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A sock drawer contains 36 pairs of socks, which are colored white, bro
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18 Dec 2023, 13:51
18 Dec 2023, 13:51
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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.
| One color | Two colors | |
| 3 | ||
| 4 | ||
| 5 | ||
| 20 | ||
| 27 | ||
| 32 |
ShowHide Answer
Official Answer
One color: 4
Two colors: 27
Re: A sock drawer contains 36 pairs of socks, which are colored white, bro
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19 Dec 2023, 12:32
19 Dec 2023, 12:32
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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
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
General Discussion
Re: A sock drawer contains 36 pairs of socks, which are colored white, bro
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01 Jul 2024, 11:07
01 Jul 2024, 11:07
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Problem type overlapping set,
lets assume number of E1 = exactly 1 colored pair, E2 = exactly 2 colored pair, E3 = exactly 3 colored pair,
Given - 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; = E3 = 5
• 25 pairs have some white;
• 28 pairs have some brown;
• 20 pairs have some black.
Total pair of socks = 36 = E1 + E2 + E3,
E1 + E2 = 36 - 5 = 31 --- Eq1
and, E1 + 2E2 + 3E3 = 25 + 28 + 20 = 73
E1 + 2E2 = 73 - 15 = 58 ---- Eq2
on solving E2 = 27
E1 = 4
lets assume number of E1 = exactly 1 colored pair, E2 = exactly 2 colored pair, E3 = exactly 3 colored pair,
Given - 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; = E3 = 5
• 25 pairs have some white;
• 28 pairs have some brown;
• 20 pairs have some black.
Total pair of socks = 36 = E1 + E2 + E3,
E1 + E2 = 36 - 5 = 31 --- Eq1
and, E1 + 2E2 + 3E3 = 25 + 28 + 20 = 73
E1 + 2E2 = 73 - 15 = 58 ---- Eq2
on solving E2 = 27
E1 = 4
