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Students were given tokens to spend at a fair with various tents to

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Students were given tokens to spend at a fair with various tents to  [#permalink]

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New post 15 Jul 2018, 02:44
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Difficulty:

  45% (medium)

Question Stats:

67% (01:41) correct 33% (01:45) wrong based on 18 sessions

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Students were given tokens to spend at a fair with various tents to visit. Each student was given 16 tokens. Some tents cost 3 tokens to enter, and some, 4 tokens. How many tents did Amelia visit?

Statement #1: Amelia spent all of her tokens.

Statement #2: Not all of the tents Amelia visited were the same token-price.

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Students were given tokens to spend at a fair with various tents to  [#permalink]

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New post 15 Jul 2018, 03:56
To find how many tents did Amelia visit.

Lets x be the number of 3 token tents and y be the number of 4 token cents Amelia visited.

Statement 1

Amelia spent all of her tokens.

=> 3x + 4y = 16

x can be 0 and y can be 4 => 4 tents

x can be 4 and y can be 1 => 5 tents

Statement 1 is not sufficient

Statement 2

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

Since there are only two types of tents, the above statement implies x>0 and y>0

Amelia might have visited just 1 tent of each type or two tents of each type.

Statement 2 is not sufficient

Combining statements 1 and 2

3x + 4y = 16 and x > 0 and y > 0

=> x = 4 and y = 1 are the only integer values that satisfies both the above statements.

Statement 1 and 2 together are sufficient.

Hence option C
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Students were given tokens to spend at a fair with various tents to &nbs [#permalink] 15 Jul 2018, 03:56
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