The drawer in the living room contains black, blue and gray gloves, including at least three gloves of each color, how many matched pairs can be removed?
(1) The drawer contains 11 gloves.
(2) The drawer contains an equal number of black and gray gloves.
Given:
Only Black, Blue and Gray Gloves
Atleast 3 gloves of each color. So minimum of 9 gloves in the drawer.
Need:
How many matched pairs can be removed
(1) The drawer contains 11 gloves.
We know that there is a minimum of 9 gloves in the drawer, So we have 3 gloves of each color. So the 10th and 11th gloves can belong to any one color or one each of different colors.
If 10th and 11th is Black and Blue, then we still have 2 pairs of Blue and Black and 1 pair of gray - we have 5 pairs of gloves.
If 10th and 11th both are black, then we will have 5 black gloves (2 Pairs), 1 pair of Blue and 1 pair of gray - so total of 4 pairs of gloves
Option 1 alone not sufficient.
(2) The drawer contains an equal number of black and gray gloves.
This does not give us how many socks the drawer has in total. Option 2 alone is not sufficient.
(1) + (2) - Lets see Option 1 and 2 together
We know total socks in drawer is 11 and we have equal number of black and gray gloves. We already have 3 gloves each in black and gray color. The number we already have are equal. So we have 2 cases
Case 1: The 10th and 11th glove is blue colored gloves [5 blue gloves]. So we have 3 black and 3 gray gloves. So we have 4 pairs of matched socks.
Case 2:The 10th glove is Black and 11th is gray color. So we have equal number of black and gray gloves - 2 pairs each. And then we have 3 blue gloves which has 1 matched pair. So we have total of 5 pairs.
We get 2 different answer choices. Option 1 and 2 together is not sufficient.
Ans:
E
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