George's drawer has 10 loose black socks, 15 loose blue socks, and 8

Question

George's drawer has 10 loose black socks, 15 loose blue socks, and 8 loose white socks. If George takes socks out of the drawer at random, how many would he need to take out to be sure that the removed socks include at least one matching pair ?

A. 3
B. 4
C. 9
D. 5
E. 31

Kudos for a correct solution.

A. 3
B. 4
C. 9
D. 5
E. 31

sunita123 · Accepted Answer

in worst scenario he will draw three different color socks and 4th draw will be a matching pair.
Answer is B

buddyisraelgmat · Answer

30 secs

Ans B = 4

600 level ... Really?

CCMBA · Answer

We plan for the worst case scenario. Let K, B, W = black, blue, white (respectively). Say we draw KBW. No matter what we pick next, we will have a matching pair. The answer is 4 (B).

Prices · Answer

Answer =  B

Worst case scenario: 
First Pick =  Blue 
 We only have one sock, so no match. 
Second Pick = Black
 Darn, a different color, still no match. 
Third Pick =  White 
 What are the odds, still no match. 
Fourth Pick = Black
 Hurrah, we now have a pair of black socks!

You can substitute the color of the fourth pick with either blue or white and the answer still hold true, we would have a match.

longfellow · Answer

Answer is 4

As there are 3 categories, fourth draw will match one of the earlier drawn category.

GMATinsight · Answer

For 1 matching pair the worst scenario is that he picks 3 socks and all 3 are different color

but in that case 4th sock picked has to be a repeated color thereby making a pair

Hence, Minimum socks needed to be picked = 4

Answer: option B

Bunuel : you might want to add an OA in this question as official answer is still not provided.

AkshdeepS · Answer

My Solution:

As we have socks of 3 different colours, in the first three picks we can take out socks of any colour. So to be sure that we have a pair of socks we need to pick forth one. It will pair up with any of the first three socks we chose.

So IMO, answer is 4. Choice B

Jihyo · Answer

What if the question asked at least two matching pairs?

AnkithaSrinivas · Answer

The question should be like max picks or min picks.

Min pick - 5 (assuming its one of the different color he picked)
since by 4 picks - he already has 1 pair and 2 different colors without a pair

Max - 
If he picked white again - no 
6th - even if he picks white again - hes good 
cause he will have 2 pairs

Else if he picks ant other color - he will still have 2 pairs

luisdicampo · Answer

Deconstructing the Question

There are 3 colors of socks: black, blue, and white. We want to guarantee that we have at least one matching pair.

Use the worst-case scenario.

Step-by-step

To avoid having a pair for as long as possible, we pick one sock of each color:

1  black,  1  blue,  1  white

Now we have  3  socks with no matching pair.

The next sock must match one of these three colors.

So with  4  socks, we are guaranteed at least one pair.

Answer B

George's drawer has 10 loose black socks, 15 loose blue socks, and 8

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

George's drawer has 10 loose black socks, 15 loose blue socks, and 8

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards