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
Each of three students is given fifteen tokens to spend at a
This topic has expert replies
GMAT/MBA Expert
- Ian Stewart
- GMAT Instructor
- Posts: 2621
- Joined: Mon Jun 02, 2008 3:17 am
- Location: Montreal
- Thanked: 1090 times
- Followed by:355 members
- GMAT Score:780
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
This is not a good question, because what you would naturally and correctly assume in any other GMAT question turns out not to be true here. If you saw a question like this, for example:
Amir goes to a store with $11 and buys at least one chair. How many chairs did he buy?
1. Chairs cost $10 each.
2. When he was in the store, he found $1000 on the floor.
everyone would say that Statement 1 is sufficient, because he can only have bought one chair. If it were possible to have a Statement like Statement 2 here, which tells us he did not have the $11 mentioned in the stem, then no information in Statement 1 could ever be sufficient, because we have no idea how much money Amir has. But if the stem says he has $11, he should have $11, because absolutely everyone would assume that to be the case, or why would the stem tell us that? But the same thing happens here:
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.
Initially Amelia has 15 tokens. But apparently she might not - Statement 1 tells us she exchanges tokens with classmates. And if a statement like Statement 1 can be true, how can we be sure, using both statements together, that she didn't also lose some of her tokens? It's simply not clear what we're allowed to assume and what not in a question written this way, which is why you could never see such a question on the GMAT.
But if we take it to mean: Amelia had 16 tokens, and spent all of them, how many tents did she visit? If they didn't all cost the same, then some cost 3, and some 4. If she visited one 4-token tent, she must have visited four 3-token tents. If she visited two or three 4-token tents, it's impossible for her to spend the rest of her tokens on 3-token tents, because she'd then have 8 or 4 tokens left, neither of which is divisible by 4. And she can't have visited four 4-token tents, because then she has no money left to visit a 3-token tent. So there's only one possible situation, and the answer is C.
Amir goes to a store with $11 and buys at least one chair. How many chairs did he buy?
1. Chairs cost $10 each.
2. When he was in the store, he found $1000 on the floor.
everyone would say that Statement 1 is sufficient, because he can only have bought one chair. If it were possible to have a Statement like Statement 2 here, which tells us he did not have the $11 mentioned in the stem, then no information in Statement 1 could ever be sufficient, because we have no idea how much money Amir has. But if the stem says he has $11, he should have $11, because absolutely everyone would assume that to be the case, or why would the stem tell us that? But the same thing happens here:
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.
Initially Amelia has 15 tokens. But apparently she might not - Statement 1 tells us she exchanges tokens with classmates. And if a statement like Statement 1 can be true, how can we be sure, using both statements together, that she didn't also lose some of her tokens? It's simply not clear what we're allowed to assume and what not in a question written this way, which is why you could never see such a question on the GMAT.
But if we take it to mean: Amelia had 16 tokens, and spent all of them, how many tents did she visit? If they didn't all cost the same, then some cost 3, and some 4. If she visited one 4-token tent, she must have visited four 3-token tents. If she visited two or three 4-token tents, it's impossible for her to spend the rest of her tokens on 3-token tents, because she'd then have 8 or 4 tokens left, neither of which is divisible by 4. And she can't have visited four 4-token tents, because then she has no money left to visit a 3-token tent. So there's only one possible situation, and the answer is C.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
ianstewartgmat.com
ianstewartgmat.com