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Percentage problem %%

by akpareek » Mon Apr 08, 2013 8:58 am
In a survey conducted, it was found that 80% of the women surveyed were using atleast one of the three brands Lali, Ren and Ana. 40% of those surveyed were using Lali, 30% of the surveyed women were using Ren and 60% of the surveyed women were using Ana. 20% of the surveyed women use all the tree brands. What percentage of women surveyed use more than one of the given three brands?
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by Anju@Gurome » Mon Apr 08, 2013 9:51 am
akpareek wrote:In a survey conducted, it was found that 80% of the women surveyed were using atleast one of the three brands Lali, Ren and Ana. 40% of those surveyed were using Lali, 30% of the surveyed women were using Ren and 60% of the surveyed women were using Ana. 20% of the surveyed women use all the tree brands. What percentage of women surveyed use more than one of the given three brands?
For three overlapping sets A, B, and C :
  • Total = (Total in A) + (Total in B) + (Total in C) - (Total in exactly two) - 2*(total in all three) + (total in none of them)
In this case,
Total using Lali = 40%
Total using Ren = 30%
Total using Ana = 60%
Total using all three = 20%
Total using none = (100 - 80)% = 20%

Let us assume that percentage of women using exactly two is x.
So, 100 = 40 + 30 + 60 - x - 2*20 + 20 = 110 - x
--> x = 110 - 100 = 10

Hence, percentage of women using more than one = percentage of women using exactly two + percentage of women using exactly three = 10 + 20 = 30
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by GMATGuruNY » Mon Apr 08, 2013 11:16 am
akpareek wrote:In a survey conducted, it was found that 80% of the women surveyed were using atleast one of the three brands Lali, Ren and Ana. 40% of those surveyed were using Lali, 30% of the surveyed women were using Ren and 60% of the surveyed women were using Ana. 20% of the surveyed women use all the tree brands. What percentage of women surveyed use more than one of the given three brands?
Here is the formula for 3 overlapping groups:

T = A + B + C - (AB + AC + BC) - 2(ABC)

The big idea with overlapping group problems is to SUBTRACT THE OVERLAPS.
When we add together everyone in A, everyone in B, and everyone in C:
Those in exactly 2 of groups (AB+AC+BC) are counted twice, so they need to be subtracted from the total ONCE.
Those in all 3 groups (ABC) are counted 3 times, so they need to be subtracted from the total TWICE.
By subtracting the overlaps, we ensure that no one is overcounted.

In the problem above:
Let T = 80%
Lali = 40.
Ren = 30.
Ana = 60.
Exactly 2 of the brands = x.
All 3 brands = 20.

Plugging these values into the formula, we get:
80 = 40 + 30 + 60 - x - 2(20)
80 = 90-x
x=10.

Since 10% use exactly 2 of the brands, and 20% use all 3 brands, the percentage who use more than one brand = 10+20 = 30.

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