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20 Feb 2006, 18:05
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Of a group of people, 10 like to eat peanuts, 11 like to eat grapes and 14 like to eat vanilla ice cream, 3 like to eat all of the foods mentioned. 20 like to eat only one of the foods mentioned. How many people like to eat two of the foods mentioned?
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20 Feb 2006, 18:18
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I think the answer should be 3 .
say x like both peanut and grape
y like both peanut and vanila
z like both peanut and grape
so the people ONLY like peanut is 10 -( 3 +x+y)
the people ONLY like Grape is 11 -(3 +x +z)
the people ONLY like Vanila is 14 -(3 +y +z)
But according to question only 20 people like only one food so
if we add all the 3 above we get 26 -2 *(x+y+z) = 20
it means x + y+ z = 3
so three people eats 2 kinds food .
say x like both peanut and grape
y like both peanut and vanila
z like both peanut and grape
so the people ONLY like peanut is 10 -( 3 +x+y)
the people ONLY like Grape is 11 -(3 +x +z)
the people ONLY like Vanila is 14 -(3 +y +z)
But according to question only 20 people like only one food so
if we add all the 3 above we get 26 -2 *(x+y+z) = 20
it means x + y+ z = 3
so three people eats 2 kinds food .
21 Feb 2006, 03:38
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Agree with 3. Here's how I've done it:
If x=Nb of people who like only 1 flavor
y=Nb of people who like exactly 2 flavors
z=Nb of people who like all 3 flavors
Total number of people=x+y+z
=20+y+3
=23+y (1)
If p=Nb of people who like peanuts
g=Nb of people who like grapes
v=Nb of people who like vanilla
We can express total nb of people by adding p, g & v. But when we add up these, we count 2 times those who like 2 flavors and 3 times those who like 3 flavors. So we must remove y and 2z.
Hence total nb of people=p+g+v-y-2z=14+11+10-y-6=29-y (2)
Finally by equating (1) with (2):
23+y=29-y
y=3
If x=Nb of people who like only 1 flavor
y=Nb of people who like exactly 2 flavors
z=Nb of people who like all 3 flavors
Total number of people=x+y+z
=20+y+3
=23+y (1)
If p=Nb of people who like peanuts
g=Nb of people who like grapes
v=Nb of people who like vanilla
We can express total nb of people by adding p, g & v. But when we add up these, we count 2 times those who like 2 flavors and 3 times those who like 3 flavors. So we must remove y and 2z.
Hence total nb of people=p+g+v-y-2z=14+11+10-y-6=29-y (2)
Finally by equating (1) with (2):
23+y=29-y
y=3
it was helpful !
