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Bunuel
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Forty-percent of the senior class decided to go on only a spring break 27 Mar 2017, 04:37
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75% (hard)

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66% (03:13) correct 34% (03:34) wrong based on 204 sessions

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Forty-percent of the senior class decided to go on only a spring break trip and a senior class trip. An additional 40 people opted just to go on a post-graduation trip, while half that number decided to participate in all three. If 10 people decided not to participate in any trips, but everyone else decided to go on more than one trip, how many of the 200 member senior class decided to go on only two of the three trips?

A. 60
B. 95
C. 115
D. 122
E. 130
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E
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Forty-percent of the senior class decided to go on only a spring break 27 Mar 2017, 23:33
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Bunuel
Forty-percent of the senior class decided to go on only a spring break trip and a senior class trip. An additional 40 people opted just to go on a post-graduation trip, while half that number decided to participate in all three. If 10 people decided not to participate in any trips, but everyone else decided to go on more than one trip, how many of the 200 member senior class decided to go on only two of the three trips?

A. 60
B. 95
C. 115
D. 122
E. 130
Show more


"...... while half that number decided to participate in all three....."

What is that here? also..

Only Spring break and SC is 40% of 200 = 80

Only PG break additional - 40

all three-20

None 10

rest - 200-((80+40+20)+10)=50

more than one(meaning 2 or 3)= 50

More than one - all three = only two?

50-20=30 (equal to two trips which is not a combination of spring break and senior class)

so SC+SB=80 + 30 =110.

Where am I going wrong?
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Forty-percent of the senior class decided to go on only a spring break 28 Mar 2017, 00:33
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SOUMYAJIT_
Bunuel
Forty-percent of the senior class decided to go on only a spring break trip and a senior class trip. An additional 40 people opted just to go on a post-graduation trip, while half that number decided to participate in all three. If 10 people decided not to participate in any trips, but everyone else decided to go on more than one trip, how many of the 200 member senior class decided to go on only two of the three trips?

A. 60
B. 95
C. 115
D. 122
E. 130


"...... while half that number decided to participate in all three....."

What is that here? also..

Only Spring break and SC is 40% of 200 = 80

Only PG break additional - 40

all three-20

None 10

rest - 200-((80+40+20)+10)=50

more than one(meaning 2 or 3)= 50

More than one - all three = only two?

50-20=30 (equal to two trips which is not a combination of spring break and senior class)

so SC+SB=80 + 30 =110.

Where am I going wrong?
Show more

You are subtracting 20 twice.

BT - Break Trip
CT - Class Trip
PT - Post Graduation Trip

Only BT and CT = 80
Only PT = 40
All three = 20
None = 10

PT and BT or PT and CT = 200 - (80 + 40 + 20 + 10) = 50

Only on two of the three trips = (BT and CT) + (PT and BT) + (PT and CT) = 80 + 50 = 130

Answer: E
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Forty-percent of the senior class decided to go on only a spring break 08 Jun 2017, 10:38
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Vyshak
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Bunuel
Forty-percent of the senior class decided to go on only a spring break trip and a senior class trip. An additional 40 people opted just to go on a post-graduation trip, while half that number decided to participate in all three. If 10 people decided not to participate in any trips, but everyone else decided to go on more than one trip, how many of the 200 member senior class decided to go on only two of the three trips?

A. 60
B. 95
C. 115
D. 122
E. 130


"...... while half that number decided to participate in all three....."

What is that here? also..

Only Spring break and SC is 40% of 200 = 80

Only PG break additional - 40

all three-20

None 10

rest - 200-((80+40+20)+10)=50

more than one(meaning 2 or 3)= 50

More than one - all three = only two?

50-20=30 (equal to two trips which is not a combination of spring break and senior class)

so SC+SB=80 + 30 =110.

Where am I going wrong?

You are subtracting 20 twice.

BT - Break Trip
CT - Class Trip
PT - Post Graduation Trip

Only BT and CT = 80
Only PT = 40
All three = 20
None = 10

PT and BT or PT and CT = 200 - (80 + 40 + 20 + 10) = 50

Only on two of the three trips = (BT and CT) + (PT and BT) + (PT and CT) = 80 + 50 = 130

Answer: E
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Hi
i did not understand this method, could you please elaborate the steps?
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Forty-percent of the senior class decided to go on only a spring break 08 Jun 2017, 11:05
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vandhita

Hi
i did not understand this method, could you please elaborate the steps?
Show more

If you draw a venn diagram with BT, CT and PT as the three circles, there will be:
1 region of BT only
1 region of CT only
1 region of PT only
3 regions of 2 circle overlaps --> (BT and CT) only, (CT and PT) only and (PT and BT) only
1 region with all 3 circle overlaps --> (BT, CT and PT) only
1 region outside all the 3 circle --> None

From the above we have BT only + CT only + PT only + (BT and CT) only + (CT and PT) only + (PT and BT) only + (BT, CT and PT) only + None = Total

Given:
Only BT and CT = 80
Only PT = 40
All three --> (BT, CT and PT) only = 20
None = 10
Because everyone else decided to go on more than one trip, Only BT + Only CT = 0

Required: Only two of the three trips = (BT and CT) only + (PT and BT) only + (PT and CT) only = 200 - 10 - 20 - 40 = 130

Hope it helps.
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Forty-percent of the senior class decided to go on only a spring break 09 Jun 2017, 03:43
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Vyshak
vandhita

Hi
i did not understand this method, could you please elaborate the steps?

If you draw a venn diagram with BT, CT and PT as the three circles, there will be:
1 region of BT only
1 region of CT only
1 region of PT only
3 regions of 2 circle overlaps --> (BT and CT) only, (CT and PT) only and (PT and BT) only
1 region with all 3 circle overlaps --> (BT, CT and PT) only
1 region outside all the 3 circle --> None

From the above we have BT only + CT only + PT only + (BT and CT) only + (CT and PT) only + (PT and BT) only + (BT, CT and PT) only + None = Total

Given:
Only BT and CT = 80
Only PT = 40
All three --> (BT, CT and PT) only = 20
None = 10
Because everyone else decided to go on more than one trip, Only BT + Only CT = 0

Required: Only two of the three trips = (BT and CT) only + (PT and BT) only + (PT and CT) only = 200 - 10 - 20 - 40 = 130

Hope it helps.
Show more


Its very clear now. Thank you so much !
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Forty-percent of the senior class decided to go on only a spring break 28 Jan 2025, 06:59
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