70% of the employees in a multinational corporation have VCD players,

Given a population where A% has a certain characteristic X and B% has another characteristic Y (assuming both aren't exclusive), then you get the minimum overlap by assuming that the entire population that doesn't have X has characteristic Y, therefore the minimum portion of the population that has both characteristics is:

B-(100-A) %

So given A=70 for employees with VCD players and B=75 for employees with microwave ovens, at least:

75-(100-70)=45% have both. Then take the output and repeat with the other appliances.

A=45 for employees with both VCD players and microwaves, B=80 for ACs

80-(100-45)=25%

A=25 for employees with VCD players, microwaves and ACs, B=85 for washing machines

85-(100-25)=10%

Answer is C

Hi Bunuel,

I tried to understand the posts presented for solution, but I could not understand how they are doing it. Can you please help me with this?

Bunuel

Superb Explanation. Now I got how others are doing. Your example really helped. I try to give you Kudos for this explanation, but I don't why it keeps on loading. Thanks !

Since 70% + 75% = 145% and subtract 100%, we have at least 45% of the employees have both VCD players and microwave ovens.

Since 45% + 80% = 125% and subtract 100%, we have at least 25% of the employees have VCD players, microwave ovens and ACs.

Since 25% + 85% = 110% and subtract 100%, we have at least 10% of the employees have VCD players, microwave ovens, ACs and washing machines.

Answer: C

hey

Can you explain the logic for your solution?

Draw a scale with 11 dash marks across the page

Label each Dash Mark:

0%...........10%.............20%..........up to.........100%


We want to draw Blocks underneath the scale representing the %percentage of people who are part of Each Set.

Our goal is to MINIMIZE the overlap where ppl are part of ALL 4 SETS as much as we can.



(1st) for the 70% (call it A)

Draw a continuous block from 0% thru 50%

Then draw another continuous block from 80% to 100%


(2nd) for the 75% (call it B)

Draw ONE Continuous block from the 25% marker (mark another dash in between 20% and 30%) all the way through the 100% marker


(3rd) for the 80% (call it C)

Drawn ONE continuous block from 0% marker to 80% marker


(4th) for the 85% (call it D)

The Goal is to try and split up the 85% beneath the other blocks that represent sets underneath the scale such that we MINIMIZE the overlap of all 4 sets.



Step 1: you can draw a continuous block from 0% marker to 25% marker

For this 25% of D, they will only be part of —-> A....C.....D



Step 2: you can draw a continuous block from 50% marker to 80% marker

For this 30% of D, they will only be a part of ——> B.....C......D


Step 3: you can draw a continuous block from the 80% marker to the 100% marker

For this 20% of D, they will only be a part of ——> A......B......D


If drawn correctly, you should see that you are able to have:

25% + 30% + 20% = 75% of the D-people as part of EXACTLY 3 groups

However, no matter where you place the last 10% of the D-people on the Scale, they will be fall underneath 3 other blocks and thus be part of 4 Sets.


Correct Answer:

The least amount that can be part of all 4 sets is = 10%

C

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