Out of 100 ladies attending the church fete, 85 had a white handbag; 7

Question

Out of 100 ladies attending the church fete, 85 had a white handbag; 75 had black shoes; 60 carried an umbrella; 90 wore a ring. How many ladies must have had all four items?

(A) 5 
(B) 10 
(C) 15 
(D) 25 
(E) 35

rajatchopra1994 · Answer

Explanation:

=100 - (15+25+40+10) 
=100 - 90
=10
IMO-B

Abhishek009 · Answer

100 - ( 15 + 25 + 40 + 10 ) = 10 , Answer must be (B)

ShankSouljaBoi · Answer

Why are you using the compliment of the set . What is the formula for such overlapping. Could you please detail your solution with some theory.

Best !!

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rsrighosh · Answer

rajatchopra1994   Abhishek009

Can you please elaborate? how we get this?

rajatchopra1994 · Answer

Dear  rsrighosh  ,

Explained explanation:
Total ladies in party = 100
Ladies with umbrella = 60 (without Umbrella = 100 - 60= 40)
Ladies with black shoes = 75 (without Shoes = 100 - 75 = 25)
Ladies with white handbag = 85 (without White Handbag = 100 - 85 = 15)
Ladies with a ring = 90 (without Ring = 100 - 90 = 10)

Need to find - Ladies must have had all four items = 100 (total) - without all the things
= 100 - (40+25+15+10)
= 100 - 90
= 10

Hope you understand.

Regards,
Rajat Chopra

Deepakjhamb · Answer

Hi Rajat

I fail to understand how total - without all 4 gives u with with all 4 , see there can be ppl 
Having 2 things together , ppl having 3 things together also . Also we are asked to find must be number which indicates minimum number of items we need to find .

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Deepakjhamb · Answer

Bunuel

How to solve this 4 items question in Venn diagram

Kinshook · Answer

Given: Out of 100 ladies attending the church fete, 85 had a white handbag; 75 had black shoes; 60 carried an umbrella; 90 wore a ring. 
Asked: How many ladies must have had all four items?

Total ladies = 100
Ladies without a white handbag = 100 - 85 = 15
Ladies without black shoes = 100 - 75 = 25
Ladies without umbrella = 100 - 60 = 40
Ladies without a ring = 100 - 90 = 10
Ladies without any one item = 15 + 25 + 40 + 10 = 90 
Ladies with all 4 items = 100 - 90 = 10

IMO B

srik410 · Answer

Total claims of all objects by ladies = 85+75+60+90 = 310
Total women under discussion = 100

So, if all women claimed only 3 objects (because we want to minimize owning 4), we get 300 objects claimed.
But total claims = 310 not 300. 
So some women must cover this slack by owning more. So if 10 women among 100 took 1 object each(of the unclaimed 10 objects), we are good

If they did so, then at least 10 women owned 4 objects or more

Rohanx9 · Answer

100 Women. 310 total items.

Think of this in reverse, how can I distribute 310 items to 100 women?

I give out each woman 3 items (giving out total 100 * 3 =300 items), but then still have 10 items left. 
Therefore I need to give 10 women one more item.

90 women own 3 items, 10 women own 4.

Out of 100 ladies attending the church fete, 85 had a white handbag; 7

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Out of 100 ladies attending the church fete, 85 had a white handbag; 7

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