#8 - Local, List

[Administrator]

Complete Question Explanation

The correct answer choice is (C).

Answer choice (A):

Answer choice (B):

Answer choice (C): This is the correct answer choice.

Answer choice (D):

Answer choice (E):

This explanation is still in progress. Please post any questions below!

[mathildebarland]

Hello,

I narrowed down my choices to A and C when doing this question, but I am not understanding why C is the correct answer as they both seem equally valid to me. Could someone please provide an explanation? Thanks!

[Adam Tyson]

The short answer here, mathildebarland, is that at least 3 of our campers will have to buy tents. K and M must always get tents, and in this case G also has to get one, because otherwise G gets just a stove, which would violate the conditions of the question (L has to be the ONLY camper who buys a stove and nothing else). J might also buy a tent, but that doesn't have to happen.

Since at least 3 campers have to get tents, we can eliminate answers A, B, and D.

We also know that K and M must buy stoves, and the conditions of the question require L to also buy one, for a minimum of 3 stoves. G might also get one, and J could as well, but we're starting with a minimum of 3. At this point, answer E looks possible - 3 tents (G, K, and M) and 3 stoves (K, L, and M). But that can't be the end of it, because J still has to get either a stove or a tent. So if there are only 3 stoves, J gets a tent, making for 4 tents. If there are only 3 tents, then J gets a stove, which makes 4 of those. We can't have 3 and 3! That eliminates E, and C is the winner.

To show this a little more visually, here's what the question requires of us:

G: T (maybe also S?)
H: R
J: RS or else RT
K: ST
L: S
M: RST

Because J has to have S or T, there will always be at least 4 stoves or else at least 4 tents.

[jailenea]

I'm confused as to what to consider here. Based on Adam's response, are we only to consider what must be true when answering this question? Particularly when analyzing G, which could get both a stove and tent but must only get a tent to satisfy all the conditions. Answer C doesn't account for G getting both a tent and a stove the way it accounts for J getting S or T.

[Adam Tyson]

When answering a Could Be True question, jailenea, start with what Must Be True. Set up the bare minimum. Then, the correct answer will be the only one that could occur within those restrictions. The wrong answers will all be things that cannot happen because they violate those minimum, mandatory conditions.

You could start by predicting all the possible combinations within those parameters. For example, it's possible that G also gets a stove, and that way you could have 4 stoves and 4 tents (if J gets a tent) or 5 stoves and 3 tents (if J gets a stove), but neither a 4-4 combination nor a 5-3 combination was given as an answer choice. But a 4-3 or 3-4 combo is possible, and answer C gives you one of those two possibilities. It's the only answer that gives a possible combo, so it must be correct.

Or, you might try the alternate approach to answering this question, which is to focus on eliminating the answers that are impossible. Here's what that might look like:

You have to have 3, 4, or 5 stoves (depending on whether G and/or J have stoves). That eliminates nothing.

You have to have at least 3 tents (G, K, and M). That eliminates answers A, B, and D.

Finally, J has to get a tent or a stove, meaning you have to have at least 4 of one or else the other (if J gets a stove, you have to have at least 4 stoves - JKLM; if J gets a tent, you need at least 4 tents - GJKM). Thus, a 3-3 combo is impossible, eliminating answer E. C is all that's left standing.

To get to what Could happen, start with what Must happen, and then work within those constraints!