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Problem Solving - Doubt on question from OG11

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Problem Solving - Doubt on question from OG11

by anuptvm » Sat Jul 10, 2010 5:42 pm
Hi Mates,

I inferred the question wrongly I believe on this one:

John has 10 pairs of matched socks. If he loses 7 individual socks, what is the greatest number of pairs of matched socks he can have left?

I assumed the worst case scenario for John that the 7 individual socks belonged to 7 pairs and hence he is left with only 3 pairs.

The answer is 6 matched pairs. ( Lowest number of matched pairs that can be made from 7 socks is 3 full pairs plus one sock of the 4th pair).

I wanted to know if there are any general guidelines to handle such cases, or is it just read and re-read the question :D
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by Stuart@KaplanGMAT » Sat Jul 10, 2010 7:56 pm
anuptvm wrote:Hi Mates,

I inferred the question wrongly I believe on this one:

John has 10 pairs of matched socks. If he loses 7 individual socks, what is the greatest number of pairs of matched socks he can have left?

I assumed the worst case scenario for John that the 7 individual socks belonged to 7 pairs and hence he is left with only 3 pairs.
It's very important to read the question carefully so you know what to assume to solve.

Here, you're asked for the "greatest number of pairs of matched socks he can have left"; so, instead of assuming the worst case scenario, you should assume the best case scenario.
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by barcebal » Sat Jul 10, 2010 10:47 pm
I answer the question this way:

John has 10 pairs of socks. Convert to actual socks. 20 actual socks. He loses 7. He only has 13 socks left. He needs two/pair. 13/2 is 6.5 pairs. He can only, at most have 6 pair.

I have a major problem with answering what they are not asking for too . I've started reading my answer choice in my mind at the end as follows:

6 pair (my answer)....is the (go to the question) "greatest number of pairs of matched socks he can have left."

In your case you would have read to your self: 3 pair of socks is the greatest number of matched socks left.

I know it's not a lot but as you do this over and over as you practice you will subconciously start to pay better attention as you read the questions because, if you're like me, you'll subconsciously or even consciously not want to read the question to yourself at the end and realize that you have to start over.
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by barcebal » Fri Jul 16, 2010 7:31 am
gmathope,

You got it!
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by ozlemmetje » Thu Apr 17, 2014 5:16 am
Hey,

there is something I do not understand in the question stem.

If John loses 7 "individual" socks, doesn't that mean that they can be no pairs which means that there should be 1 from each pair but no 2 socks in one pair? so he is indeed left with 3.
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by Brent@GMATPrepNow » Thu Apr 17, 2014 5:22 am
ozlemmetje wrote:Hey,

there is something I do not understand in the question stem.

If John loses 7 "individual" socks, doesn't that mean that they can be no pairs which means that there should be 1 from each pair but no 2 socks in one pair? so he is indeed left with 3.
"individual" just means 1.
It doesn't mean that we are selecting exactly 1 sock from each pair. It just means that we are removing 7 socks.

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by Quasar Chunawala » Thu Apr 17, 2014 5:57 am
Problems where they'd ask what's the greatest or what's the least, in my mind, I apply a technique similar to this :

The maximum number of pairs that could remain = 10 - Min(No. of Sock pairs lost)

It's easy to imagine with 7 individual socks, you could form 3 pairs + 1 or 2 pairs + 3 or 1 pair + 5 or 7. So, the best you can do is 3 pairs + 1 lose sock

You would now have 6 pairs. Hope that's neat!
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by Dblooos » Sat Apr 11, 2015 3:50 pm
I got this question right in an earlier attempt but this time I got tricked. The way I interpreted the question this time was that each sock in a pair is same in color but one for left foot is different from one for right foot in shape. They are still matched. This makes each pair unique. I understand the reasoning explained above. But am I wrong in the way I am thinking? This is how i wear my socks every day. I can tell from the subtle difference in shape which one is for right foot and which one is for left. Of course they are color matched but not in shape. Is this question ambiguous?

For example: Socks can be paired this way :11, 22, 33, 44, 55, 66, 77, 88,.... and so on. They are matched to each other within a pair but not between pairs. Now if I lose one sock each from first 7 pairs. I can't make pairs like 12, 34, 56 etc.

I need some clarity, where in the question, this is distinguished. Please advise.

Thank you,
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by [email protected] » Sun Apr 12, 2015 12:59 pm
Hi Dblooos,

The original question doesn't state anything about "left sock" and "right sock", so we can't go making up details that don't exist. Even WITH that consideration though, the correct answer does not change - it's still 6.

Using your example, you could remove the socks 11, 22, 33 and 4.....which would leave you with 4, 55, 66, 77, 88, 99, 1010.

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by Dblooos » Sun Apr 12, 2015 5:21 pm
Rich,

I appreciate your response but I am not assuming anything that question does not state. My confusion is that question is ambiguous.

Where in the question is clarified that socks are matched within and between the pairs?

In your response you are assuming that 7 socks are removed 11, 22, 33 and 4

But socks from seven pairs can be removed in this way too 1, 2, 3, 4, 5, 6, 7 also.

This leaves you with only 3 pairs 88, 99, 1010..

Where in the question is this differentiated? Please explain.
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by [email protected] » Sun Apr 12, 2015 6:11 pm
Hi Dblooos,

The question asks for the GREATEST number of pairs that can be left (after removing 7 socks). The correct answer is the SAME regardless of how you interpret the question, so any ambiguity in the wording is irrelevant.

As far as the 'intent' that you're looking for in the wording, the phrase "10 pairs of matched socks" implies that we have 10 "pairs" of two and that each sock has 1 unique "partner sock." If we were meant to assume that all socks were interchangeable, then the phrase would likely have been "John has 20 socks...." (or equivalent).

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