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A drawer contains 12 socks, of which 8 are black and 4 are

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by AAPL » Thu Nov 22, 2018 2:50 am

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Princeton Review

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.

OA A.
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Thu Nov 22, 2018 11:22 pm
AAPL wrote:Princeton Review

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.

OA A.
Let's take each statement one by one.

(1) The socks that remain in the drawer have a ratio of 2 black to 1 white.

Say the out of the 3 removed socks, x were black, thus, (3 - x) were white.

Number of black socks (now) = 8 - x;
Number of white socks (now) = 4 - (3- x) = 1 + x;

Ratio of Black socks to White socks = (8 - x) : (1 + x) :: 2 : 1

=> x = 2

The number of socks that remain in the drawer black = 8 - 2 = 6. Sufficient.

(2) One of the first two socks removed is black.

We have no information about the third. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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by deloitte247 » Sat Nov 24, 2018 11:51 am
After removing three socks
remaining socks =12-3 = 9 socks
The 3 socks removed could be either 3 blacks, 3 whites , 1 black and 2 whites, 2 blacks and 1 white
$$let\ black\ =B\ and\ white\ =W$$

Statement 1
The socks that remain in the drawer have a ratio of 2B to 1W
$$9\ socks\ =\frac{\left(2B+2B+2B\right)}{\left(1W+1W+1W\right)}=\frac{6B}{3W}=6B:2W$$
Hence, there are 6 Blacks remaining in the drawer.
$$Statement\ 1\ is\ INSUFFICIENT$$

Statement 2
One of the first two socks removed is black, This means that from the first two socks removed, at least one of them is Black.
From the question, three socks were removed from the three socks there are two different possibilities;
1B and 2W or 2B and 1W ; this information doesn't tell us about the remaining 9 socks.
Hence Statement 2 is INSUFFICIENT

Statement 1 alone is SUFFICIENT
$$answer\ is\ option\ A$$
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