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Thinking Skills (A/ASLevel) Please Help!

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firoze
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Thinking Skills (A/ASLevel) Please Help!
Hi guys, I'm trying to practice for the Oxford TSA exam by doing some thinking skills exercises but I just don't understand how to find some of the answers... I'd really appreciate it if someone could help me out It's mostly logic problems and I feel silly for not getting it :3
I need help answering questions 6, 10, 17, 23 and 28 of this paper:
http://www.cie.org.uk/images/157585nove...per11.pdf
Here's the answer sheet: http://www.cie.org.uk/images/155594nove...eme11.pdf
Keep in mind that I'm looking for the METHOD of getting to the answer, not the answer itself!
Thanks!


08122015 09:38 PM 

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vonunov
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RE: Thinking Skills (A/ASLevel) Please Help!
#6
Requirements:
 Buy as many cards as you can
 Have a mixture of designs
 Have no more than 4 cards of any one design
Facts:
 Each design occurs only in one type of pack
 Each pack of cards has the same number of cards for each design [e.g., the pack of 20 cards with 4 designs has 5 cards of each design]
 Packs of a type are identical
Bear in mind the requirements, especially that you cannot have more than 4 cards of any one design, and the facts, especially that each pack of cards has the same number of cards per design. This allows us to eliminate several items.
"Number of designs: 2; number of cards in pack: 8; price: 0.40" will be notated as 2/8/0.40.
2/8/0.40 has 4 cards of each design, so it's OK. (8/2 = 4; if the result >4 then we can't use it)
2/16/0.80 has 8 cards of each design, so we can't use it. (16/2 = 8)
Using this method we eliminate the following:
2/16/0.80 (8)
4/20/1.40 (5)
4/40/1.60 (10)
2/10/0.50 (5)
4/32/2.00 (8)
8/40/2.40 (5)
[Total items: 6]
And we are left to use these:
2/8/0.40 (4)
5/20/1.00 (4)
4/12/0.80 (3)
5/10/1.30 (2)
[Total items: 4]
We have eliminated 6 items and kept 4, so that all 10 items in the table are accounted for.
Now to blow up that table for easy reference:
2 designs in 8 cards for 40c
5 designs in 20 cards for 100c
4 designs in 12 cards for 80c
5 designs in 10 cards for 130c
In total, that is 50 cards for a total of 350 cents.
According to this, the average price (350/50) of each card will be 7 cents so someone else should check over this as I must have missed something.
Answer key says 8 cents.
==========
#10
Start with the simplest part. In July he paid $50 and used 400 units. That's $0.125 per unit.
At that rate,
500 units is $62.50,
1000 units is $125,
and 300 units is $37.50.
This will let us better refer to the values in each of the possible answers.
Now let's look at March. He used 800 units and paid $92.50.
At the rate from July, 800 units would cost $100 (800 * .125). So there is clearly a lower rate after a certain amount of units.
According to the answers, the lower rate may begin after 300, 500, or 1000 units.
Since we can see that there is a lower rate at some point, answer C is eliminated.
Since we can see that the lower rate kicked in by the time we reached 800 units, answer B is eliminated.
Answer D is hard to test because we don't know what the fixed charge would be, and since the 300 unit threshold is below our reference point of $50 for 400 units, it's difficult to find where the lower rate would begin.
So in hopes of getting lucky, we will test answer A first.
At the rate of $0.125 per unit, the first 500 units (of the 800 on the March bill) would cost $62.50.
That leaves us with 300 units to account for, costing a total of $30 (92.50  62.50 = 30)
30/300 = $0.1
This tells us that the standard rate is $0.125, and the reduced rate, which begins after 500 units, is $0.1.
Now for the final test.
He paid $132.50 in January for 1200 units.
The first 500 units are billed at $0.125 = $62.50
The other 700 units are billed at $0.1 = $70.00
$70.00 + $62.50 = $132.50
Thus the rule is proven and answer is A in agreement with the answer key.
If this did not resolve as expected, then we would be left to assume that the correct answer is D.
I have to come back later for the rest.


08132015 07:51 AM 

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magikarp
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RE: Thinking Skills (A/ASLevel) Please Help!
(08132015 07:51 AM)vonunov Wrote: #6
Requirements:
 Buy as many cards as you can
 Have a mixture of designs
 Have no more than 4 cards of any one design
Facts:
 Each design occurs only in one type of pack
 Each pack of cards has the same number of cards for each design [e.g., the pack of 20 cards with 4 designs has 5 cards of each design]
 Packs of a type are identical
Bear in mind the requirements, especially that you cannot have more than 4 cards of any one design, and the facts, especially that each pack of cards has the same number of cards per design. This allows us to eliminate several items.
"Number of designs: 2; number of cards in pack: 8; price: 0.40" will be notated as 2/8/0.40.
2/8/0.40 has 4 cards of each design, so it's OK. (8/2 = 4; if the result >4 then we can't use it)
2/16/0.80 has 8 cards of each design, so we can't use it. (16/2 = 8)
Using this method we eliminate the following:
2/16/0.80 (8)
4/20/1.40 (5)
4/40/1.60 (10)
2/10/0.50 (5)
4/32/2.00 (8)
8/40/2.40 (5)
[Total items: 6]
And we are left to use these:
2/8/0.40 (4)
5/20/1.00 (4)
4/12/0.80 (3)
5/10/1.30 (2)
[Total items: 4]
We have eliminated 6 items and kept 4, so that all 10 items in the table are accounted for.
Now to blow up that table for easy reference:
2 designs in 8 cards for 40c
5 designs in 20 cards for 100c
4 designs in 12 cards for 80c
5 designs in 10 cards for 130c
In total, that is 50 cards for a total of 350 cents.
According to this, the average price (350/50) of each card will be 7 cents so someone else should check over this as I must have missed something.
Answer key says 8 cents.
The problem is with the last kind of pack [that wasn't already eliminated]. There are 2 cards with each design in the pack, so that means you can buy 2 packs for a total of 4 cards of each design. The extra pack brings the total number of cards to 60 and the total price to 480 cents for an average price of 8 cents.
"Do we treat straight public sex differently than we do gay public sex? Of course. Straight people are so proud of their public sex that they named a cocktail after it."


08142015 01:58 PM 

magikarp
Valerie Solanas
Posts: 1,146
Joined: Jan 2007
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RE: Thinking Skills (A/ASLevel) Please Help!
17. First find the total he can increase the price to for an average week:
40 visits*25c/visit = 1000c
300 km*10c/km = 3000c
Therefore, the current total is 4000c. If he can increase this by 10%, the new total would be 4400c.
Since he wants the maximum price per kilometer, we would ideally want to use all the money for that. However, we need some amount for the visit AND the price per kilometer must be a whole number of cents.
4400c/300km ~= 14.67c/km
So the price per kilometer could be at most 14c. This would leave 200c for visits:
4400c  (14c/km * 300km) = 200c
Now we have to check if the average number of visits divides evenly into 200c:
200c/40 visits = 5c/visit
It does so we're almost done. The new rate is 14c/km and 5c/visit. Now find the price for 1 visit with 20km of travel:
5c + (14c/km * 20km) = 285c
Therefore the answer is B.
===
23. This question is not that clear but I think it means you are not in the same lane as the truck (??) otherwise there's not enough information given.
If you are traveling at 120km/ and the truck is traveling at 100km/h, you are moving at 20km/h wrt the truck. You need to move a total of 100m wrt the truck  25m gap, 25m of the truck itself, 50m gap. So divide to find the total time:
0.1km/(20km/h) = 0.005h
You are moving at 120km/h relative to the highway. So the distance traveled in that time is:
120km/h * 0.005h = 0.6km
This puts you 1.4km from the junction because it was 2km away:
2km  0.6km = 1.4km
Therefore the answer is B.
===
Last one is for vonunov if he gets time because I'm too sleepy.
"Do we treat straight public sex differently than we do gay public sex? Of course. Straight people are so proud of their public sex that they named a cocktail after it."
(This post was last modified: 08142015 02:43 PM by magikarp.)


08142015 02:40 PM 

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vonunov
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RE: Thinking Skills (A/ASLevel) Please Help!
#28
Imagine someone turns 66 the day before the minimum age rises for the first time, and gets a free bus pass that day. The next day, the minimum age is 66 and 3 months. Another person can be a little under 3 months older than the first person without being eligible for a free bus pass.


08152015 04:28 PM 

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