From a drawer containing black, blue and gray solid-color socks, inclu

Question

From a drawer containing black, blue and gray solid-color socks, including at least three socks of each color, how many matched pairs can be removed?

(1) The drawer contains 11 socks.

(2) The drawer contains an equal number of black and gray socks.

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2pumpchump · Accepted Answer

Statement 1  tells us that the sum of the 3 different colors = 11.
With the given constraint of at least 3 of each color, we can have 5 black socks, 3 blue and 3 gray. This would give us 4 matching pairs (2*2 black, 2*1 blue, 2*1 gray). 
We could also have 4 black, 4 gray, and 3 blue. This would give us 5 matching pairs. (2*2 black, 2*2 gray, 2*1 blue).

We get 2 different answers. We can eliminate A and D.

Statement 2  tells us that there is an equal number of black and gray. No need to explain this. We can have 100 black, 100 gray, hence 100 different matching pairs. (50*2 black, 50*2 gray). We could also have 4 gray and 4 black. 
 Unlimited different answers from this. We can eliminate B.

Statement 1+2  together:
Black and gray are equal, total number of socks = 11.
Ex: 5 blue, 3 gray and 3 black. = 4 different pairs.
4 black, 4 gray, 3 blue = 5 different pairs.

Eliminate C.

E is the correct answer .

satya2029 · Answer

From 2
BLACK...........BLUE............GRAY
l- - - l l- - -l l- - -l 3 PAIRS
l- - - -l l- - -l l- - - -l 5 PAIRS
FROM 1
BLACK..........BLUE..............GRAY
l- - -l l- - - -l l- - - -l 5 PAIRS
l- - -l l- - - -l l- - -l 4 PAIRS
l- - - -l l- - -l l- - - -l 5 PAIRS
statement 2 is contained in statement 1
E:)

QuantMadeEasy · Answer

(1) The drawer contains 11 socks.
Number of Blue, Black or gray socks could be 3, 3,5 OR 4,4,3 Insufficient

(2) The drawer contains an equal number of black and gray socks.
Insufficient

(1)+(2); Number of Blue, Black or gray socks could be 3, 3,5 OR 4,4,3 Insufficient

E is correct.

Thelionking1234 · Answer

This problem cannot be solved through formula. Given that the drawer contains at least three socks of each color, we know that at least one matched pair of each color can be removed. From the first nine socks, we can therefore make three pairs, leaving three ‘orphans.’ To think through the problem, it is useful to conceptualize removing those nine socks from the drawer. We will need additional information about any socks left in the drawer to solve the problem.

(1) INSUFFICIENT: Once those first nine socks have been removed, only two socks remain, but we do not have sufficient information about the color of the two socks to solve the problem. If the two remaining socks are a matched pair, we can add this final pair to the first three. This scenario results in four pairs and three orphans. However, if the final two socks are mismatched, each will make a new pair with one of the original three orphans, resulting in five pairs and one orphan.

(2) INSUFFICIENT: This statement gives no information about how many socks are in the drawer.

(1) AND (2) INSUFFICIENT: Given that the drawer contains 11 socks and that there are an equal number of black and gray socks, there are two possible scenarios. Three black, three gray, and five blue socks would yield four pairs total. Four black, four gray, and three blue socks would yield five pairs total.

The correct answer is E.

bumpbot · Answer

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