There are 5 locks and 5 keys and each of the 5 keys

Question

There are 5 locks and 5 keys and each of the 5 keys matches each of the 5 locks. What is the minimum and the maximum trial numbers of attempts needed to confirm that each of the 5 keys matches each of the 5 locks?
A. 5,15 
B. 4,15 
C. 5,10
D. 4,10 
E. 5,20

pls. explain in detail.

GoLeafsGo · Accepted Answer

Assume you have locks 1-5 and keys A-E.

Minimum: assume you are lucky to find the correct key/combo on the first try. So, 1 -> A, 2 -> B, 3 ->C, and 4 -> D, then 5 must match with E. Therefore, you only need to try 4 combos at a minimum.

Maximum: assume that it takes as many guesses as possible. So, with the first key you try A, B, C, and D with no success, therefore E must be the match (so 4 attempts). For key 2 you no longer have E available so you try A, B, and C, with no success, therefore D must be the match (3 attempts). And so on for key 3 (2 attempts) and key 4 (1 attempt). Key 5 matches with the remaining lock for a total of 4 + 3 + 2 + 1 = 10 attempts.

kartiktpr · Answer

hi
this is a derangement question. Basically we need to de-arrange the 4 keys. if all 4 keys goes in correct lock then the fifth key will automatically go into the correct lock. 
so the minimum number is 4.

for the maximum number consider cases

so if you want to de arrange 1 thing you can do it in 0 ways. Incase of 2, you can do it in 1 way. put 1 wrong key in wrong lock. In case of 3 you can do it in 2 ways such that no key goes into the correct lock. similarly for 4 its 9 ways. now the 10 one will be the one where the keys of 4 lock matches the correct lock. since 4 are matched the 5th key will be matched itself.

hope it helps !!!

mvictor · Answer

very good question.
I thought what are the actual number of tries that we need to "unlock" all the lockers, and got into the trap 5-15.
of course, if we do not need to unlock the lockers, but just simply to check..
minimum # of attempts is 4.
maximum is 10, as explained above.

very tricky one.

cbh · Answer

I don't know guys, maybe you've already got this GMAT mindset, the way of thinking, I am still on my way
the description clearly asks
 
So basically the first part is an assumption, that we need to confirm, otherwise there wouldn't be a question, right? 
The second part asks about total min/max number of attempt to confirm the assumption, that all 5 keys match all 5 locks
Let's assume that the keys are A, B, C, D and F. And locks are 1, 2, 3, 4, and 5.

So If A matches 1, it doesn't mean by default that this gonna match 2, as this ideal cross-matching is the assumption that we need to check.
So to develop, I should try A for all 5 locks in order to confirm the assumption.
You want to check your understanding of the question, just don't read the responses.

I have certain problems with understanding this GMAT wording for such kind of questions. With math or geometry based question I have no such problem

chetan2u · Answer

Hi...

Pl post as per the rules of forum.
Give topic name as first few words of Q and search before posting.

Now as per Q..
Min..
All fit in correctly.
When first four have fit in, fifth is not required to be tested as it has to fit.
So 4
Max..
Choose the right key as last possibility.
First lock - 5th one Correct, so 4 attempts
Similarly others 3,2,1..
Total 4+3+2+1=10

D

EMPOWERgmatRichC · Answer

Hi All,

This is a poorly-worded question, so you might want to consider studying with practice materials that are better "designed'.' That having been said, the 'intent' of this question is probably that there are 5 locks and 5 keys - and each of the keys opens exactly one of the 5 locks. We're asked for the least/most number of attempts that it would take to determine the proper 'pairing' of each key to each lock.

To start, you should notice that the answer choices are all relatively small, so you can probably 'brute force' the solution - just 'map out' how the attempts would have to go (without need of any complex math).

Let's call the locks: A, B, C, D and E 
Let's call the (matching) keys: a, b, c, d and e

IF.... we 'luck out' and manage to place each key with each lock on the first try, there would be... 
a in A = 1st attempt 
b in B = 2nd attempt 
c in C = 3rd attempt 
d in D = 4th attempt 
Based on what we're told, with just one lock and one key left, there'd be no reason to make an attempt - that key would have to fit that lock. Thus, the LEAST number of attempts would be 4. Eliminate Answers A, C and E.

In that same way, we can now determine what would happen if we were 'unlucky' and took the maximum number of tries to open each lock..... 
a in B/C/D/E = 4 attempts... and then we'd know that a would have to 'match' A. 
b in C/D/E = 3 attempts... and then we'd know that b would have 'match' B. 
c in D/E = 2 attempts... and then we'd know that c would have to 'match' C. 
d in E = 1 attempt... and then we'd know that d would have to 'match' D. 
That would leave just e in just E, which would not require an additional attempt. 
Thus, the MOST number of attempts would be 10.

Final Answer:  D

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

AweG · Answer

dont we have 5 keys that work in all keylocks ? im a bit confused

gmatforfun · Answer

The Answer does not align with the Question's request. If this were a GMAT question I would feel cheated by the system.

I get the purpose and trickiness of the question. Nonetheless, the question is very badly formulated if it expecting us to have an answer = to D (4,10). The answer should be A (5,15)... Why? simply because until you have tested and unlocked the door you cannot confirm that keyY matches lockY.

Read CAPS as  bold .
The problem lies in the fact we are asked to CONFIRM (test) the ARGUMENT. We cannot take the ARGUMENT for granted due to the formulation of the QUESTION
ARGUMENT. "There are 5 locks and 5 keys and  each of the 5 keys matches each of the 5 locks "
QUESTION: asks to confirm that a part of the ARGUMENT is true ie:  "confirm that each of the 5 keys matches each of the 5 locks"

In the most lucky attempt, I cannot assertain that each key can unlock the respective lock until I trigger the mechanism. Key 5 could unlock lock6 and is misplaced. Goes without saying that in the unluckiest of settings I would need "5!" attempts to solve the issue (5!=15 attempts). Because on each lock tested I have to try all the keys before i can  CONFIRM  that the fifth key matches the lock. it is primordial to understand that we are seeking to confirm the ARGUMENT and thus must be critical and cannot take it for granted...

The Problem should be presented in the following manner: There are 5 locks and 5 keys and each of the 5 keys matches each of the 5 locks. What is the minimum and the maximum trial numbers of attempts needed to  confirm that    match   each of the 5 keys  matches each of the 5    with each of the   locks?

leonardBe · Answer

I 100% agree with  gmatforfun  and I would feel cheated if this question appeared and I got it wrong because the wording is off. It asks us to 'confirm' that the keys match the 5 locks. This implies that there is a possibility for example that one of the keys do not match any of the locks. Otherwise, the question should be phrased: "What is the minimum and the maximum numbers of attempts needed to match the five keys to the five locks."

Vishalcv · Answer

If each of the keys match with each of the locks, all 5 locks can be unlocked using any of the keys. The only way to confirm this to try each key on each lock. There is no minimum or maximum. You HAVE TO have 25 attempts.

I think the question to the answer should have been " Each of the 5 locks can be unlocked using the respective keys. What are the min and max attempts to match each lock with its respective key?"

yahya729 · Answer

Yes, the wording is terrible. It should say that each of the keys matches exactly one of the locks, and we know that.

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There are 5 locks and 5 keys and each of the 5 keys

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