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UCAT > Quantitive Reasoning > Flashcards

Quantitive Reasoning Flashcards

1
Q

For Celcius to Farenheit questions, if it is a change, ignore the -32

A

Shortcut to find VAT = divide by 6

Another way is to do:

VAT = Total cost - (Total cost / 1.2)

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2
Q

Mean mark = divide by percentage of total mark

A

Percentage change: Than ‘X’ = change/X

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3
Q

For currency conversion commission questions, multiply by
1.(percentage commission)

A

km/h -> m/s : *1000 then /3600

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4
Q

If ‘X’ takes place from 1st Aug to 20th Aug, it is 20 days NOT 19

A

Don’t be intimidated by two separate currency exchange: use ratios

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5
Q

If it is a graph, make sure you can see what TYPE it is and go from there

A

(Range = Highest - Lowest) This is NOT the same as difference

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6
Q

For weighings(eg for grades), multiply weighing percentage to normal percentage

OR credits:
do sum(mark*credits) / sum of credits

A

Keep in mind if a cost is £10/min, you need to do X/min * £10

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7
Q

If charged a surplus you can use percentages (e.g charged once and then charged again but 50% discount = 150% increase)

A

For monthly rates over a span of months, try and find the rate in one month

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8
Q

Don’t try to convert mph, convert time to hours

A

To calculate journey time, switch to same timezone and calculate

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9
Q

REMEMBER UNIT CONVERSIONS

A

For bus journeys, if you need to find distance, do not forget to omit bus stops.

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10
Q

Flat fee = constant(no change)

A

When converting miles to km or vice versa, make sure that you set 1 mile = …km or 1km = …miles

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11
Q

To find X weeks worth of something, divide by 365 and multiply by days in X weeks

A

If given X percentage of something and the number of something as well as the average of the total of something, do (X * No. of something) + (1-X * other) = average value given (https://app.medify.co.uk/m/ucat/exams/completed/2024-08-03:U:FjGB:3XRG/52708)

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12
Q

May need to multiply a percentage with another from a table

A

Profit = amount sold - amount made

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13
Q

Ratios are 3:4 is 3/4 not 3/7

A

52 weeks in a year

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14
Q

1cm^3 = 1ml = 0.001 l

A

Certain shapes are worth double

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15
Q

If you need to find area from population and population density: do population / population density

A

To represent anything in a pi chart, do (thing you have) / 360

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16
Q

If you get a percentage mark question, make sure you multiply the percentage by the total amount of marks you can get

A

If VAT needs to be removed, divide by 1.2 (or whatever VAT is)

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17
Q

If you have a difficult to find area, try and use a reverse phantom way of solving by trying to make a uniform shapes

A

To find average speed, do total distance/total time

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18
Q

‘The rest is X’ is a clear divider with no exceptions - note this when asked to calculate only one variable

A

A couple = 2 peoples

19
Q

To find the rate of increase (e.g last year ticket A was £4 and is now £6 this year, how many years from now will the ticket cost more than £15. You would need to do [£6-£4]/£4 and then work out how many years from there.)

Basically (New - Old) / Old

A

When finding percentage increases greater than 100%, (do 1 + percentage) * value, as the one represents the 100% of the current value

20
Q

Estimate the population of a condition:

Fraction where condition is true * estimated total population

A

Be careful with date tables as some of them may count ALL previous years and not just the current year

21
Q

Bonds = Winning Odds * Number of prizes

e.g if winning odds are 200,000:1 (1/200,000) and there are 40,000 prizes, then the bonds are 200,000 * 40,000

Keep in mind there may be an interest rate you need to multiply at the end

A

If given two diagrams with percentages and told that there is a proportion of information from both diagrams (e.g 3/4), make an algebraic formula linking both pieces to this proportion (3X : 4Y).

Multiply the proportionality with the decimal percentage and set them to the sum of the proportionality (7 in this case) and do (proportionality percentage * decimal percentage) / sum

(https://app.medify.co.uk/m/ucat/exams/completed/2024-08-15:U:FjGB:lPzG/47661)

22
Q

Area/Perimeter of picture frame/border guide:
1) Set up an algebraic formula for length and width
(perimeter = 2L + 2W) and (area = L*W)

2) To represent the expression for the area of the frame, atone for the four outer boxes when calculating (For example if inner width is 2 units, then you would need to consider the extra 2 units at the front and the end of the line of the side so:
(W + 4)(L + 4) = area

HOWEVER, you need to take away the area of the inside of the frame which is just W*L

SO:
(W + 4)(L + 4) - W*L = area

A

Fractions are ratios

23
Q

For any percentage multiplication, stick to decimal format

A

Algebra is OK TO USE!!!!

24
Q

Density always stays the same to the original shape

A

Betting:

x = winning money y = stake (original amount of money payed for bet)

One paid bet (e.g you bay £30) and odds are x/y;

If you win, you receive £30 * x and you get y (stake) back

If you lose:

You get nothing

May also have a free bet (eg you get free £8 bet with odds 8/7)

Then if you win: you get £7 + £8 UNLESS if told in the question that if you LOSE first bet, then you dont get £8 back

If you lose:

You get nothing

25
Q

Median = (n+1)/2

remember that it is smallest to largest

A

To calculate how much an item was worth in a past year after it has depreciated in value, you need to divide by (1 - percentage.)

You can repeat this step as much as possible if it is more than 1 year ago

26
Q

Mentally circle info from stem/question and link them together

A

Pipe rate questions:

  • If given rates of liquid in and out and asked to find how long it will take to fill out the tank, find the net total flowing in and go from there
  • To find the combinations of pipes that need to be opened/closed, find the net again (make sure it’s SAME UNITS) and go from there
27
Q

If given the length of a train/bus/any vehicle, then there is a fairly strong indicator that you need to add the length if a speed = distance/time graph is used

A

Discount price percentage * Amount = Discounted amount

28
Q

Understand 3d -> 2d scaling questions:

https://app.medify.co.uk/m/ucat/exams/completed/2024-08-24:U:FjGB:d5QH/48976

A

Remember that there are 2 lengths and sides of a pool but only one surface

https://app.medify.co.uk/m/ucat/exams/completed/2024-08-24:U:FjGB:d5QH/48979

29
Q

If asked to find bestselling (best anything), check if there are multiple of the same people first

A

If asked to predict when something will happen after being given how much money something will make in a time period, find the amount of money made in a day, take away money expected by current money made and divide this value by how much money made in a day

30
Q

A room has four walls and if you are installing a wallpaper, then the door and windows do not count

A

Journey time = Total time taken to travel - breaks

31
Q

If given two different speeds and given a total time which the task has been completed do this:

1) set up two t = d/s equations with a constant at d and speed laid out as (distance / speed at the bottom)

2) Sum both of these and equal them to the total amount of time taken

3) Find the constant

A

If it says ‘in proportion to’ remember that you need to divide with a value

32
Q

Look for units on table and question

A

Bills need to be multiplied, not divided.

e.g) Water bill is £7 a week and it has been 4 weeks

7 * 4 = £28 total

33
Q

1st year to 7th year is SIX years not seven

A

To find the time taken for an overtake do:

t = distance / (change in speed)

34
Q

Make sure to remember that if only one item is in a discount, NO OTHER items are also in a discount

A

In tax questions, if given two incomes, add both of them up before taxing

35
Q

To find the X proportion of something that is not Y, you will have to do number of (X - number THAT IS Y) / X

https://app.medify.co.uk/m/ucat/exams/completed/2024-08-27:U:FjGB:uUaH/49893

A

Average value of play = sum(percent*odds if winning)

36
Q

High profit means lower expenditure

A

‘100% more’ - means ratio

37
Q

If given two tables representing year 1 and year 2 and question mentions ‘over the two years’, then you need to take both tables into account and not just the second one.

A

Deposits are not counted in interest

38
Q

Just because someone is faster, it does not mean that a graph will have a high value as less time = more speed

A

1 ml = 1000mg

38
Q

52 cards in a deck = 26 red / 26 black

A

Formulate your own distances if not given enough information

e.g Road split into three 1/3 sections then assume the whole distance is 3 miles

39
Q

Do not use absolute increase as the change in a percentage change question ever. Find the change by finding difference in original and absolute difference

A

If told something is (Something * x) greater than something else and told to find the ‘how much greater’ then:

original = x
new bigger item = multiplier(x)

multiplier(x) - x

divide by original * 100

40
Q

Proportion equation = (item)/population of original * scaled population

A

cm^2 -> m^2

/10000

41
Q

‘The rest’ of a fraction is 1 - (original fraction)

A

Check if you can run systems simletaneously

42
Q
A
43
Q

mean percentage weighting is just sum of (marks * weight)

NO DIVISION

A

UCAT (5 decks)

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