or ride a bicycle.

Since 1/7 of the remaining employees ride a bicycle to work, the fraction who walk to work is 1 - 1/7 = 6/7 of the remaining employees.

Thus, the fraction who walk to work is:

7/20 x 6/7 = 6/20 = 3/10

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At Pedantic Publishing Corporation, 1/5 of the employees take the bus  [#permalink]

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20 Feb 2019, 19:56
Bunuel wrote:
At Pedantic Publishing Corporation, 1/5 of the employees take the bus to work and 1/3 drive to work. Of the employees who do not take the bus or drive to work, 1/4 take the subway and the rest either walk or ride a bicycle. If 1/7 of the remaining employees ride a bicycle to work, what fraction of the employees walks to work?

A. 1/10
B. 1/5
C. 3/10
D. 2/5
E. 1/2

__________
To solve this problem I chose to pick a "smart number" (60) that was common to 1/5, 1/3, and 1/4.

1/5*60= 12 out of 60 take the bus
1/3*60= 20 out of 60 drive
Total =32 out of 60 who take the bus or drive

Then the question states "of the people who do not take the bus or drive" 1/4 take the subway
So the remaining is 60-32=28*1/4= 7 who take the subway

1/7 of the remaining employees ride a bicycle, and what is left over will be those who walk
Total = 12+20+7= 39 and so the remaining is 21
21*1/7= 3 who ride a bicycle

12+20+7+3=42 with 18 remaining who walk
The final total remaining is thus 18/60 = 3/10
_________
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At Pedantic Publishing Corporation, 1/5 of the employees take the bus   [#permalink] 20 Feb 2019, 19:56
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