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02 Mar 2026, 20:00
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
73% (02:06) correct
27%
(02:39)
wrong
based on 116
sessions
History
Date
Time
Result
Not Attempted Yet
The following shows the liking pattern of 125 members of a club.
50 like pizza.
70 like burger.
45 like salad.
25 like pizza and burger.
30 like burger and salad.
20 like pizza and salad.
20 like none of the three.
How many members of the club like pizza, burger, and salad?
A. 0
B. 5
C. 10
D. 15
E. 30
50 like pizza.
70 like burger.
45 like salad.
25 like pizza and burger.
30 like burger and salad.
20 like pizza and salad.
20 like none of the three.
How many members of the club like pizza, burger, and salad?
A. 0
B. 5
C. 10
D. 15
E. 30
02 Mar 2026, 22:55
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I REALLY need to get better at overlapping sets, but here are the base rules to follow always I've kept atleast.
When you need to find, individual sets where ONLY 1 item is liked --> Calculate total and subtract the extra --> The extras here are 2(2items)+3(all 3 items)
BUT
When asked for total number of ppl involved you ONLY subtract 1(2items) + 2(3items) Why? Because you are taking a union of all and for union you still have to include the 2items and 3items list.
When it was just single item you totally exclude the 2 items and 3 items list and hence you are subtracting 1 extra time.
This is a mistake I have done countless times and it is good to note.
____________________________
Using these points now:
Total of pizza+burger+salad = 50+70+45 = 165.
This total includes the excess AND the none portion so lets add that too
165+20=185
Calculate extra:
185-125 members = 60
This 60 = 1(2items) + 2(3 items) (Taking union like mentioned above)
60 = 1(20-x+30-x+25-x) + 2(x) (Here the items liked twice also includes liking 3 times, this you can even if ur unsure notice in the salad portion 45 like salad but if 2 items were exclusive then 25+30<=40 but its NOT. Hence it is indeed inclusive of liking 3 items as well. Hence take 3 items to be x here)
Solving for x:
x=15
This is our group of ppl liking all 3 as asked!
Answer: Option D IMO
When you need to find, individual sets where ONLY 1 item is liked --> Calculate total and subtract the extra --> The extras here are 2(2items)+3(all 3 items)
BUT
When asked for total number of ppl involved you ONLY subtract 1(2items) + 2(3items) Why? Because you are taking a union of all and for union you still have to include the 2items and 3items list.
When it was just single item you totally exclude the 2 items and 3 items list and hence you are subtracting 1 extra time.
This is a mistake I have done countless times and it is good to note.
____________________________
Using these points now:
Total of pizza+burger+salad = 50+70+45 = 165.
This total includes the excess AND the none portion so lets add that too
165+20=185
Calculate extra:
185-125 members = 60
This 60 = 1(2items) + 2(3 items) (Taking union like mentioned above)
60 = 1(20-x+30-x+25-x) + 2(x) (Here the items liked twice also includes liking 3 times, this you can even if ur unsure notice in the salad portion 45 like salad but if 2 items were exclusive then 25+30<=40 but its NOT. Hence it is indeed inclusive of liking 3 items as well. Hence take 3 items to be x here)
Solving for x:
x=15
This is our group of ppl liking all 3 as asked!
Answer: Option D IMO
ExpertsGlobal5
02 Mar 2026, 23:34
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Let x be the members who prefer all 3
Number of people who prefer exactly 2 out of 3 = (25-x)+(20-x)+(30-x)=75-3x
People who prefer pizza=p=50
People who prefer burger=b=70
People who prefer salad=s=45
(50+70+45) -(75-3x)-2x+None=125
165-75+3x-2x+20=125
110+x=125
x=15
Ans D
Number of people who prefer exactly 2 out of 3 = (25-x)+(20-x)+(30-x)=75-3x
People who prefer pizza=p=50
People who prefer burger=b=70
People who prefer salad=s=45
(50+70+45) -(75-3x)-2x+None=125
165-75+3x-2x+20=125
110+x=125
x=15
Ans D
