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

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Each of three students is given fifteen tokens to spend at a fair with  [#permalink]

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New post 23 Feb 2015, 03:14
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A
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C
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Difficulty:

  65% (hard)

Question Stats:

59% (02:05) correct 41% (01:59) wrong based on 90 sessions

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


Kudos for a correct solution.

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Re: Each of three students is given fifteen tokens to spend at a fair with  [#permalink]

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New post 23 Feb 2015, 05:01
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Quote:
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.


Statement 1 says Amelia bought one token from another classmate, and spent all the tokens in her possession.
=> Amelia had a total of 15 + 1 = 16 tokens
Case 1: She could have visited 4 tents {4, 4, 4, 4}
Case 2: She could have visited 5 tents {3, 3, 3, 3, 4}
Statement 1 is not sufficient.

Statement 2 says Not all of the tents Amelia visited were the same token-price.
We have no information about the number of tokens Amelia has spent.
=> We cannot determine the number of tents Amelia has visited.
=> Statement 2 is not sufficient.

If we use both the statements together, we know that she has spent 16 tokens and all the tents did not have the same token price.
This is only possible when she visits 5 tents with prices {3, 3, 3, 3, 4} (As shown in Case 2 of Statement 1)
=> We can say that Amelia definitely visited 5 tents.

We have solved the question using both the statements together.
Correct Answer: C
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Each of three students is given fifteen tokens to spend at a fair with  [#permalink]

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New post 23 Feb 2015, 05:04
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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)
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Re: Each of three students is given fifteen tokens to spend at a fair with  [#permalink]

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New post 02 Mar 2015, 07:00
Bunuel wrote:
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.


Kudos for a correct solution.


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)
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Re: Each of three students is given fifteen tokens to spend at a fair with  [#permalink]

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New post 05 Sep 2017, 06:04
Ans is C
A-15 tokens
B-15 tokens
C-15 tokens
T1=3 tokens and T2=4 tokens

1) Amelia A got 1 token extra => total token in possession =16, also she has to consume all tokens
16=4x4 => 4 T2 = 4 Tents
16=12+4 => 3x4+4 => 4T1 + T2 = 5 Tents
INSUFFICIENT
A and D are out

2) Not all tents visited of same tokens
=> Probably she may have visited T1 and T2 = 2 Tents as it is not explicitly mentioned to finish all tokens
or => 2 T2 and 1 T1 = 3 Tents

INSUFFICIENT
B is out

Now Combine 1&2
Clearly 2nd statements solves ambiguity case from 1st by ruling out same tent option 4T2 is ruled out
Hence 5 Tents she visited , 4T1 and 1 T2
Definite ans and so C
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Re: Each of three students is given fifteen tokens to spend at a fair with   [#permalink] 05 Sep 2017, 06:04
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