Problem Solving

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

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.

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.

gmathope,

You got it!

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.

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!

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,

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.