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

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

by BTGmoderatorLU » Wed Aug 08, 2018 2:28 pm

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

The OA is C.
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by Jay@ManhattanReview » Thu Aug 09, 2018 1:24 am

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BTGmoderatorLU wrote:Source: 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 their possession.
(2) Not all of the tents Amelia visited were the same token-price.

The OA is C.
Say Amelia visited x numbers of tents that cost 3 tokens and y numbers of tents that cost 4 tokens

=> 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 their possession.

=> 3x + 4y = 16

Case 1: At x = 0 and y = 4 => x+y = 0 + 4 = 4
Case 2: At x = 4 and y = 1 => x+y = 4 + 1 = 5

No unique answer. Insufficient.

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

=> x > 1 and y > 1

Can't get the unique value of x + y. Insufficient.

(1) and (2) together

We see that now Case 1 of Statement 1 is invalid, thus, x + y = 5. Sufficient.

The correct answer: A

Hope this helps!

-Jay
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