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# How many girls have had all these four items brain teaser?

Brain teasers which require a little math and reasoning are always fun to solve. Here is another such brainteaser. You need to find out that How many girls have had all these four items which are bag, shoe, umbrella and ring.

100 girls were attending a party.
85 of them had a red bag,
75 of them have worn brown shoes,
60 of them came with an umbrella and,
90 girls wore a ring.
How many girls have had all these four items?

Here are your 4 options, let’s see if you can find correct answer:

A. 5
B. 10
C. 20
D. 30

Also Try: If you like challenging puzzles then try, WHO IS THE COIN THIEF PUZZLE and STRONGBOX 6 DIGIT COMBINATION PUZZLE

Explanation:

For simplicity let us assume

Girls with umbrella A=60

wearing Brown shoes B=75

with red bag C=85

wearing a ring D=90

Solve this brain teaser like below:

### Explanation 1

Now, There must be 60 + 75 – 100 = 35 girls having both A and B
Similarly, 60+85-100=45 girls sharing A and C
Then, 60+90-100=50 girls sharing A and D

Add equation1 (A, B) and equation2 (A, C) and subtract A to find A, B, C
So, 35+45-60=20 girls sharing A, B and C.

Now, in order to find out all girls which share A, B, C and D. We need to add last two equations (A, B, C and A, D and the subtract A)

Finally 20+50-60=10 girls are sharing A,B,C and D.

### Explanation 2

Other way of solving this brain teaser is by assuming in reverse like

Girls with umbrella A=60. –> Which means there are 40 girls with no umbrella.

wearing Brown shoes B=75 –> Which means there are 25 girls with no shoe.

with red bag C=85 –> Which means there are 15 girls with no bag.

wearing a ring D=90 –> Which means there are 10 girls with no ring.

If you do the sum of all 4, it would be 40 + 25 + 15 + 10 = 90 which means, there are 90 girls which do not have at least one of these items. So, it gives us our answer 10 girls who have all 4.

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