The Student Room Group

Thinking Skills Specimen (Problem Solving)

1.On the M53 is a sign 'Warrington 20'. Just over half a mile further on is another sign
'Warrington 19'.
This is not really surprising, since the distances are rounded to the nearest whole number of miles e.g. numbers of 4.5 and over but less than 5 become 5,
numbers of 4 and over but less than 4.5 become 4. Half a mile futher along

The distance to Warrington must now be between

A 17.5 miles and 17.6 miles

B 17.6 miles and 18.0 miles

C 18.0 miles and 18.2 miles

D 18.2 miles and 18.4 miles

E 18.4 miles and 18.5 miles

The answer given is E.Do not understand why the difference is 0.1miles.Shouldn't it be 1 miles?In my understanding,0.5 miles is the largest diffence between two signs,aren't three signs and two difference means 1 miles?


2.My mother still makes tea with the old saying:

"one spoon per person and one for the pot".
We used to buy a packet of tea every week but since grandmother came to live with us
we have to buy two packets every fifth week and one otherwise.
How many people were at home before grandmother arrived?

A 4

B 5

C 6

D 9

E 11

Do not understand the question?
Reply 1
1. First sign: Washington 20 = 19.5 to 20.5 miles
Just over 0.5 miles later:
Second sign: Washington 19 = 18.5 to 19.5 miles
Using previous sign: ~19.0 to ~20.0 miles
So actually: ~19.0 to 19.5 miles
0.5 miles later:
~18.5 miles to 19.0 miles
Answer: E 18.4 miles and 18.5 miles
The 0.1 mile difference is due to the "Just over half a mile further on".

2. y = 1 + x; where x = number of people
Used to be: y = 1 per week
Now: 2 packets every 5th week and 1 otherwise
Considering 5 weeks:
Used to be: y = 5
Now: y = 6
Sub in 5 before: 5 = 1 + x; x = 4
Answer: A 4
akiromuchi
1.On the M53 is a sign 'Warrington 20'. Just over half a mile further on is another sign
'Warrington 19'.
This is not really surprising, since the distances are rounded to the nearest whole number of miles e.g. numbers of 4.5 and over but less than 5 become 5,
numbers of 4 and over but less than 4.5 become 4. Half a mile futher along

The distance to Warrington must now be between

A 17.5 miles and 17.6 miles

B 17.6 miles and 18.0 miles

C 18.0 miles and 18.2 miles

D 18.2 miles and 18.4 miles

E 18.4 miles and 18.5 miles

The answer given is E.Do not understand why the difference is 0.1miles.Shouldn't it be 1 miles?In my understanding,0.5 miles is the largest diffence between two signs,aren't three signs and two difference means 1 miles?
?



The question doesn't make sense unless you missed out a bit saying there was a sign wit 'Warrinton 18', which I suspect you have. If that is the case, then 18.4-18.5 would be what they are looking for, though it is still unjustified (since it could be 18.39, for example, depending on what they mean by 'Just' in the "Hust over half a mile further on")

Take a look a go again.



akiromuchi


2.My mother still makes tea with the old saying:

"one spoon per person and one for the pot".
We used to buy a packet of tea every week but since grandmother came to live with us
we have to buy two packets every fifth week and one otherwise.
How many people were at home before grandmother arrived?

A 4

B 5

C 6

D 9

E 11

Do not understand the question?


You have a packet of tea and you make a pot of tea by taking n+1 spoons from the packet and putting them into the pot. When grandmother arrives, clearly the amount of consumption goes up because they say that they have to buy an extra packet of tea every 5th week. So, how much has concumption gone up by, and how can you use this to work out how many people were drinking tea when they were buying one packet of tea per week?
Reply 3
Why 5 = 1 + x but not 6= 1+1+x ,since 6 means 6 weeks and 1 means grandmother is included?
Reply 4
akiromuchi
Why 5 = 1 + x but not 6= 1+1+x ,since 6 means 6 weeks and 1 means grandmother is included?

2 packets every 5th week and 1 otherwise means 6 in 5 weeks, not 6 weeks.
Reply 5
For the second part,

In a 5 week period before she came, the spoonfuls of tea used would be

k(x+1)

where x is the number of people and k is the number of pots made

After she arrived, the amount of tea used would be

k(y+1) where y=x+1 (the extra being the grandmother)

Relating that to the bags of tea (there would be a constant but it's irrelevant)

Before = 5 bags After = 6 bags

Therefore
k(x+1) = 5
k(y+1) = k((x+1)+1) = k(x+2) = 6

cancel k's, solution for x in both is 4.

I've over-complicated it a fair bit to try and make it easier to see what I've done.
Oh lord, the thing is every morning we have a thinking skills class. And I thought I was pretty decent at problem solving. But I don't seem to move and get thins right. And that seems to bring the whole day to a dump. Problem solving is getting to me. And I thought I wanted to go into Law. What will I do in Law when I cant seem to get a problem in Thinking Skills right? Any suggestions on how to go about the problems in a more systematic way?
Reply 7
lightages_60
Oh lord, the thing is every morning we have a thinking skills class. And I thought I was pretty decent at problem solving. But I don't seem to move and get thins right. And that seems to bring the whole day to a dump. Problem solving is getting to me. And I thought I wanted to go into Law. What will I do in Law when I cant seem to get a problem in Thinking Skills right? Any suggestions on how to go about the problems in a more systematic way?


what kinda thinking skills do they teach?
Reply 8
lets suppose number of people in house = x.
And everyone drinks tea once a week.
So number of spoons in one packet = x+1

when grandma comes to the house the number of spoons used in 1 weeks become x+1+1
number of spoons used in 6 weeks before grandma were 6(x+1) which are equal to number of spoons used in 5 weeks after grandma's arrival 6(x+2)
so
6(x+1) = 5(x+2)

6x+6 = 5x+10

x = 4

Option A is the answer
Reply 9
Original post by vector
For the second part,

In a 5 week period before she came, the spoonfuls of tea used would be

k(x+1)

where x is the number of people and k is the number of pots made

After she arrived, the amount of tea used would be

k(y+1) where y=x+1 (the extra being the grandmother)

Relating that to the bags of tea (there would be a constant but it's irrelevant)

Before = 5 bags After = 6 bags

Therefore
k(x+1) = 5
k(y+1) = k((x+1)+1) = k(x+2) = 6

cancel k's, solution for x in both is 4.

I've over-complicated it a fair bit to try and make it easier to see what I've done.


Amazing explanation
my take on tea

For the second part assume you only make tea once a week so a packet holds n+1 spoons

Now in 5 weeks you need 6n+6 spoons

Before you were using 5n+5 spoons

so Grandma uses n+1 spoons in 5 weeks

We know she has a spoon a week so n+1 = 5

n=4

I put it because I think it is nice that we each use slightly different thinking but all get the same answer
Nearly reached it's 5th birthday. Perhaps have a :party:
Original post by ghostwalker
Nearly reached it's 5th birthday. Perhaps have a :party:


lol

my only excuse is

I was not around then so for me it looks new
Reply 13
I just didn't understand the "two every fifth week and one otherwise"...

My thinking was that would mean 6 in five weeks, and one otherwise? What does the one otherwise mean? :lol:
For the tea question:

Let y = number of packets of tea

Let x = number of people at home

Before the grandmother arrived, in 5 weeks they bought 1 packet of tea per week, so 5y.
After the grandmother arrived, in 5 weeks they bought 1 packet of tea for 4 weeks and 2 packets on the final week, so 6y.

Before the grandmother arrived, they used one spoonful of tea per person and one for the pot, so x + 1 spoonfuls of tea.
After the grandmother arrived, they continued to use one spoonful of tea per person and one for the pot, so x + 2 spoonfuls of tea.

Therefore,

5y = x + 1 (equation 1)
and
6y = x + 2 (equation 2)

We now have a pair of simultaneous equations which can be solved.

Multiplying equation 1 by 6 gives, 30y = 6x + 6
Multiplying equation 2 by 5 gives, 30y = 5x + 10

Both of the right hand sides of these 2 equations equal 30y, so therefore they also equal each other, so,

6x + 6 = 5x + 10

Rearranging this equation gives,

6x - 5x = 10 - 6

So x = 4 and the answer is A.
(edited 10 years ago)
Number increase, more packets
Let x=person , p=packets
(x+1)∝p
(x+1)/p=k
When x=n,p=5
When x=n+1, p=6
(n+1)/5=(n+1+1)/6
6n+6=5n+10
n=4

A
(edited 3 years ago)