John has 10 pairs of matched socks. If he loses 7 individual

Question

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?

(A) 7
(B) 6
(C) 5
(D) 4
(E) 3

fameatop · Accepted Answer

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?
(A) 7
(B) 6
(C) 5
(D) 4
(E) 3

Because we have to maximize the pair of matched socks, we will remove 3 pairs(6 socks) out of 10 pairs & 1 sock from the 4th pair. 
Thus the no of matching socks pair remaining = 10 -4 = 6
Answer B

If we were asked minimum no of pairs of matched socks, we would have removed all the 7 socks from 7 different pairs out of 10 pairs. 
Thus the no of matching socks pair remaining = 10 -7 = 3
Answer E

Hope it helps

Bunuel · Answer

SOLUTION

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?

(A) 7
(B) 6
(C) 5
(D) 4
(E) 3

General rule for such kind of problems:  
to maximize one quantity, minimize the others; 
to minimize one quantity, maximize the others.

The lowest number of pairs we can make from 7 individual socks is 3 pairs and one sock from a fourth pair. Hence, the greatest number of pairs of matched socks John can have left is 10 - 4 = 6.

Answer: B.

dexerash · Answer

Since question is asking the Greatest number of pairs left after John loses 7 socks, it is better to count the socks in pairs.

In total 7 socks are lost, which can be counted as 3 pairs of socks (3x2) + 1 single socks. So in total 4 pairs are lost as 1 single sock can not be counted in a pair.

So, 10 - 4 = 6 pairs of socks.

B

feat · Answer

I'm thinking that if he has 10 pairs, that is 20 socks. If he loses 7 individual socks, then the greatest number of socks he could have left is:

20-7= 13 -> 6 pairs, since 13/2 is not an integer.

Hence, the answer is B.

chibimoon · Answer

Hi there
This might sound silly but when I read this question I initially drew out aa bb cc etc as his socks and crossed out one letter of each 7 pairs which left me with 3 pairs left, could someone explain how clearly this is a wrong approach? How do I know that his socks are all the same. Thank u

TimeTraveller · Answer

If he loses 7 socks, to maximise the number of pairs of matching socks we should assume that he lost 3 pairs of socks and 1 sock from a different pair, so that rules out 4 pairs. maximum possible pairs he is left with is 6.

JeffTargetTestPrep · Answer

Let’s label each pair of socks with letters.

AA = pair 1

BB = pair 2

CC = pair 3

DD = pair 4

EE = pair 5

FF = pair 6

GG = pair 7

HH = pair 8

JJ = pair 9

KK = pair 10

We are given that he loses 7 individual socks and need to find the greatest number of pairs of matched socks he can have left. Strategically, this means that if we lose one sock from a particular pair of socks, we also want to lose the other sock from that same pair. So, for instance, John could lose the following:

A, A, B, B, C, C, D

The pairs of socks John has left are as follows:

EE, FF, GG, HH, JJ, and KK.

Thus, the greatest number of pairs of matched socks John could have left is 6 pairs.

The answer is B.

susheelh · Answer

I used the answer choices to help me get to the answer

A. 7 Pairs left. Means initially he has 7*2+7 = 21 Socks. Not possible, since he had total of 10 pairs (20 Socks)
B. 6 Pairs left. Means initially he has 6*2+7 = 19 Socks. Possible.

Rest all options will decrease the pair of Socks. Since the MAX pair possible is asked, the right answer has to be B.

adkikani · Answer

Bunuel   niks18   VeritasPrepKarishma

Is below approach correct:
Total no of socks: 20
No of socks lost: 7
No. of socks remaining: 13

Out of 13 socks, I can make only 6 matched pairs at max.

Bunuel · Answer

_____________________
Yes.

karan12345 · Answer

Individual socks lost = 7
3 pairs are lost and 1 socks but a pair is not completed with only 1 sock.
Hence, maximum number of pairs of matched socks he can have left = 10 - 4 = 6 pairs
So, Answer choice is (B).

rushimehta · Answer

Bunuel   chetan2u   VeritasPrepKarishma

The above question is a CAN question. Hence, we need to take the maximum number of pairs possible right? and thus we end up with the answer 6.
In case if the same question (CAN) - asked us about the minimum number of possible pairs - the answer would be 3.

But, what if we have the same question as a MUST question. 
Reframing as below - 
"John has 10 pairs of matched socks. If he loses 7 individual socks, what is the greatest number of pairs of matched socks he must have been left with?"

I think in this scenario - the answer would be 3 right ???

Please correct me if my understanding is wrong in anyway.

Thank you in advance!

rushimehta · Answer

Bunuel   KarishmaB   chetan2u

Can you guys please help me out with this query ?

Thank you!

chetan2u · Answer

Hi
The question will not be what you have written. 
It would be 'What will be the MINIMUM number......' and the answer would be three in that case...

KarishmaB · Answer

You cannot use "greatest number" and "must have been" together like this to get the answer as 3. 
Greatest number means there is a range possible. 
Must have means you are looking for a definite answer.

We can say the greatest number of pairs of matched socks he COULD have been left with is 6. 
Or we can say he MUST have been left with AT LEAST 3 pairs.

John has 10 pairs of matched socks. If he loses 7 individual

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