3 interesting math and 1 PAT questions

[wjrmonkey]

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Hi, all. I am going to take DAT in mid-August. Here are some math questions I think quite interesting:

1.Joe needs to transport 10 tons of cargo crates. Each crate is no more than 1 ton, and Joe can only get trucks of 3-ton load capacity. In order to ensure all the cargo be carried at once (no second trips), what is the least number of trucks needed?
A. 3.3 B. 4 C. 5 D. 3.4 E. as many as Joe can afford

2.A tournament has 30 basketball teams holding matches with each other. If each game between any two teams must produce a winner, and the losing team is disqualified, then how many matches in total are needed to produce a champion?
A. 2^30 B. 30! C. 60 D. 29 E. 15

3.This might be a little too difficult:
Molly has a simple scale with only 6 weights: 1 g, 2g, 4g, 8g, 16g and 32g. The weights can only be put on one side of the scale to balance any object on the other side. What is the number of different masses that she can weigh?

Also, my PAT question (again):
1.For those who have taken the real DAT, do the angles in angle-ranking appear at the center of the monitor or at the upper-left corner?

Many thanks in advance!

 

[BenignDMD]

Hi, all. I am going to take DAT in mid-August. Here are some math questions I think quite interesting:

1.Joe needs to transport 10 tons of cargo crates. Each crate is no more than 1 ton, and Joe can only get trucks of 3-ton load capacity. In order to ensure all the cargo be carried at once (no second trips), what is the least number of trucks needed?
A. 3.3 B. 4 C. 5 D. 3.4 E. as many as Joe can afford

2.A tournament has 30 basketball teams holding matches with each other. If each game between any two teams must produce a winner, and the losing team is disqualified, then how many matches in total are needed to produce a champion?
A. 2^30 B. 30! C. 60 D. 29 E. 15

3.This might be a little too difficult:
Molly has a simple scale with only 6 weights: 1 g, 2g, 4g, 8g, 16g and 32g. The weights can only be put on one side of the scale to balance any object on the other side. What is the number of different masses that she can weigh?

Also, my PAT question (again):
1.For those who have taken the real DAT, do the angles in angle-ranking appear at the center of the monitor or at the upper-left corner?

Many thanks in advance!

1. B
2. D
3. 63 combinations

 

[heyitscyndi]

Question, if the truck only holds 3 tons, if you fill it with 3 crates holding one ton each, wouldn't the truck driver's body weight put the total weight over the 3 ton limit? So would the answer be 5?

 

[dat_student]

Question, if the truck only holds 3 tons, if you fill it with 3 crates holding one ton each, wouldn't the truck driver's body weight put the total weight over the 3 ton limit? So would the answer be 5?

These are my answers:

1) C: 5

(I don't think we need to worry about how much the driver weighs. The question says that each crate is no more than 1 ton. So, the weight of each crater should be considered. )

2) D: 29
3) 63

 

[Darby_O'Gill]

If this is anything like the QR section, I'm accepting nothing less than a 30 in that section.

 

[Lostinbul]

Hi, all. I am going to take DAT in mid-August. Here are some math questions I think quite interesting:

1.Joe needs to transport 10 tons of cargo crates. Each crate is no more than 1 ton, and Joe can only get trucks of 3-ton load capacity. In order to ensure all the cargo be carried at once (no second trips), what is the least number of trucks needed?
A. 3.3 B. 4 C. 5 D. 3.4 E. as many as Joe can afford

2.A tournament has 30 basketball teams holding matches with each other. If each game between any two teams must produce a winner, and the losing team is disqualified, then how many matches in total are needed to produce a champion?
A. 2^30 B. 30! C. 60 D. 29 E. 15

3.This might be a little too difficult:
Molly has a simple scale with only 6 weights: 1 g, 2g, 4g, 8g, 16g and 32g. The weights can only be put on one side of the scale to balance any object on the other side. What is the number of different masses that she can weigh?

Also, my PAT question (again):
1.For those who have taken the real DAT, do the angles in angle-ranking appear at the center of the monitor or at the upper-left corner?

Many thanks in advance!

As far as your PAT question is concerned, the angles appear in the center of the monitor, just a little towards the top however so to allow you to see your answer options.

 

[eapleitez]

How are you guys getting D for #2, and can someone tell me how you work out the combinations for the third problem. Sorry, the QR seems to be my biggest weakness. I can never seem to even finish it in time.

 

[Comet208]

How are you guys getting D for #2, and can someone tell me how you work out the combinations for the third problem. Sorry, the QR seems to be my biggest weakness. I can never seem to even finish it in time.

First you need 15 matches for 30 teams... that eliminates 15 teams. For the 15 teams remaning, they play 8 matches (you cant have 7.5 games). that eliminates 8 and 7 teams remain. then there are 4 matches for the 7 remaining and 2 for the last 3.

15 + 8 + 4 + 2 = 29

another way, answers A B and C seem too high. E is very low.... so we are left with D.

 

[Flipper405]

How are you guys getting D for #2, and can someone tell me how you work out the combinations for the third problem. Sorry, the QR seems to be my biggest weakness. I can never seem to even finish it in time.

If anyone has time, I would also like an explanation of #3. 👍 🙂

 

[wjrmonkey]

The answer are #1. 5 trucks needed, just think if there are 13 crates then 4 trucks won't be enough. #2. 29 matches, you could do it really simple because out of 30 teams there is only 1 champion and each team is out per game, so 30-1=29. #3. 63 different masses, one could do it the easy way: the maximum sum is 63 and you find each natural number from 1 to 63 can be represented by various combinations of the weights; or you can do it the hard way: since they are 2^0, 2^1, 2^2, 2^3, 2^4, 2^5, they look like a binary number system (composed of only 0 and 1's), and in that system the total sum will be 111111, which is translated into 63 in our denary number system.

 

[Mustt Mustt]

If this is anything like the QR section, I'm accepting nothing less than a 30 in that section.

That's exactly what I thought when I took the first time. I didn't study for this section and didn't get 30. 30 in QR is probably the easiest to get if your good at math but make sure you do some studying. I didn't and I was little upset during the test that on 3 questions I had to guess and I probably made some stupid errors but QR is really easy if you are good at math. It's always good to set bar high so you atleast get respectable scores. Good luck with that and I am shooting for 30 in QR as well this time with some studying.

if anyone else has anymore good questions like this post here. This is fun.

 

[rayray2fly]

The answer are #1. 5 trucks needed, just think if there are 13 crates then 4 trucks won't be enough. #2. 29 matches, you could do it really simple because out of 30 teams there is only 1 champion and each team is out per game, so 30-1=29. #3. 63 different masses, one could do it the easy way: the maximum sum is 63 and you find each natural number from 1 to 63 can be represented by various combinations of the weights; or you can do it the hard way: since they are 2^0, 2^1, 2^2, 2^3, 2^4, 2^5, they look like a binary number system (composed of only 0 and 1's), and in that system the total sum will be 111111, which is translated into 63 in our denary number system.

Can you elaborate on #1 and tell me how u came up with 5 trucks, I thought it would be four since he has a total of 10 tons of crates, each truck can fit 3 tons of crates, so 3 tons of the crates could go in the first 3 trucks and 1 ton worth of crates would be left over, so that could go in a forth truck, so why would a 5th truck be needed? The question didnt mention that there was a limit on the actual number of crates that could go in a truck, just a weight limit. So even if there were thirteen crates or fifty, they still must weigh 10 tons since thats his total and still should be able to fit in 4 trucks with a 3 ton weight capacity. Help me out with this one, maybe im reading it wrong!

 

[luder98]

The answer are #1. 5 trucks needed, just think if there are 13 crates then 4 trucks won't be enough. #2. 29 matches, you could do it really simple because out of 30 teams there is only 1 champion and each team is out per game, so 30-1=29. #3. 63 different masses, one could do it the easy way: the maximum sum is 63 and you find each natural number from 1 to 63 can be represented by various combinations of the weights; or you can do it the hard way: since they are 2^0, 2^1, 2^2, 2^3, 2^4, 2^5, they look like a binary number system (composed of only 0 and 1's), and in that system the total sum will be 111111, which is translated into 63 in our denary number system.

What if Molly had 1, 2, 4, 8, 16 and 33 instead of 32?

 

[HITMAN]

Can you elaborate on #1 and tell me how u came up with 5 trucks, I thought it would be four since he has a total of 10 tons of crates, each truck can fit 3 tons of crates, so 3 tons of the crates could go in the first 3 trucks and 1 ton worth of crates would be left over, so that could go in a forth truck, so why would a 5th truck be needed? The question didnt mention that there was a limit on the actual number of crates that could go in a truck, just a weight limit. So even if there were thirteen crates or fifty, they still must weigh 10 tons since thats his total and still should be able to fit in 4 trucks with a 3 ton weight capacity. Help me out with this one, maybe im reading it wrong!

You're not reading it wrong, the answer is 4. There are 10 crates, not 13. Also, the driver's body weight is not factored into the load. The load capacity refers to the max load that can be carried in the bed of the truck. Most drivers sit in the cabin, not in the bed of the truck. Heyitscyndi, you're screwed if you really needed an explanation for this.

 

[dat_student]

You're not reading it wrong, the answer is 4. There are 10 crates, not 13. Also, the driver's body weight is not factored into the load. The load capacity refers to the max load that can be carried in the bed of the truck. Most drivers sit in the cabin, not in the bed of the truck. Heyitscyndi, you're screwed if you really needed an explanation for this.

Be carefule: the problem says

"...Each crate is no more than 1 ton..."

You should consider the weight of each crate.

 

[wjrmonkey]

I do not believe the QR will be any more difficult than these problems. One just needs to be extra extra careful. For probelm #1, If there are 13 crates and their total mass is 10 tons, then each crate is 10/13 ton, now you need to realize any single truck avaliable (3-ton cargo capacity) cannot carry 4 such crates - only 3! So 4 trucks can only carry 12 crates with 1 more left over.
It is such problems that no one can complain about their math difficulty, but then they are often the ones that keep us from getting 30 in QR.

 

[lcinva]

I do not believe the QR will be any more difficult than these problems. One just needs to be extra extra careful. For probelm #1, If there are 13 crates and their total mass is 10 tons, then each crate is 10/13 ton, now you need to realize any single truck avaliable (3-ton cargo capacity) cannot carry 4 such crates - only 3! So 4 trucks can only carry 12 crates with 1 more left over.
It is such problems that no one can complain about their math difficulty, but then they are often the ones that keep us from getting 30 in QR.

i'm sorry to keep dragging this on....but where do we get 13 crates from? all it says is that there are 10 tons' worth of crates...

 

[luder98]

My assumption: all trucks carry the same weight.

Let x be the un-used capacity of the truck. x must be positive or equal zero and less than 1 (otherwise one more crate can be loaded on)
Let n be the number of trucks. Note: n must be a positive integer.

We have the below equation:
(3-x)n = 10 or 3 -x = 10/n or x = 3 -10/n

As mentioned, x must be between 0 and 1, including 0. Therefore,

0<= 3-10/n <1 or 10/3 <= n < 5 or 3.333 <= n < 5

The only integer in [3.33,5) is 4.

IMO, the question is ambiguous. One way or another, we need to make some assumption to solve it.

Rayray2fly's way also makes sense but then one may question, "what if you can't fit exactly 3 tons on each of the first three trucks?" Regardless, I think this is the way to quickly pick the least incorrect choice.

 

[dat_student]

My assumption: all trucks carry the same weight.

Let x be the un-used capacity of the truck. x must be positive or equal zero and less than 1 (otherwise one more crate can be loaded on)
Let n be the number of trucks. Note: n must be a positive integer.

We have the below equation:
(3-x)n = 10 or 3 -x = 10/n or x = 3 -10/n

As mentioned, x must be between 0 and 1, including 0. Therefore,

0<= 3-10/n <1 or 10/3 <= n < 5 or 3.333 <= n < 5

The only integer in [3.33,5) is 4.

IMO, the question is ambiguous. One way or another, we need to make some assumption to solve it.

Rayray2fly's way also makes sense but then one may question, "what if you can't fit exactly 3 tons on each of the first three trucks?" Regardless, I think this is the way to quickly pick the least incorrect choice.

Hi Luder,
I got 5 for the answer. This is how I did it:

Given:
#1) 10 tons of cargo crates.
#2) Each crate is no more than 1 ton,
#3) trucks of 3-ton load capacity.
Find:
what is the least number of trucks needed?

Max for each truck is 3 tons
Weight of each crate (i.e. container) is 1 ton (i.e. max weight)

Cargo that can be carried by each truck 3 - 1 = 2 tons

(10 tons of cargo) / 2 (tons per truck) = 5 trucks

 

[HITMAN]

i'm sorry to keep dragging this on....but where do we get 13 crates from? all it says is that there are 10 tons' worth of crates...

Unless wjrmonkey left some information out of the problem, it does not state that there are 13 crates. It also does not state the weight of each crate. It does state that the sum of the weights of all of the crates is equal to 10 tons, and that no crate weighs more than 1 ton. It says that each truck can carry a max load of 3 tons, so it is reasonable to assume that each truck will carry this max weight. Therefore, three trucks will carry 3 tons worth of crates, and the fourth can carry the remaining 1 ton worth of crate(s). The answer is 4.

 

[luder98]

Hi Luder,
I got 5 for the answer. This is how I did it:

Given:
#1) 10 tons of cargo crates.
#2) Each crate is no more than 1 ton,
#3) trucks of 3-ton load capacity.
Find:
what is the least number of trucks needed?

Max for each truck is 3 tons
Weight of each crate (i.e. container) is 1 ton (i.e. max weight)

Cargo that can be carried by each truck 3 - 1 = 2 tons

(10 tons of cargo) / 2 (tons per truck) = 5 trucks

IMO,

1. "No more than" means less than or equal.
2. Your solution assumes each truck carries only one crate.
3. If you separate the cargo from the crate, there is no way to solve the problem. I think "each crate is no more than 1 ton" implies cargo crate, not the crate itself.

 

[dat_student]

IMO,

1. "No more than" means less than or equal.
2. Your solution assumes each truck carries only one crate.
3. If you separate the cargo from the crate, there is no way to solve the problem. I think "each crate is no more than 1 ton" implies cargo crate, not the crate itself.

oops ! I misunderstood the question then. I thought each crate weighs 1 ton or less and we can load each crate up to 2 tons to make the total weight 3 tons. I definitely misunderstood the question. Thanks luder. I don't feel like studying anymore and my brain's become rusty....Gotta find a way to encourage myself to study...