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A drawer contains 12 socks, of which 8 are black and 4 are white. If 3

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A drawer contains 12 socks, of which 8 are black and 4 are white. If 3  [#permalink]

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New post 16 May 2017, 11:43
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87% (01:12) correct 13% (01:18) wrong based on 31 sessions

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A drawer contains 12 socks, of which 8 are black and 4 are white. If 3 of the socks are removed, how many of the socks that remain in the drawer are black?

(1) The socks that remain in the drawer have a ratio of 2 black to 1 white.
(2) One of the first two socks removed is black.

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Re: A drawer contains 12 socks, of which 8 are black and 4 are white. If 3  [#permalink]

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New post 17 May 2017, 03:12
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Out of 12 socks, 8 are black 4 are white
After removing 3 socks, we are left with 9 socks

3 socks removed could be 3B, 3W, 1B2W, 2B1W

From option (1) After removing 3 socks, we have ratio of 2:1 of black and white. it means that we have left 6 Black and 3 White (Ratio is equal to 2:1)

It clearly shows 6 black socks are left.

From option (2) There could be 2 different possibilities 1B2W, 2B1W

Hence, A is the correct answer.

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Re: A drawer contains 12 socks, of which 8 are black and 4 are white. If 3  [#permalink]

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New post 17 May 2017, 04:45
If 3 socks are removed, 9 socks will remain out of which some will be black and some will be white.

Statement 1. Black and white are in the ratio 2:1.
Divide 9 in this ratio we get 6 black and 3 white socks remaining. Sufficient.

Statement 2. Out of the first two, one is black (this means other is white).
Now if 3rd sock removed is black, 6 black socks will remain. But if 3rd sock removed is white, 7 black socks will remain.
So Insufficient.

Hence A.

(May I put forward another way to look at statement 1. Not directly related to this question maybe but a learning nevertheless.
Initially the black (8) and white (4) socks in the drawer are in the ratio 2:1
After removal of 3 socks, ratio of black and white is still 2:1
This can only happen when the socks removed also are in the ratio 2:1
Hence we can conclude that out of 3 socks removed, 2 must be black and 1 must be white)
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Re: A drawer contains 12 socks, of which 8 are black and 4 are white. If 3 &nbs [#permalink] 17 May 2017, 04:45
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A drawer contains 12 socks, of which 8 are black and 4 are white. If 3

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