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Joined: 23 Jan 2021
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Concentration: , International Business
Three students need to read 50 proposals. Each student has to read at
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02 Nov 2021, 22:45
02 Nov 2021, 22:45
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Three students need to read 50 proposals. Each student has to read at least one proposal. Student A read 38 of them, Student B read 36 of them, while Student C read 28 of them. At least how many proposals are read by at least two students?
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26
Post a detailed solution and get kudos!
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Re: Three students need to read 50 proposals. Each student has to read at
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04 Mar 2022, 01:41
04 Mar 2022, 01:41
2
COolguy101 wrote:
Three students need to read 50 proposals. Each student has to read at least one proposal. Student A read 38 of them, Student B read 36 of them, while Student C read 28 of them. At least how many proposals are read by at least two students?
Post a detailed solution and get kudos!
Show: ::
26
Post a detailed solution and get kudos!
Use Venn diagram;
Total Students = A + B + C - (A and B) - (B and C) - (A and C) - 2(A, B and C) + Leftovers
50 = 38 + 36 + 28 - (A and B) - (B and C) - (A and C) - 2(A, B and C) + 0
(A and B) + (B and C) + (A and C) + 2(A, B and C) = 102 - 50 = 52
At least how many proposals are read by at least two students?
which means: (A and B) + (B and C) + (A and C) must be least i.e. (A, B and C) must be the maximum
This is possible when (A and B) + (B and C) + (A and C) = 0
Therefore, 0 + 2(A, B and C) = 52
So, (A, B and C) = 26
Re: Three students need to read 50 proposals. Each student has to read at
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06 Mar 2024, 23:02
06 Mar 2024, 23:02
1
This can be solved using overlapping sets method
AUBUC = A+B+C- (exactly 2)-2(all three) + Neither
Neither =0 as each student read atleast 1 proposal
A= 38, B=36, C=28
50= 102 -(exactly 2)-2(all three)
(exactly 2) +2 (all three) = 52
Let exactly 2= x
all three =y
x+2y = 52
Required least value of x+y
x+y= 52-y
we can see that x+y will be minimum when y is maximum. to get the maximum value of y we have to make x=0, thus
2y=52
or y=26
Thus the required value of x+y will be
x+y = 52-26 =26
AUBUC = A+B+C- (exactly 2)-2(all three) + Neither
Neither =0 as each student read atleast 1 proposal
A= 38, B=36, C=28
50= 102 -(exactly 2)-2(all three)
(exactly 2) +2 (all three) = 52
Let exactly 2= x
all three =y
x+2y = 52
Required least value of x+y
x+y= 52-y
we can see that x+y will be minimum when y is maximum. to get the maximum value of y we have to make x=0, thus
2y=52
or y=26
Thus the required value of x+y will be
x+y = 52-26 =26
