Melinda's lights went out. She has 3 pairs of red socks in her drawer

Question

Melinda's lights went out. She has 3 pairs of red socks in her drawer, 2 pairs of black socks, and 5 pairs of white socks. What is the minimum number of pairs she must remove from the drawer to ensure that she has a pair of each color?

A. 3
B. 5
C. 7
D. 9
E. 10

A. 3
B. 5 
C. 7
D. 9
E. 10

Bunuel · Answer

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Kinshook · Answer

She has to take out = 5 W + 3 R + 1 B = 9 pairs

IMO D

Archit3110 · Answer

total pairs 10
red ; 3 , black 2 and white ; 5
so she would have to take out 5 white+ 3 red + 1 black ; 9 pairs to ensure that she ends up with a pair of same color
IMO D

Sayon · Answer

We need at least 1 pair of each color.

We have-

Red- I I I   
 Black- I I  
  White- I I I I I

Let's consider the  worst-case scenario :  
We pick up   5   - All turn out to be   White  
Then we pick up   3   more - All turn out to be   Red  . 
So, till now  we picked up 8 socks  and have pairs of  2 colors  (White and Red).

The  9th one  we pick -  Has to be Black  (as it will be the only color left).

Hence,  Melinda needs to remove a minimum of 9 pair from the drawer to ensure that she has a pair of each color.
 
 Answer D

saukrit · Answer

In worst case, Melida may have 5 pairs of white , 3 pairs of red and 1 pair of black socks to ensure that she has at least 1 pair of each color.

Total pairs= 5+3+1=9

Hence, IMO D is the answer

ogmega · Answer

If someone could help me here, I don't understand why we are considering the worst case scenario for minimum number of pairs.

If the question says maximum number of pairs to remove to get each coloured pair then it should be 9, while minimum should be 3 ( the best case )

saukrit · Answer

If it was.just ,3 you could have taken out all 3 from.the.5 pairs of same color.

Rephrase the question as ...Minimum numbers of socks I must pick to be 100% sure that I got at least one pair of each color

For doing that I need all 5+ all 3 and 1 more(for the third.color

Even if I choose 8 not 9 I may still be choosing just 5 pairs of first color and 3 pairs of second color and not end up getting one pair of each color.

Hope this helps

Posted from my mobile device

fireagablast · Answer

I think this question is worded poorly. 
"What is the minimum number of pairs she must remove from the drawer to ensure that she has a pair of each color?"
I interpreted this as "how many does she have to remove from the drawer to ensure she has a pair of each in the drawer?".

Also, as other people have pointed about, the best case scenario from take out socks (and ending up with a pair of each outside the drawer) would be 3. But this is missing the "certainty" part of this question. Recommend rephrasing to "What is the minimum number of pairs she must remove from the drawer to ensure that she has a pair of each color with 100% certainty?"

ScottTargetTestPrep · Answer

If she removes 8 pairs of socks, she might have all 3 pairs of red socks and all 5 pairs of white socks, but no pairs of black socks. However, if she removes 1 more pair of socks, she will have a pair of socks of each color since the final pair of socks must be a matching black pair.

Answer: D

sarphant · Answer

Since we need to be sure, so we will go for the worst case scenario - 
First 5 pair drawn are all white,
Next 3 drawn are all red,
Now certainly one more pair drawn and we have all the three pairs.
So the Answer is 5+3+1 = 9

Melinda's lights went out. She has 3 pairs of red socks in her drawer

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Melinda's lights went out. She has 3 pairs of red socks in her drawer

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