Some basic arithmetic problems..!!

So these are sums I came across while preparing for the Oxford TSA and I have no idea how to go about doing them. Any help would be appreciated.

Go to the last post in the thread please :colondollar:

Bob has £140 to spend on paving slabs for his patio garden. Paving slabs are 70 x 70 cm square and cost £2.80 each.

He finds that, using whole slabs, he is only able to buy enough to lay an area which is twice as long as it is wide but will not cover the whole patio.

He decides to leave the remainder as a rectangular flower bed down one side.

If his patio garden is 5 m wide, how wide is the flower bed?

Answer is 3.5m.

(edited 13 years ago)

Reply 1

asdfg0987

Original post by PerigeeApogee

For the first one, the ratios 48/24 and 40/20 are the same: 2:1. Every other ratio is unique.

So you have 12 different ways to order the cogs in pairs, but 2 of those ways give the same gear ratio result.

Hmm thanks a lot!

For the second question I should have put in the options, I will edit the post once I get on from the computer, but anyway these are the options for second question:

A 595

B 612

C 667

D 726

Reply 2

asdfg0987

The cog sizes and chain length on a bicycle are designed to even out wear, so that the same hole in the chain does not encounter the same tooth on the cog in every revolution. The chain wheel (front cog) of a particular bicycle has 48 teeth, the rear cog has 18 teeth and the chain has 90 holes.

How many revolutions must the front cog do before the chain and both cogs are back in exactly the same relative positions (i.e. the same holes are encountering the same teeth on both cogs)?

A 5
B 8
C 15
D 20
E 30

The answer is C, any idea how to do this?

PerigeeApogee

Reply 3

Mr ABC

Original post by asdfg0987

firstly, think about a certain tooth on the front cog. for each rotation of the chain, by how many places does the tooth move?

see if you can work out what to do from there

Reply 4

asdfg0987

Original post by Mr ABC

firstly, think about a certain tooth on the front cog. for each rotation of the chain, by how many places does the tooth move?

see if you can work out what to do from there

Ahh ffs LCM :colonhash:

.

Any suggestions for this one? sorry for shamelessly asking help for one question after another but the test is tomorrow and it's getting really frustrating..

A bus company needs to have 13 buses operating every day of the week. Cleaning and
servicing requirements mean that each bus is not available for operating services two days per week.

What is the smallest number of buses the company must have to ensure that 13 buses can be available every day?

A 17
B 18
C 19
D 20
E 21

Answer is C. but to me only A makes sense?

(edited 13 years ago)

Reply 5

Good bloke

Original post by asdfg0987

Ahh ffs LCM :colonhash:

This is trivial mental arithmetic. The company requires 91 bus-days per week (13x7). Each bus is available for 5 days. Therefore 19 buses (91/5=18.2, must round up to a whole number of buses) are needed to meet the requirements.