Pairing Problem

[STEVEN SPIELBERG]

Q: 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)15

e)31

Source:Kaplan

I have a question regarding this problem. The answer given to this question is 4. But even if we get a pair of socks of the same color, how can we be sure that the two socks make a pair. For example, it's possible that both are of left foot or both are of right foot, so how does both make a pair. For a pair of socks we need one sock for the right foot and the other sock for the left foot. So how can we be sure that the two socks of same color are one for the right foot and the other for the left foot.

Or, is there some special meaning of the word ' loose socks' ? Are loose socks some special type of socks that have no left-right difference ? What am I missing ? Please advice.

[Brent@GMATPrepNow]

The idea here is that any two socks of the same color will make a pair.
I've never heard of a left sock and a right sock (other than those strange socks with toes)
To remove ambiguity, we could use marbles instead of socks and then ask how many we need to select to ensure that 2 are the same color.

By the way, are you sure the answer is 3? If we draw 3, we could get 1 black, 1 blue socks, and 1 white.
At that point, if you drew a 4th sock, it would surely match one of the 3 socks.
So, the answer should be 4.

Cheers,
Brent

[STEVEN SPIELBERG]

Hi Brent,

Yes, there has been an error. It's 4 which I have corrected. Though it's true that there are no distinct marks specifying left or right socks, we can distinguish left or right sock from the shape of the sock itself. Nevertheless, if the basic idea was to get a pair of socks of same color, then left-right distinction is irrelevant

Thanks!

[[email protected]]

Hi STEVEN SPIELBERG,

You pose an interesting question. The GMAT rarely offers questions with that level of detail (re: left socks vs. right socks), although you might see one. When that issue arises, the question will CLEARLY state the details though. In this prompt, there is NO mention of left socks or right socks....just socks, and the goal of selecting a matching color-pair.

GMAT writers are also really good at eliminating "interpretive bias", meaning that if you interpret the question in an incorrect way, then the answer that you would be looking for WILL NOT be in the answer choices. This will help you to re-evaluate the work that you did and interpret the question as intended. To go back to your original issue, what if ALL of the socks were right-toed socks? Then there wouldn't be an answer. Thus, the question cannot be about left vs. right.

GMAT assassins aren't born, they're made,
Rich

[GMATinsight]

Q: 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)15

e)31

Source:Kaplan

I have a question regarding this problem. The answer given to this question is 4. But even if we get a pair of socks of the same color, how can we be sure that the two socks make a pair. For example, it's possible that both are of left foot or both are of right foot, so how does both make a pair. For a pair of socks we need one sock for the right foot and the other sock for the left foot. So how can we be sure that the two socks of same color are one for the right foot and the other for the left foot.

Or, is there some special meaning of the word ' loose socks' ? Are loose socks some special type of socks that have no left-right difference ? What am I missing ? Please advice.

Such Questions has appeared in GMAT numerous times and the question only has to be attacked considering that a sock for left leg will be same as for right leg. Since the question doesn't specify any dictiction between the two so certainly we don't have to involve our own perception and get confused here.

The answer is straight 4 which I hope you have got

The KEY is to look for worst possible scenario and still make sure that the pair has been picked (favorable outcomes has been achieved)