Hey guys
For questions like this I use a triple Venn diagram that I've included below
The total T is 500
Let:
A = 210 for the total number of biscuit based sweets
B = 160 for milk based
C = 150 for coconut based
n = 200 for the number that don't have any of those ingredients
In a triple venn diagram like this, the total T must be equal to all of the small component letters:
T = a + b + c + d + e + f + g + n
This makes sense because it is just adding up the sweets that only have biscuits, only have milk, only have coconut, have biscuits and coconut but no milk, have all the ingredients, have none of the ingredients, and so on
If you were to add up just A + B + C you would get 530, which is larger than the total
The reason for this is you would be counting the sweets that have two ingredients twice and the ones that have all three ingredients three times
d, e, f would be counted twice and g would be counted three times
In fact A + B + C = a + b + c + 2d + 2e + 2f + 3g
These formulas come in handy in some triple Venn diagram questions and hopefully help conceptualize the meaning behind the diagram better
If something is unclear please ask, these questions are tricky at first but easy once you get the hang of it
So essentially we are given many of the elements of the diagram and the equation and if we plug them in we can derive the ones that we need to answer the question
We are told that:
e = 80 (milk and coconut, no biscuit)
d = 70 (milk and biscuit, no coconut)
f = 60 (biscuit and coconut, no milk)
We are asked how many have all 3, we are asked for the value of g
T = a + b + c + d + e + f + g + n = 500
Let's plug in what we know
500 = a + b + c + 70 + 80 + 60 + g + 200
a + b + 210 + g = 300
a + b + c + g = 90
g = 90 - a - b - c
(D) is eliminated because it is too high
How do we find out the value of a, b, and c?
A = a + d + f + g = a + 70 + 60 + g = a + 130 + g = 210
210 = a + 130 + g
a + g = 80B = b + d + e + g = b + 70 + 80 + g = b + 150 + g = 160
160 = b + 150 + g
b + g = 10C = c + f + e + g = c + 60 + 80 + g = c + 140 + g = 160
160 = c + 140 + g
c + g = 20You can now put a, b, and c in terms of g and plug it into the original equation
a = 80 - g
b = 10 - g
c = 20 - g
Recall from above:
a + b + c + g = 90
(80 - g) + (10 - g) + (20 - g) + g = 90
110 - 3g + g = 90
110 - 2g = 90
-2g = -20
g = 10
The answer is (A)
That's a lot of letters. No more alphabet soup for me
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