Each of three students is given fifteen tokens to spend at

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Magoosh

Each of three students is given fifteen tokens to spend at a fair with various tents to visit. Some tents cost 3 tokens to enter, and some, 4 tokens. How many tents did Amelia visit?

1) Amelia bought one token from another classmate and spent all the tokens in her possession.
2) Not all of the tents Amelia visited were the same token-price.

OA C

[Jay@ManhattanReview]

Magoosh

Each of three students is given fifteen tokens to spend at a fair with various tents to visit. Some tents cost 3 tokens to enter, and some, 4 tokens. How many tents did Amelia visit?

1) Amelia bought one token from another classmate and spent all the tokens in her possession.
2) Not all of the tents Amelia visited were the same token-price.

OA C

Say the number of tents Amelia visited that cost 3 tokens = x and the number of tents Amelia visited that cost 4 tokens = y;

Thus, the total tokens spent by Amelia = 3x + 4y

We know that each student has only 15 tokens; thus, 3x + 4y ≤ 15

We have to get the value of (x + y).

Let's take each statement one by one.

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

=> 3x + 4y = 16

Case 1: Say y = 4, then x = 0; thus, x + y = 0 + 4 = 4.
Case 2: Say y = 1, then x = 4; thus, x + y = 4 + 1 = 5.

There is no other possibility.

No unique answer. Insufficient.

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

Certainly insufficient.

(1) and (2) together

Given that not all of the tents Amelia visited were the same token-price, Case 1 discussed in Statement 1 is not a valid case. Thus, only Case 2 is valid. Thus, Amelia visited 5 tents. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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