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JasminJanuary 14, 2020
please explain this question
VictoriaSeptember 17, 2020
Hi @Jasmin,
Happy to help! It's kind of tough to set this question up on a computer, so I hope that this makes sense. Please let me know if you need me to clarify anything for you.
We know that a lake contains exactly five islands: J, K, L, M, and O.
Contractors are planning to build a network of bridges connecting the islands. This network will satisfy the following conditions.
Rule 1 - each bridge directly connects exactly two islands with each other and no two bridges intersect.
Rule 2 - no more than one bridge directly connects any two islands.
This means that no two islands are connected to one another by more than one bridge.
Rule 3 - no island has more than three bridges that directly connect it with other islands.
Therefore, each island can have a maximum of three bridges extending from it.
Rule 4 - J, K, and L are each directly connected by bridge with one or both of M and O.
Rule 5 - J is directly connected by bridge with exactly two islands.
Rule 6 - K is directly connected by bridge with exactly one island.
This means that K can only be directly connected to either M or O.
Rule 7 - a bridge directly connects J with O and a bridge directly connects M and O.
The question stem tells us that a bridge directly connects L with M and a bridge directly connects L with O.
So, what does this give us so far?
L | \ J - O - M
The only thing we need to do is connect K.
Notice that Rule 4 is partially satisfied. J is connected with O and L is connected with both M and O. This means we need to connect K to either O or M.
However, Rule 3 tells us that no island has more than three bridges that directly connect it with other islands. O is already connected to three islands as required by Rule 7 and the additional condition imposed by the question stem (i.e. O must be connected to J, M, and L).
Therefore, K must be connected to M.
We are looking for the answer choice which must be true. Therefore, our incorrect answers do not necessarily have to be true i.e. we are looking for one possible set-up where the condition imposed by the answer choice does not have to be true.
Notice that the deduction we made above is one of our answer choices. This must be true because Rule 4 tells us that K must be connected with either M or O and O is already connected to three other islands. If we connected O and K, this would violate Rule 3.
Answer choice (A) is incorrect because we could connect J to either L or M.
I can't really diagram the J - M connection on the computer because it would require a strange line, but it wouldn't intersect with any of our other bridges, thereby not violating Rule 1.
We could connect J with L like this:
L / | \ J - O - M | K
Answer choice (C) is incorrect because we have already deduced that we cannot connect K with O.
Answer choice (D) is incorrect because L could be connected to J. This would mean that there would be exactly three bridges connecting L with other islands.
Answer choice (E) is incorrect because we can see from our diagram above that M is connected to three other islands.
Hope this helps! Keep up the good work and please let us know if you have any further questions.
