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04 Feb 2021, 11:09
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D
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Difficulty:
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Question Stats:
55% (01:57) correct
45%
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wrong
based on 244
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In a class of 100:
80 have at least one pen;
65 have at least one pencil;
70 have at least one slate.
If a is max no of classmates having all three and b min no of classmates having all three, a - b is:
A. 15
B. 20
C. 35
D. 50
E. 60
80 have at least one pen;
65 have at least one pencil;
70 have at least one slate.
If a is max no of classmates having all three and b min no of classmates having all three, a - b is:
A. 15
B. 20
C. 35
D. 50
E. 60
04 Feb 2021, 20:15
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Bunuel
Max number is when all 65 who have pencil have other two items too => a=65
Least is when we fill up the 100s first before starting any overlap.
80 have pen, that is 20 don’t have pens.
65 have pencil.
=> so fill up 20 who don’t have pen. This will leave 65-20 to have both.
So 45 have both, and remaining 55 have only one of the twos. : 80-45=35 have pen only, and 20 have only pencil
70 have at least one slate.
=> So fill up 55 who have just one item.
The remaining 70-55 have to be adjusted with those who have both.
Final status : 15 have all three, and remaining 85 have two items only. => b=15
a-b=65-15=50
D
09 Feb 2021, 22:52
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At least 1 pen = 80
Means: pens only + only pen and pencil + only pen and slate + pen and pencil and slate = 80
Basically means: the circle for pens is 80
So no pen = 100-80=20
At least 1 pencil = 65
the circle for pencils is 65
So no pencil = 100-65=35
At least 1 slate = 70
the circle for slates is 70
So no slate = 100-70=30
# Max of all 3 = min of 80,65,70 = 65
Min of all 3:
Let's think u have only pen and pencil
Min overlap = x
So, 80+65-x=100
x= 45
(We equate to 100 so that there is nothing that is neither pen nor pencil; this ensures that the overlap is also min)
Now, think of overlap with this 45 and slate:
Min overlap = y
So: 45+70-y = 100
y = 15
# So minimum overlap of all three = 15
Answer = 65-15 = 50
Option D
Posted from my mobile device
Means: pens only + only pen and pencil + only pen and slate + pen and pencil and slate = 80
Basically means: the circle for pens is 80
So no pen = 100-80=20
At least 1 pencil = 65
the circle for pencils is 65
So no pencil = 100-65=35
At least 1 slate = 70
the circle for slates is 70
So no slate = 100-70=30
# Max of all 3 = min of 80,65,70 = 65
Min of all 3:
Let's think u have only pen and pencil
Min overlap = x
So, 80+65-x=100
x= 45
(We equate to 100 so that there is nothing that is neither pen nor pencil; this ensures that the overlap is also min)
Now, think of overlap with this 45 and slate:
Min overlap = y
So: 45+70-y = 100
y = 15
# So minimum overlap of all three = 15
Answer = 65-15 = 50
Option D
Posted from my mobile device
