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# The drawer in the living room contains black, blue and gray glov

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The drawer in the living room contains black, blue and gray glov  [#permalink]

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14 Mar 2020, 18:26
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Difficulty:

55% (hard)

Question Stats:

48% (01:48) correct 52% (01:15) wrong based on 25 sessions

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GMATBusters’ Quant Quiz Question -6

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.

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Re: The drawer in the living room contains black, blue and gray glov  [#permalink]

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14 Mar 2020, 19:16
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?

Black gloves >3, blue gloves>3 and gray gloves>3
We need exact no. of pairs.

(1) The drawer contains 11 gloves.
At least 3 pairs,1 pair of each color, (total 6) can be removed. There are 5 more gloves.
If Black = 2 out of 5 and blue = 2 and gray =1, out of 5 more gloves, then total 5 pairs are removed
If black = 1, blue = 1 and grey = 3, then total 4 pairs are removed. Hence, no unique value. Insufficient.

(2) The drawer contains an equal number of black and gray gloves. No exact information about any color gloves. Insufficient.

1) + 2) Total = 11 nos.
Black = 4, Blue = 3 and Gray = 4, total 5 pairs removed. Sufficient.

Imo. C
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Re: The drawer in the living room contains black, blue and gray glov  [#permalink]

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14 Mar 2020, 20:07
1
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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Re: The drawer in the living room contains black, blue and gray glov  [#permalink]

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14 Mar 2020, 20:29
Quote:
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 : BL BL BL BU BU BU G G G (at the very least)

(1) The drawer contains 11 gloves.

We can have : BL BL BL BU BU BU BU G G G G. So we get 1+2+2 = 5 Matching Pairs

We can have : BL BL BL BU BU BU BU BU G G G. So we get 1+2+1 = 4 Matching Pairs
Not Sufficient.

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

Since we don't know the total number of gloves we can technically remove infinite number of matching paris.

Not Sufficeint.

Try Combined:

We can see that we will have only one case as below:
BL BL BL BL BU BU BU G G G G. So we get 1+2+2 = 5 Matching Pairs

Sufficient.

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Re: The drawer in the living room contains black, blue and gray glov  [#permalink]

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14 Mar 2020, 21:04
OA is supposedly E
As been asked how many matching pairs can be removed
Statement 1: 11 gloves are there. It's not sufficient as we only know. There are atleast 3 of each colour so it can be more of two of them or 1 of them either. Not specific answer. (Not sufficient)
Statement 2: Blue and Gray are in equal no. But that doesn't give any specific no. Either.
So statement 2 is insufficient.
Combining both we get two cases.
Such as there will be either 3,3 and 5 gloves of blue , gray and black or 4,4&3. No specific no. Is answered here. So OA is E

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Re: The drawer in the living room contains black, blue and gray glov  [#permalink]

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15 Mar 2020, 01:50
Given: The drawer in the living room contains black, blue and gray gloves, including at least three gloves of each color.

Asked: How many matched pairs can be removed?

(1) The drawer contains 11 gloves.
The drawer contains 3 black, 3 blue & 3 grey gloves. There are 2 more gloves of black, blue or grey colors.
Since the exact number of black, blue and grey gloves in unknown
NOT SUFFICIENT

(2) The drawer contains an equal number of black and gray gloves.
Since the total number of gloves is not known
NOT SUFFICIENT

(1) + (2)
(1) The drawer contains 11 gloves.
(2) The drawer contains an equal number of black and gray gloves.
Case 1;
The drawer contains 3 black, 3 grey & 5 blue gloves
Number of matched pairs that can be removed = 3C2 + 3C2 + 5C2 = 3 + 3 + 10 = 16
Case 2:
The drawer contains 4 black, 4 grey & 3 blue gloves
Number of matched pairs that can be removed = 4C2 + 4C2 + 3C2 = 6 + 6 + 3 = 15
NOT SUFFICIENT

IMO E
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Re: The drawer in the living room contains black, blue and gray glov  [#permalink]

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15 Mar 2020, 02:05
There are at least 3 gloves of each color so there are already 3 matched pairs (1 pair of each color) in the drawer.
So Initial gloves list: BBB, GGG, Blue Blue Blue
Pairs: BB, GG, Blue Blue

$$Statement 1:$$ Drawer contains 11 gloves
As per initial statement, we have 3 matched pairs (mentioned above).
There are 2 conditions for remaining 2 gloves:
1. Both gloves are of same color. Then they would form a pair.
So total matched pairs = 3+1 = 4

2. Both gloves are of different colors. They would form 2 pairs along with the unmatched glove of same colors.
So total matched pairs = 3+2 = 5

Since we are getting 2 answers, Not Sufficient

$$Statement 2:$$The drawer contains an equal number of black and gray gloves.
We already have 3 matched pair (1 pair of each color)

Let total no. of blue gloves be 4 and total no. of gray/black gloves be 6 each. (Total = 4+6+6=16)
So there would be total of 2 pairs of blue gloves, 3 pairs each of gray and black

But if there are 4 blue gloves, 3 gray and 3 black gloves.
There would be 2 pairs of blue, 1 pair of gray and 1 pair of black gloves.

Thus, matched pairs would vary.
Not sufficient

Statement 1 & 2 together:
Total 11 gloves. Minimum 3 pairs. Equal no. of black and gray gloves.
We need to find options for 2 gloves.

1. blue gloves = 5. So 2 pairs of blue gloves.
black = 3 gloves
gray = 3 gloves
Total matched pairs: 4

2. Blue = 3 gloves
Black = 4 gloves
Gray = 4 gloves
Total matched pairs: 5

Option: E
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Re: The drawer in the living room contains black, blue and gray glov  [#permalink]

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15 Mar 2020, 03:58
Statement-1
Possible combination of groups:4,4,3 and 3,3,5
Different combinations have different pairs of matched gloves
Not sufficcient
Stat -2:
equal number of black n grey
but we don't know number of each colour
Not sufficient
1+2: combining 1 n 2 both have different combination as 4,4,3and 3,3,5 not sufficient
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Re: The drawer in the living room contains black, blue and gray glov  [#permalink]

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15 Mar 2020, 18:55
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.

1) Several cases are possible. 4 Black, 4 Gray and 3 Blue (5 matching pair). 3 Black, 3 Blue , 5 Gray ( 4 matching pair).Not sufficient.
2) We have no information about the number of total gloves. Not sufficient.
Together, there are still 2 possibilities (3 of each from Black and Gray and the rest 5 are Blue (4 pairs) and 4 from each of Black and gray and 3 are Blue (5 matching pairs). Not sufficient.

Re: The drawer in the living room contains black, blue and gray glov   [#permalink] 15 Mar 2020, 18:55