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Bunuel
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Three students need to read 50 proposals. Each proposal has to be read 24 Oct 2022, 09:15
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D
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Difficulty:

95% (hard)

Question Stats:

43% (02:33) correct 57% (02:43) wrong based on 130 sessions

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Three students need to read 50 proposals. Each proposal has to be read by at least one student. 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?

A. 16
B. 18
C. 22
D. 26
E. 28
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D
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rajtare
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Three students need to read 50 proposals. Each proposal has to be read 25 Oct 2022, 04:13
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Bunuel
Three students need to read 50 proposals. Each proposal has to be read by at least one student. 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?

A. 16
B. 18
C. 22
D. 26
E. 28
Show more

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
hence D
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chowdhurysakib71
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Three students need to read 50 proposals. Each proposal has to be read 26 Oct 2022, 00:44
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rajtare
Bunuel
Three students need to read 50 proposals. Each proposal has to be read by at least one student. 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?

A. 16
B. 18
C. 22
D. 26
E. 28

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
hence D
Show more


I didn’t get the formula of overlapping set. Why all 3 was multipled by 2?

Posted from my mobile device
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rajtare
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Joined: 05 Nov 2014
Last visit: 18 Feb 2026
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Given Kudos: 12
Location: India
Concentration: Operations, Leadership
Schools: Sloan '26 Columbia CBS'26 Goizueta '26 Kellogg '26
GPA: 3.99
Products:
My Reviews
Schools: Sloan '26 Columbia CBS'26 Goizueta '26 Kellogg '26
Posts: 183
Kudos: 290
 [1]
Three students need to read 50 proposals. Each proposal has to be read 26 Oct 2022, 01:13
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chowdhurysakib71
rajtare
Bunuel
Three students need to read 50 proposals. Each proposal has to be read by at least one student. 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?

A. 16
B. 18
C. 22
D. 26
E. 28

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
hence D


I didn’t get the formula of overlapping set. Why all 3 was multipled by 2?

Posted from my mobile device
Show more

There is a very detailed article by bunuel on the same, you can check it out !

https://gmatclub.com/forum/advanced-ove ... 44260.html
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Three students need to read 50 proposals. Each proposal has to be read 03 Oct 2025, 01:17
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