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In a certain sock drawer, there are 4 pairs of black socks, 3 pairs of
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21 Jul 2022, 01:24
21 Jul 2022, 01:24
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In a certain sock drawer, there are 4 pairs of black socks, 3 pairs of gray socks and 2 pairs of orange socks. If socks are removed at random without replacement, what is the minimum number of socks that must be removed in order to ensure that two socks of the same color have been removed?
A. 4
B. 7
C. 9
D. 10
E. 11
A. 4
B. 7
C. 9
D. 10
E. 11
Part of the project: GRE QCQ & PS 3 Questions Every One DAILY Challenge - (2022)
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GRE Math Essentials (2022)
GRE Geometry Formulas for a Q170
GRE - Math Book
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GRE Math Essentials (2022)
GRE Geometry Formulas for a Q170
GRE - Math Book
Re: In a certain sock drawer, there are 4 pairs of black socks, 3 pairs of
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21 Jul 2022, 02:26
21 Jul 2022, 02:26
1
Solution -
The question asks us how many socks have to be chosen at random in order for us to be SURE that we chosen at least two socks of the same colour.
The information given in the question is -
Black socks = 8 as there are 4 pairs of black socks,
Gray socks = 6 as there are 3 pairs of gray socks,
Orange socks = 4 as there are 2 pairs of orange socks.
Out of them, if 3 socks are removed,
then it can be 2 socks of one colour and 1 sock of another colour,
OR
3 socks of one single colour,
OR
1 of each colour, each of the 3 socks is of 3 different colours.
Since 1 of each colour is possible, and hence, we might not get a pair.
If 4 socks are removed, then it can be 1 of each colour and the 4th sock removed has to form a pair with one of the three colours.
If we consider any other case, it will also have a pair.
Hence 4 should be the minimum.
Therefore, the correct answer is option A.
The question asks us how many socks have to be chosen at random in order for us to be SURE that we chosen at least two socks of the same colour.
The information given in the question is -
Black socks = 8 as there are 4 pairs of black socks,
Gray socks = 6 as there are 3 pairs of gray socks,
Orange socks = 4 as there are 2 pairs of orange socks.
Out of them, if 3 socks are removed,
then it can be 2 socks of one colour and 1 sock of another colour,
OR
3 socks of one single colour,
OR
1 of each colour, each of the 3 socks is of 3 different colours.
Since 1 of each colour is possible, and hence, we might not get a pair.
If 4 socks are removed, then it can be 1 of each colour and the 4th sock removed has to form a pair with one of the three colours.
If we consider any other case, it will also have a pair.
Hence 4 should be the minimum.
Therefore, the correct answer is option A.
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Re: In a certain sock drawer, there are 4 pairs of black socks, 3 pairs of
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21 Jul 2022, 06:18
21 Jul 2022, 06:18
1
Carcass wrote:
In a certain sock drawer, there are 4 pairs of black socks, 3 pairs of gray socks and 2 pairs of orange socks. If socks are removed at random without replacement, what is the minimum number of socks that must be removed in order to ensure that two socks of the same color have been removed?
A. 4
B. 7
C. 9
D. 10
E. 11
A. 4
B. 7
C. 9
D. 10
E. 11
If we remove 1 black sock, 1 gray sock, and 1 orange sock, then we still don't have a matching sock. So, we can select 3 socks WITHOUT having a matching pair.
However, if we pick ANY sock for our fourth sock, that sock MUST match one of the first 3 socks selected.
Answer: A
