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Jamboree and GMAT Club Contest: In a class of 100 students, 80 passed

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Joined: 14 Jun 2016
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Re: Jamboree and GMAT Club Contest: In a class of 100 students, 80 passed [#permalink]

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New post 01 Aug 2017, 06:11
Vyshak wrote:
In a class of 100 students, 80 passed Physics, 70 passed Chemistry, and 40 passed Math. If 10 students failed in all the three subjects, at least how many of the students passed all the three subjects?

Total = A + B + C - (Sum of 2 overlaps) - 2(all 3 overlaps) + Neither
100 = 80 + 70 + 40 - (Sum of 2 overlaps) - 2(all 3 overlaps) + 10
100 = 200 - (Sum of 2 overlaps) - 2(all 3 overlaps)

(Sum of 2 overlaps) + 2(all 3 overlaps) = 100 --- (1)
Also, max value of (Sum of 2 overlaps) + (all 3 overlaps) = 90 --- (2)
(1) - (2)
All 3 overlaps = 10.

Number of students who passed all 3 subjects = 10

Answer: C


Can anyone please explain the area "Also, max value of (Sum of 2 overlaps) + (all 3 overlaps) = 90 --- (2)" How can we say this?
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Re: Jamboree and GMAT Club Contest: In a class of 100 students, 80 passed [#permalink]

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New post 01 Aug 2017, 07:40
buan15 wrote:
Vyshak wrote:
In a class of 100 students, 80 passed Physics, 70 passed Chemistry, and 40 passed Math. If 10 students failed in all the three subjects, at least how many of the students passed all the three subjects?

Total = A + B + C - (Sum of 2 overlaps) - 2(all 3 overlaps) + Neither
100 = 80 + 70 + 40 - (Sum of 2 overlaps) - 2(all 3 overlaps) + 10
100 = 200 - (Sum of 2 overlaps) - 2(all 3 overlaps)

(Sum of 2 overlaps) + 2(all 3 overlaps) = 100 --- (1)
Also, max value of (Sum of 2 overlaps) + (all 3 overlaps) = 90 --- (2)
(1) - (2)
All 3 overlaps = 10.

Number of students who passed all 3 subjects = 10

Answer: C


Can anyone please explain the area "Also, max value of (Sum of 2 overlaps) + (all 3 overlaps) = 90 --- (2)" How can we say this?


If you tend to get confused with formulas then refer the following explanation
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Re: Jamboree and GMAT Club Contest: In a class of 100 students, 80 passed [#permalink]

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New post 01 Aug 2017, 21:52
GMATinsight wrote:
buan15 wrote:
Vyshak wrote:
In a class of 100 students, 80 passed Physics, 70 passed Chemistry, and 40 passed Math. If 10 students failed in all the three subjects, at least how many of the students passed all the three subjects?

Total = A + B + C - (Sum of 2 overlaps) - 2(all 3 overlaps) + Neither
100 = 80 + 70 + 40 - (Sum of 2 overlaps) - 2(all 3 overlaps) + 10
100 = 200 - (Sum of 2 overlaps) - 2(all 3 overlaps)

(Sum of 2 overlaps) + 2(all 3 overlaps) = 100 --- (1)
Also, max value of (Sum of 2 overlaps) + (all 3 overlaps) = 90 --- (2)
(1) - (2)
All 3 overlaps = 10.

Number of students who passed all 3 subjects = 10

Answer: C


Can anyone please explain the area "Also, max value of (Sum of 2 overlaps) + (all 3 overlaps) = 90 --- (2)" How can we say this?


If you tend to get confused with formulas then refer the following explanation


I can understand the later part of the explanation but can't follow the first line i.e. 2(a+b+c)+d+e+f=80...
Where from can we derive the same?
Please explain....
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Re: Jamboree and GMAT Club Contest: In a class of 100 students, 80 passed   [#permalink] 01 Aug 2017, 21:52

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Jamboree and GMAT Club Contest: In a class of 100 students, 80 passed

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