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06 Sep 2021, 23:16
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Difficulty:
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Question Stats:
71% (02:30) correct
29%
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wrong
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Students in a college have to choose at least two subjects from chemistry, mathematics and physics. The number of students choosing all three subjects is 18, choosing mathematics as one of their subjects is 23 and choosing physics as one of their subjects is 25. The smallest possible number of students who could choose chemistry as one of their subjects is
A 22
B 19
C 20
D 21
E 23
A 22
B 19
C 20
D 21
E 23
07 Sep 2021, 00:21
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Let T = the total number of students
II = # of students who take exactly 2 classes
18 = # of students who take exactly 3 classes
Since students must take at exactly 2 or all 3 classes:
T = II + 13
C = # of students who take chemistry as a class
23 = # of students who take Math
25 = # of students who take Physics
—————————
C + 48 = # tallies of people taking a class
The # of students who take 2 classes will be double counted in the above tallies
The # of students taking 3 classes (18) will be triple counted in the above tallies
Thus
C + 48 = 2 * (II) + 3 * (18)
C + 48 = 2(II) + 54
C = 2(II) + 6
since II stands for the number of people who take exactly 2 classes, it must be an integer.
This means the number of students who take chemistry must be an EVEN number.
20 is the minimum number
If C = 20
20 = 2(II) + 6
14 = 2(II)
II = 7 students who take exactly 2 classes
18 students take exactly 3 classes
This gives us a total of 25 students
To prove the numbers work:
2 can take chemistry and physics; 18 take all 3 ——> 20 take chemistry
0 can take math and chemistry; 5 can take math and physics: and 18 take all three———> 23 take Math
2 take chemistry and physics: 5 take physics and math; and 18 take all three——-> 25 take Physics
The numbers work
20 is the minimum
Posted from my mobile device
II = # of students who take exactly 2 classes
18 = # of students who take exactly 3 classes
Since students must take at exactly 2 or all 3 classes:
T = II + 13
C = # of students who take chemistry as a class
23 = # of students who take Math
25 = # of students who take Physics
—————————
C + 48 = # tallies of people taking a class
The # of students who take 2 classes will be double counted in the above tallies
The # of students taking 3 classes (18) will be triple counted in the above tallies
Thus
C + 48 = 2 * (II) + 3 * (18)
C + 48 = 2(II) + 54
C = 2(II) + 6
since II stands for the number of people who take exactly 2 classes, it must be an integer.
This means the number of students who take chemistry must be an EVEN number.
20 is the minimum number
If C = 20
20 = 2(II) + 6
14 = 2(II)
II = 7 students who take exactly 2 classes
18 students take exactly 3 classes
This gives us a total of 25 students
To prove the numbers work:
2 can take chemistry and physics; 18 take all 3 ——> 20 take chemistry
0 can take math and chemistry; 5 can take math and physics: and 18 take all three———> 23 take Math
2 take chemistry and physics: 5 take physics and math; and 18 take all three——-> 25 take Physics
The numbers work
20 is the minimum
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globaldesi
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07 Sep 2021, 00:32
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all subjects = 18
mathematics
total = 23
so only two subjects where Math is one and other subject is either physics or chemistry is 23-18 =5
physics is 25 so physics being oen and math/chemistry are =7
to minimise chemistry
out of 7 5 be the one whose two subjects are maths and physics are 5
hence remaining 2 are the one whose 2 subjects are chem and physics
thus chem total =2+18= 20
C
mathematics
total = 23
so only two subjects where Math is one and other subject is either physics or chemistry is 23-18 =5
physics is 25 so physics being oen and math/chemistry are =7
to minimise chemistry
out of 7 5 be the one whose two subjects are maths and physics are 5
hence remaining 2 are the one whose 2 subjects are chem and physics
thus chem total =2+18= 20
C
