Each of three students is given fifteen tokens to spend at a fair with

Three friends including Amelia received 15 tokens to spend at a fair.

The tents at these fair costs either 3 tokens OR 4 tokens to enter.

How many tents did Amelia visit ?

Statement 1:

(1) Amelia bought one token from another classmate, and spent all the tokens in her possession.

Amelia initially has 15 tokens. With a token bought from another classmate. The number of tokens with Amelia post buying is 16 tokens.

given that she spent all the tokens in her possession. It means she has spent the entire 16 tokens.

3x + 4y =16

when x =0, y =4 or

when x = 4, y =1 .

As, the total tents visited can be either (0+4) =4 or (4+1) = 5 .

Hence, Insufficient.

Statement 2:

(2) Not all of the tents Amelia visited were the same token-price.

This is considering she has visited all the tents.

3x + 4y = 15

Possible cases,

Case 1: y= 0, and x=5

Case 2: y=3, and x =1 .

since, case 1 contradicts the statement itself. We eliminate it.

case 2 results in total tents visited as (3+1) = 4 .

Suppose, if she has not visited all of the tents. Hence Insufficent.

Combining statements 1 and 2, we get .

Amelia has visited 5 tents. Option C

I am eagerly awaiting to see the OA. Your answer gave a different perspective to this question.

Bunuel

Can you check my explanation?
I think the answer should be E.

It is mentioned that she purchased one token from someone and used all tokens that she had. However, this doesn't imply she spent 16 tokens. Just like she purchased a token from someone, someone else could have purchased tokens from her (this is not explicitly mentioned).
So ideally, we don't know how many tokens she used.

I understand your explanation, and you're right that the wording could have been clearer. However, the intended meaning of the question is that Amelia ended up with 16 tokens (after receiving one more) and spent all of them.

So under that interpretation, she used exactly 16 tokens, making the answer C. That said, I do agree with you in principle.

MAGOOSH OFFICIAL SOLUTION:

This is a tricky problem.

Statement #1: Amelia had 16 tokens in total, and spent them all. How could she do this with a combination of 3-token tents and 4-token tents? Well, there are two possibilities.
Case I: Amelia visited four 4-token tents, four tents in total.
Case II: Amelia visited one 4-token tent and four 3-token tents, five tents in total
Since this statement leaves us with the ambiguity with four vs. five tents, we cannot give a definitive answer to the prompt question. This statement, alone and by itself, is insufficient.

Statement #2: This statement, by itself, tells us very little. How many tokens did Amelia have? Did she spend all the tokens in her possession? We have no way of knowing, so no way to answer the prompt question. This statement, alone and by itself, is insufficient.

When we combine the statements, the second one becomes more significant. Of the two cases given in statement #1, the first involves four trips to tents of the same token-price, so case #1 is not consistent with statement #2. That leaves only case #2, which means that Amelia had to have visited exactly five tents. Combining the statements allows us to give a definitive answer to the prompt question. Combined, the statements are sufficient.

Answer = (C)