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08 Jul 2025, 05:48
Kudos
Bookmarks
Option B is the correct answer.
Lets understand the question and information mentioned in it before trying to solve it.
So the question starts by telling us that at a charity event everyone who is expected attending the event belongs to exactly one of the six groups: donors, press, volunteers, entertainers, organizers, or sponsors. Then it tells us about the information about the number of expected people per group who will be the part of the event i.e. "Among the invited guests, 4/7 were donors, 1/5 were press, and the remainder were divided equally among the other four groups". Then the question gives us information about the number of people who actually attended the event i.e. "On the day of the event, however, twice as many press guests arrived as were invited, only half of the invited volunteers attended, and the entertainers did not attend due to a last-minute boycott. The donors, organizers, and sponsors showed up as expected". And in the end asks us what fraction of people who actually attended the event were donors.
Now lets try solving the question but before that lets assume the total expected number of people from all the six groups to be 70 people, we have take total expected number to be 70 so that we can get the values in integer form which will make the calculations easy for us as well as the number of people can never be in decimal for so that's the another reason.
So, as per our assumption Total expected count of people = 70 People
Total expected count of Donor = 70*(4/7) => 40 People
Total expected count of Press = 70*(1/5) => 14 People
Total expected count of Volunteers = (70-40-14)*(1/4) => 16*(1/4) => 4 People
Total expected count of Entertainers = 16*(1/4) => 4 People
Total expected count of Organizers = 16*(1/4) => 4 People
Total expected count of Sponsors = 16*(1/4) => 4 People
Now as per the question the information regarding the number of people who actually attended the event is "twice as many press guests arrived as were invited, only half of the invited volunteers attended, and the entertainers did not attend due to a last-minute boycott. The donors, organizers, and sponsors showed up as expected".
Members of Press who actually attended the event = 2*14 => 28 People
Members of Volunteers who actually attended the event = 4/2 => 2 People
Members of Entertainers who actually attended the event = 0 People
Members of Donors who actually attended the event = 40 People
Members of Organizers who actually attended the event = 4 People
Members of Sponsors who actually attended the event = 4 People
Total number of people who actually attended the event = 28+2+0+40+4+4 => 78 People.
Now the asks us what fraction of people who actually attended the event were donors = Number of donors who attended the event/Total number of people who attended the event
= 40/78 => 20/39 (Option B)
So from here we get Option B as our answer.
Lets understand the question and information mentioned in it before trying to solve it.
So the question starts by telling us that at a charity event everyone who is expected attending the event belongs to exactly one of the six groups: donors, press, volunteers, entertainers, organizers, or sponsors. Then it tells us about the information about the number of expected people per group who will be the part of the event i.e. "Among the invited guests, 4/7 were donors, 1/5 were press, and the remainder were divided equally among the other four groups". Then the question gives us information about the number of people who actually attended the event i.e. "On the day of the event, however, twice as many press guests arrived as were invited, only half of the invited volunteers attended, and the entertainers did not attend due to a last-minute boycott. The donors, organizers, and sponsors showed up as expected". And in the end asks us what fraction of people who actually attended the event were donors.
Now lets try solving the question but before that lets assume the total expected number of people from all the six groups to be 70 people, we have take total expected number to be 70 so that we can get the values in integer form which will make the calculations easy for us as well as the number of people can never be in decimal for so that's the another reason.
So, as per our assumption Total expected count of people = 70 People
Total expected count of Donor = 70*(4/7) => 40 People
Total expected count of Press = 70*(1/5) => 14 People
Total expected count of Volunteers = (70-40-14)*(1/4) => 16*(1/4) => 4 People
Total expected count of Entertainers = 16*(1/4) => 4 People
Total expected count of Organizers = 16*(1/4) => 4 People
Total expected count of Sponsors = 16*(1/4) => 4 People
Now as per the question the information regarding the number of people who actually attended the event is "twice as many press guests arrived as were invited, only half of the invited volunteers attended, and the entertainers did not attend due to a last-minute boycott. The donors, organizers, and sponsors showed up as expected".
Members of Press who actually attended the event = 2*14 => 28 People
Members of Volunteers who actually attended the event = 4/2 => 2 People
Members of Entertainers who actually attended the event = 0 People
Members of Donors who actually attended the event = 40 People
Members of Organizers who actually attended the event = 4 People
Members of Sponsors who actually attended the event = 4 People
Total number of people who actually attended the event = 28+2+0+40+4+4 => 78 People.
Now the asks us what fraction of people who actually attended the event were donors = Number of donors who attended the event/Total number of people who attended the event
= 40/78 => 20/39 (Option B)
So from here we get Option B as our answer.
Bunuel
08 Jul 2025, 05:52
Kudos
Bookmarks
We can solve this by creating a table and choosing smart numbers
We know 4/7 were donors and 1/5 was press so we can take their LCM that is 35 as total number of people.
With 35 as total members we can see
Donors were 4/7 of 35 that is 20
Press was 1/5 of 35 that is 7
Together they are 27
and others members are equal so (35-27=8)
4 groups 8 members so 2 members each
On the day of event:
2 times press guest came, only half of volunteer came and entertainer didnt attend so new table will look like as w
Fraction of actual donor attendee: 20/39
Answer B: 20/39.
We know 4/7 were donors and 1/5 was press so we can take their LCM that is 35 as total number of people.
With 35 as total members we can see
Donors were 4/7 of 35 that is 20
Press was 1/5 of 35 that is 7
Together they are 27
and others members are equal so (35-27=8)
4 groups 8 members so 2 members each
| Donor | Press | Volunteer | Entertainer | Organizer | Sponsor | Total |
| 20 | 7 | 2 | 2 | 2 | 2 | 35 (Assumed) |
2 times press guest came, only half of volunteer came and entertainer didnt attend so new table will look like as w
| Donor | Press | Volunteer | Entertainer | Organiser | Sponsor | Total | |
| Before Event | 20 | 7 | 2 | 2 | 2 | 2 | 35 |
| On the event day | 20 | 14 | 1 | 0 | 2 | 2 | 39(new total) |
Fraction of actual donor attendee: 20/39
Answer B: 20/39.
Bunuel
08 Jul 2025, 05:54
Kudos
Bookmarks
D= 4/7 =20 4/7
P= 1/5 2/5
V=2/35 1/35
E=2/35 0
O=2/35 2/35
S=2/35 2/35
Total 35 39 (Actual number of attendees)
Based on LCM 35 the actual numbers of attendees was 39 meaning the fraction of donors was 20/39
P= 1/5 2/5
V=2/35 1/35
E=2/35 0
O=2/35 2/35
S=2/35 2/35
Total 35 39 (Actual number of attendees)
Based on LCM 35 the actual numbers of attendees was 39 meaning the fraction of donors was 20/39
Bunuel
