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

Question

70% of the employees in a multinational corporation have VCD players, 75 percent have microwave ovens, 80 percent have ACs and 85 percent have washing machines. At least what percentage of employees has all four gadgets?

(a) 15%
(b) 5%
(c) 10%
(d) 20%
(e) 25%

(a) 15% 
(b) 5% 
(c) 10% 
(d) 20%
(e) 25%

RMD007 · Accepted Answer

Hi AR15J,

Let me put the same answer with a different theory.

Consider that you have plane square with 100 units and we need to fill this with 4 colors A- with 70 units B- 75 units C- 80 units and D-85 units. Now with this, questions asks us to find minimum units which contains all 4 colors when we add colors to the square sequentially.

Step1 Add color A with 70 units so the remaining area is 30 units.

Now step 2 onward add colors so that the remaining part of the previous color is filled first.

Step2: Add B to the remaining units of A which is 30. So units that contains A and B is 75- 30= 45

Step3 Add C to the remaining units of A+B = 100-45 = 55. So units that contains A and B and C is 80-55 = 25

step4 Add D to the remaining units of A+B+C = 100-25 =75 So units that contain A, B, C and D are 85-75 = 10

Hope this helps. :D

Vodolaz · Answer

so 30% employees don't have VCD devices.

25% employees don't have MO

20% employees don't have ACs

15% employees don't have WM

Summ of employees that don't have some device = 30%+25%+20%+15% = 90% < 100% 
So definitely at least 10% employees have 4 devices.

another way to calculate this: 
85% and 70% --> 55% have at least 2 devices (WM and VCD)
55% and 80% --> 35% have at least 3 devices (WM, VCD and ACs)
35% and 75% --> 10% have at least 4 devices

ans: C

jmikery · Answer

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

AR15J · Answer

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?

AR15J · Answer

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 !

JeffTargetTestPrep · Answer

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

Fdambro294 · Answer

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

Posted from my mobile device

DiveshR · Answer

jmikery   JeffTargetTestPrep  - in this question, why don't we consider the population that has neither of the gadgets?

For example,

70% (VCD) + 75% (Microwave) - x% both + y% neither = 100 // however, every solution has ignored the y% neither aspect and concluded x% = 45%. Why so?

Since we're trying to minimize the overlap (find the least), shouldn't we then MAXIMIZE the y% - where am I going wrong?

Rohanx9 · Answer

Solved in 1 min 02 seconds. The most intuitive way and quickest way for me:

There are 310 total items and 100 people to share the items with. How can I minimise the number of people with 4 items?

Give everyone 3 items each = 300 items. I'm still left with 310-300 = 10 items to handout. I need to give 10 items to 10 people who already have 3 items, making 90 people have 3 items, and 10 people have 4 items.

Answer = 10.

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

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

Prep Toolkit

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