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

Question

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

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

KanishkM · Answer

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

Archit3110 · Answer

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

ScottTargetTestPrep · Answer

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

Answer: C

ckadams · Answer

__________
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
 Answer: C 
_________
I hope this helps. Feel free to give me my first Kudo if you like my solution!
Warmest Regards,
Rumi Qadri

ThatDudeKnows · Answer

A few good posts already in this thread that mention using the "Hidden Plug In" approach of just picking a number for the total number of employees. I agree. But sometimes people get scared of picking a "bad" number if there are a bunch of things to consider for factors or if there's a clue that they might end up needing a funky number (like a relatively large multiple of 23). If you see a question like this and want to plug in, but aren't sure what to use, it's sometimes possible to get to the finish line without a ton of stress just by using percentages.

100% total
20% bus
33.33% drive
So, 53.33% either bus or drive.
That leaves 46.66%, 1/4 of whom subway.
So, 11.66% subway.
65% are accounted for already, so 35% unaccounted for.
1/7 of those bike, so 5% bike.
That leaves 30% walk.
3/10

Answer choice C

ThatDudeKnowsHiddenPlugIn

Ale300503 · Answer

7/15 * 3/4 * 6/7 = 3/10

Answer: (C)

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

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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