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A sock drawer contains 36 pairs of socks, which are colored white, bro

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Re: A sock drawer contains 36 pairs of socks, which are colored white, bro [#permalink]
brp616
We know there are 36 pairs of socks

total 'colors' = 25 + 28 + 20 = 73

If 5 socks have all 3 colors, we know 5 pairs are counted in all 3 buckets, and we should de-duplicate by subtracting 5 * 2 = 10 - so we get 63 pairs...

But wait! this is much more than our total of 36 socks. So we need to find how many are still double counted. If a sock has 2 colors it is counted twice in our 63 color total, so to get the number of 2-color pairs we can do total colors - total socks = 63 - 36 = 27 - we know 27 pairs have 2 colors, and that gives us our answer for that part.

For the number of 1 color socks, we can do total - 3 color - 2 color or 36 - 27 - 5 = 36 - 32 = 4 pairs!

And this makes sense - if we have 73 total colors, we can do 4 + 27*2 (27 pairs w 2 colors) +5*3 (5 pairs w 3 colors) = 4 + 54 + 15 = 73
This is a good solution! ­I understand everything in here except the fact that how does subtracting the number of 2-color pairs from total socks ( 63 - 36 = 27 ) gives us the number of 2 color socks?
@KarishmaB @Bunuel Can you please explain this? I'm also curious how one would solve this using Venn diagrams, if possible at all.­
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Re: A sock drawer contains 36 pairs of socks, which are colored white, bro [#permalink]
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­from figure, we can write that
73-2(x+y+z)+(x+y+z)+5 = 36
(x+y+z) = 27 (2 colored socks)

for one colored socks
(20-x-y)+(23-x-z)+(15-y-z) = 58-2*27 = 4
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Re: A sock drawer contains 36 pairs of socks, which are colored white, bro [#permalink]
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Data Insights (DI) Butler 2023-24 [Question #159, Date: Dec-18-2023] [Click here for Details]

A sock drawer contains 36 pairs of socks, which are colored white, brown, or black, in some combination as follows:

• 5 pairs are colored with all three colors;
• 25 pairs have some white;
• 28 pairs have some brown;
• 20 pairs have some black.

In the table, select the number of pairs that have only one color and the number of pairs that have exactly two colors. Make only two selections, one in each column.

A very very quick logical answer to the question.

Since there are five pairs with all three colours, remaining 36-5 or 31 have exactly one or exactly two.

Look at the options that add up to 31. It is 4+27.
80 to 90% of the battle is already won.

A simple glance at numbers 25, 28 and 20 result of just 36 pairs of socks will tell that there will be many more with two colours than single colour.

Single: 4
Exactly two colours: 27

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Re: A sock drawer contains 36 pairs of socks, which are colored white, bro [#permalink]
Akshaynandurkar
­from figure, we can write that
73-2(x+y+z)+(x+y+z)+5 = 36
(x+y+z) = 27 (2 colored socks)

for one colored socks
(20-x-y)+(23-x-z)+(15-y-z) = 58-2*27 = 4
­Thanks! This was helpful. I tried solving this question using Venn diagram and got stuck because I took 25 as pairs with ONLY white,
28 as pairs with ONLY some brown and 20 pairs with ONLY black.
Re: A sock drawer contains 36 pairs of socks, which are colored white, bro [#permalink]
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