2+4+7
Picking up 8 is a good move as it means he can win on the next hand with different numbers rather than just relying on one number
Robin will win the game because on the next move. This is because he can win with more permutations of the remaining cards than Susan. Eg Robin could pick up a 1 or 3 and win the game as an example. Susans options are limited
D
Add up all of the heights which comes to 221,642. Then divide by the number of instances which is 8
Nearest is D 27,700
A
Go in 3 stages per below
21:20 to 22:00 = 00:40
22:00 to 06:00 = 08:00
06:00 to 06:15 = 00:15
Add them up to get 08:55
C
6+7 = 13 minutes marking.
13+2 = 15 minutes marking + checking
15 * 28 = 420minutes
420/60 = 7 hours
D
Numbers going up in 9s. So next will be 72 and 81
A
Add up all of the numbers and divide it by the number of instances:
So answer is 69
D
Work backwards. So 95+8 = 103
1033 = 100
100/5 = 20
a) £4
200 x 2p = 400p
b) £9.50
150 x 1p + 160 x 5p
c) See below:
d) No part d in question
e) £40.60
£156.50 – (150x1p) – (200x2p)(160x5p)(120x20p)(90x50p)(55x£1)
£156.50 – £1.50 – £4 – £8 – £2.40 – £45 – £55 = £40.60
a) Louise
b) 6kg
4135
c) Gillian & Fatima
d) 3
Jeannie, Sarah & Fatima
e) 11 months
f) 224kg
37+41+35+38+34+39
g) See below..
a) 15
9984
b) 9
63 – 54
a) 26
b) (32+9+6)=47 * (96) = 141 – (96) = 138
a) 5
b) 3
(2×3)/2
c) 22
(3×6)+(2*2)
Substitution
a) 14
b) Bus
c) 41
Bicycle 9; Bus 2; Car 14; Lorry 6; Motorbike 3; Van 7
3/10 or 0.3
3 green/ total number of crayons
a) 5
Mode is the most common/frequent number in the sequence
b) 5
Mean is the average of all of the numbers once added together. Total/Number of numbers
So 50/10
a) Twentythousand four hundred
b) 21
A + * by a – is always a –
c) 27
BIDMAS. Brackets first
d) 8
y=16/2 = 8
e)i) x = 7
e)ii) x = 5
You firstly have x = 5 which is the same as x = 5
f) 6
g) 1:3
For the above, work backwards. So for example, 25075 = 175. Etc
72cm
(15 * 4) + (3*4) = 60 + 12
a) 2
Mode is the most common number
b) 15
Range is highest – lowest
c) 4
Mean = Average. Add up all of the numbers and divide by the number of instances
40/10
13/40
 You have 1/4 shaded of the first square. 2/5ths shaded of the second square
 This is a question of being able to convert both fractions to the same denominator
 So this would be 20. 1/4 becomes 5/20 and 2/5ths is 8/20
 Then add both these together to get 13/40. Note its not 13/20 as you have to add the squares together which is unlike a normal fraction addition
a) 39
1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39
b) 23
23 & 25
c) NO. 42 is not in the sequence
Going up in 3s. So next is 20,23,26,29,32,35,38,41,44
d) To be updated
a) 4
BIDMAS. Do multiplication first. So 1612 = 4
b) 70%
When converting decimals to percentages, just move the decimal place 2 places to the right. So 0.7 becomes 70.
c) 0.6
3/5ths as a decimal. To convert denominator to 100, multiply both numerator and denom by 20. So 60/100 = 0.6
d) 18
15/100 * 120/1
e) 20 – 10 /5 = 18
Do division first according to BIDMAS. Then subtraction. So 202 = 18
f) 16+(32/8/2)1 = 16 + 2 – 1 = 17
25
1 + 2 x 3 x 4 = 25
C
(2210+8) / 4
C
 5((6*9)+(7*3)(8*6))
 This gives 5(54+2148)
 This gives 5(27)
 Answer 135
a) 4mins
Sally less Anna
b) 80mins
15 + 17+ 14+ 18+ 16
c) 16mins
80/5
d) 1km
Peter took 15mins. If its 4km/h he walks, then after 15mins, he walks 1km
a) £102
10metres would be £10.20 * 10 = £102
b) 2.5metres
£10.20 * 2 = £20.40. This leaves £5.10 (£25.50 – £20.40)
£5.10 is exactly half of £10.20. So therefore total is 2.5 metres
a) 8.52am
8.15am + 37mins = 8.52am
b) 5.46pm
6.23pm – 37mins.
Slightly harder to calculate so take off 23mins first to get to 6pm. This leaves 14mins (3723). So then take 14mins off 6pm
So 5.46pm
a) 1/15
 Convert to the same denominator
 So this would mean Tom 3/5 = 9/15 and Jerry 1/3 = 5/15
 In total, 14/15ths has been eaten leaving 1/15
b) 250g
 If Tom had 3/5 = 150g, then 1/5 = 50g
 Therefore 5/5 = 250g
a) 83
(14*2)+55 = 28+55 = 83
b) 13
(9*2) = 18
3118 = 13
c) 22
d) 0
So for d), try c = 4 and 4 = 4. This will mean that 4*2 + 4 = 12 and this is equal to 4*2 + 4 as c & d are the same. So cd or dc = 0
462cm
Large Triangle = 16cm * 3 (all sides same as its equilateral). So 48cm
Middle Triangle = 7cm * 3 triangles * 3 sides (7 small triangles of 1cm each on the horizontal base tells us its a 7x7x7 triangle). So 63cm
Next size Triangle of which there are 3 = 3cm * 3 triangles * 3 sides = 27cm. There are 3 of them so 27cm
Smallest triangle = 36 small triangles all of 1cm per side. So 3cm *36 triangles * 3 sides = 324cm
Total of all of these is 48 + 63 + 27 + 324
16
5 numbers with mean 28 = 140 in total (5 * 28)
12 numbers with mean of 11 = 132 in total (12 * 11)
Total = 272
Mean = 272/17
64cm
Perimeter = 14+3+4+6+7+2+17+11
11/35
 Convert to the lowest common denominator which is 35
 So 2/5s becomes 14/35 and 2/7s becomes 10/35
 Add together so 24/35
 This leaves 11/35
a) See below. 1.52
Convert to the same metric. So in this case, its better to convert to decimals
b) 0.3
For this, you should use reverse bus stop. So 70 goes outside the bus stop with 21 inside.
Then add zeros on so that you can work out the answer to 2 decimal places
Then change the answer by the number of decimal places you added. So if you added 2 zeros, then your answer of eg. 70 would become 0.7
120
 Use BIDMAS
 20 + (1 x 7) = 27
 (20 + 1) x 7 = 147
 14727
2614
a) 1.32
0.75+0.4+0.17 = 1.32
Convert 2/5 & 17/100 to decimals
b) 16
Use the approach below which is “reverse bus stop”
74
 (4+2) x 13 = 104
 4 + (2×13) = 30
 Difference = 104 – 30
1267
a) 0.24
6/25 = 24/100 = 0.24
b) 1.20
Convert all to decimals
So 0.35 + 0.6 + 0.25
70
 Use BIDMAS. (7+3) x 11 = 10 x 11 = 110
 7+ (3×11) = 40
 11040 = 70
1019
a) 8 minutes
Mode is most common number.
b) 6 minutes
Range is highest less lowest. 10 – 4
c) 7 minutes
Mean is Average. So add up all the times and divide by number of times
35/5 = 7 minutes
d) 1 minute
If mean is 6 and there are 6 days on record, then the total number of minutes late is 6 * 6. Remember , mean= total/number of instances. So 6=total/number of instances
So 36 – 35 = 1 minute
e) Bus was not late on the other days as the mean is 4 and number of days is 9. So 36 minutes late in total which is the same as the end of day 6
a) 7 hours 45 minutes
 With time questions, always work on going to the next key mark. So see below for the illustration:
 22:45 – 23:00 = 15minutes
 23:00 – 06:00 = 7 hours
 06:00 – 06:30 = 30 minutes
 Then add together = 7 hours 45 minutes
b) 17:20
 London to Hong Kong = 22:45 + 11 hours 35 mins
 Time would be 10:20
 But Hong Kong is 7 hours ahead. So time would be 17:20
1002
10:40
 Difference between 9am and 11am is 2 hours.
 Your dealing with ratios here 5:1. So 6 parts
 If you have 2 hours this is 120 minutes and each part is 20 minutes
 So 5 of these are 100 minutes. 1 part is 20 minutes
 So 100 minutes has passed which would mean 9am + 100mins = 10:40am
a) 7
Mode is the most common number. This is 7
b) 8
8+7+11+6+9+7 = 48
48/6
c) 5
Range is highest minus lowest
267,120
742
53424
26748
 Add a zero on. So 267,120
 Its rearranging the formula so it becomes 742 = 26712/36
 Double the base answer of 26712 so it becomes 53424
 Add on 36 to the original answer. So its 26712 + 36 = 26748. (ie an extra 1 x 36 since number changes from 742 to 743)
11
 24 people. 4 got off so this left 20. X people got on
 Assume zero got on for now at the last stop
 Second stop . 20 with 3 people getting on leaving 23
 If there were then 34 people, it means 11 people got on at the first stop
2 cucumbers
 5 tomatoes = 2 pounds weight = £3.00 cost
 So green peppers they bought 3 = 40p x 3 = £1.20 cost
 If they got 20p change and spent £4.20, then 60p was spent on cucumbers
 60p/ 30p = 2 cucumbers
1.25
 0.012 + 1.238 = 1.250
a) 45
 May is 14 and her father is 53
 Mays mother is therefore 45
b) 16
 If 5 marbles cost £7.50, then 10 would cost £15. 15 would cost £22.50
 Each marble costs £1.50
 So remaining £1.50 to take you to £24 would get you 1 marble
 Total number being 16 marbles
8C°
 12C + 4C as it increases for TuesFri
£5.50
 A+B+C = £19.70
 2nd £7.50, 1st £5.50, 3rd £6.70
Cubes 14
Triangular Blocks 6
42
 Work through the multiples and add on the remainder where necessary
 4 – So multiples with 2 added on would be 6,10,14,18,22,26,30,34,38,42
 5 – So multiples with 2 added on would be 7,12,17,22,27,32,37,42
 6 – 6,12,18,24,30,36,42,48
a) 9.30am – 11.30am
9 hours back from 6.30pm is 9.30am. From 8.30pm its 11.30am
b) 6pm
USA 4am means 9am UK time.
UK is 9 hours behind Australia so the time then in Australia will be 6pm
£1.11
 3mins * 7p = 21p
 18mins * 5p = 90p
 Total cost = 111p
Cheese £5.30
Bananas £0.90
Chocolate £1.12
Total Cost £7.32
Change = £2.68
6
By second hand, the question is referring to the seconds handle that moves around the clock
Therefore, if its pointing to 2, after one minute it will still point to 2 as it will go around 360 degrees
Add on 20 seconds which represents 4 numbers on the clock (12 numbers = 60 seconds so 1 number move = 5 seeconds)
Therefore add 4 onto 2 to get 6
a) x=65
x+80=15
x=1580
b) y=11
6y=46+20
6y=66
y=11
c) g=9.8
10g+15g = 645400
25g = 245
g=9 20/25
g = 9.8
Use BIDMAS
£20.90
 £25.50 x 3 = £76.50
 £1.30 x 2 = £2.60
 Total = £79.10
 Change = £100 – £79.10
3
 Work backwards
 38 + 7 =45
 45 /15 = 3
^{13}/_{24}

 Convert to Lowest Common Denominator
 ^{ 9}/_{24} + ^{4}/_{24}
 ^{13}/_{24}
38
 Triple 16 = 48 points. Double 20 = 40 points
 Total so far is 88 points
 He therefore needs 38 with this final dart
175
 To paint houses, 14 days per house x 14 houses = 168 days
 Add 4 days holiday = 172
 Add 3 days sick leave = 175
5.75kg
 Total weight is best done by converting into common metric. So lets say kg
5.25kg
a) 5
b) 26
c) 112
Apply the rules of BIDMAS. Brackets, Indices, Division, Multiplication, Addition, Subtraction
a) 10
Mean is average. So its 17+12+8+16+2+5+10 = 70 / number of instances = 70/7
b) 15
Range is Highest – Lowest
c) 14
If mean is 10, then work backwards. Mean = Total/number of instances
This means 40 = Total/4
So total has to come to 40 and therefore, missing number is 405712
a) 1/3
b) 7/8
c) 1/3
d) 6 4/7
a) 672
b) 264
c) 1,081
d) 843
A
 10:28 to 11:00 is 32 minutes
 11:00 to 16:00 is 5 hours
 16:00 to 16:06 is 6 minutes
 Add them together gives 5 hours 38 minutes
B
 180 – 25 – 107 = 48
B
 Go 09:34 to 10:00 = 26 minutes
 Go 10:00 to 13:00 = 3 hours
 Go 13:00 to 13:21 = 21 minutes
 Total is therefore 3 hours 47 minutes
i) The warmest day at midday was Friday
ii) The coldest day at midday was Thursday
iii) Sunday temperature was +4C (1 + 5)
10kg
 Add up all of the numbers
 3+6+9+22+28+1+6+5 = 80
 8 sharks so average weight is 10kg
a. £22.50
 2 Adults = £6.25 * 2 = £12.50
 4 Children = £2.50 * 4 = £10.00
 Total = £22.50
b. 8 children
 4 adults = £5 * 4 = £20.00
 Remaining is £24
 £24/£3 = 8 children
7,11 & 39
 The multiples of 13 are 13,26,39,42,55
 The different factors of 77 are 1,11 and 7
 Answer is 7,11 & 39 = 57
16 & +4
 Six less than 10 is working backwards on the number line. So 16
 Twelve more than 8 = 8+12 = +4
116cm
 Number of days = 5
 Height sunflower grows is (68 – 48) = 20cm
 Per Day growth therefore = 4cm
 Taking 21st August through to 2nd September = 12 days
 Therefore, growth during this period is 48cm
 Adding on the height as of 21st August of 68cm = 116cm
28th July
 Work Backwards. 4cm per day = 12 days
 Therefore, 12 days from 16th August 4th August
 Then take a week off this and you get 28th July
11,908,368
 Just add on 123
 11,908,245 + 123
25
 17J + 8C = 25 sweets
 If even chance of a toffee, then there must be 25 toffees
36
8, 12, 16
Use the inverse operation of 17 * 11 = 187
E
Use substitution of values:
Orange costs 10p, Apple costs 5p
A – 35p (2 x 10p) + (3 x 5p)
B – 35p
C – 35p (1 x 10p) + (5 x 5p)
D – 35p (3 x 10p) + (1 x 5p)
E – 40p
Put numbers in a neat column format
95p
 85p x 3 = £2.55
 30p x 5 = £1.50
 Total Cost = £4.05
 Change = £5.00 – £4.05 = 95p
60 miles
Break it down one route by one route:
 Drive to HABs – 10miles
 HABs to Southgate – 9miles
 Southgate to Harpenden – 18miles
 Harpenden to HABs – 13miles
 HABs to Home – 10miles
90 hours
 Monday to Saturday = 14 hours per day. So 6 x 14 = 84 hours;
 Sunday = 6 hours;
 Total = 90 hours
£46,200
 Barbie earns £23,450
 Ken earns £22,750
 Total is therefore £46,200
Total Cost of Family of 2 adults and 3 children = £6,020
 Calculate each component at a time;
 Read the question carefully as infants (children <2) travel free;
 So real cost is 2 adults and 2 children;
 (2 x 1550) + (2×900) + (2×320) + (2×240) = £6,020
Difference of cost to stay at Portomento Bay = £790
 Calculate the cost of each sub part;
 Portomento Bay = £2050 + £1040 + £320 + £240 = £3,650
 South Seas = £1,450 + £850 + £320 + £240 = £2,860
 Difference = £790
By buying online, they save £300
 25% of …..So 25/100 * [(320×3) + (240)]
 Therefore, 25% of £1,200
 £300
Holiday Mill
 This is because 3 adults cost (3×1550) = £4,650
 Cost of child = £900
 Therefore, cost is £5,550
112 minutes
 Must read the question. It is asking for minutes and not hours
 So work on basis
 0942 – 1000 = 18 minutes
 1000 – 1100 = 60 minutes
 1100 – 1134 = 34 minutes
 Total time is (18+60+34) = 112 minutes
Years Elapsed – 42
Total Height of 2 buildings – 2,523 feet
 Years Elapsed = 19311889 = 42
 Total Height of 2 buildings 1051+1472 = 2523 feet
See below. The clue as to how to complete it is given by the fact that the diagonals given add up to 15. So all horizontal, vertical and diagonals need to add up to 15
a i) 80
ii) 23
Work backwards. 120/4 = 30. 30 minus 7 = 23
b) x2 6 OR 3 x2
7392
a) 9
Work backwards. 47 – 2 = 45. 45/5 = 9
b) 48
Work backwards. 5 + 3 = 8. x 6 = 48
c) 12
(50x)/2 = 19
50x = 38
x=12
d) 8
100 – (x + x) = 36
x² = 100 – 36
x² = 64
x = 8
See below
Ensure BIDMAS rules are applied
Start with 7 and the permutations for 7 and work from there
So (1,6), (2,5), (3,4) etc
a) James
b) £8
Joe £8; Samuel £11; James £4; Olivia £12; Sarah £7 = £42. Therefore, £8 remaining to be saved
a) £8.05
(6 bananas = £4) + (2 grapefruit = £1.80) + (1/2kg Cherries = £2.25)
b) £11.95
a) 1 hour 47 mins
Ensure you look at the departure time from Sidcot
b) 9.42
 2 hours 32 mins Burnley to Wester
 If I arrive in Wester at 12.14pm, I have to take away 2 hours 32 mins
 Take away 2 hours to give 10.14am.
 Then take away 32mins which gives 9.42am
 To sense check, re add back 2 hours 32mins to 9.42am
£2,636
Classic maths questions whereby its just converting all the words to numbers
0,0,1,1
13,602
a) £25.80
 Cost of Tickets – 2 Adults + 2 Children. (£6.50 x 2) + (£3.00 x 2) = £19
 Popcorn – 2 Small bags + 1 Large Bag. (£1.50 x 2) + (£2.20) = £5.20
 Total Cost is £24.20
 Change is therefore £50.00 – £24.20
b) 1 hour 5 minutes
 14:30 + 3 hours = 17:30.
 So 17:30 less 16:25 leaves 1 hour 5 minutes
a) 2
12 x 50p = £6.00
18 x 20p = £3.60
7 x 10p = 70p
12 x 2p = 24p
Total = £10.54
b) £4.46
If she has spent £10.54, she would need to spend a further £4.46
a) 5
Applying the rules, = 3 x 3 – 4
b) 6
Working backwards, 32+4 =
So 36 = 6 x 6
c) 9
Slightly trickier. But you need a multiple of 72 with one option being 9
x² – x – 72 = 0
a) 23C
 Assess what each marker represents. This is 2C
 Therefore, answer is 23C
b) 12C (Minus 12C)
c) 35C
d) i) 68F
20/5 = 4 * 9 = 36 + 32 = 68
d) ii) 15C
 Work backwards
 59F – 32 = 27 / 9 =3 * 5 = 15
£563
 There are 3 free adult tickets because you get 1 free adult ticket with every 10 student tickets
 So its 32 student tickets + 1 adult ticket to buy
 (32 * 14) + (15 * 1) = 448 + 15 = 563
b) x by 7 and then +3
9,012,213
Putting numbers in a column format helps with these types of questions
27,427
a) 2
b) 5
c) 11
 With this question, you have to work backwards by each statement
 “He eats one more and gives the last one to Sean”. So before he did this, he had 2
 “He then eats another and then shares the rest out equally between himself and Detti”. So if he shared equally per sentence 2, then he had 4 before he ate one to start with. So this gives 5
 “He eats one and then shares the rest out equally between himself and Emily”. He had 10 before he ate one at the start of sentence 4. So he had 11
a) 2
b) 1
c) 13
1+3+4+2+1+2
Change from £5 = £5£1.39 = £3.61
55p + 84p = £1.39
500g of Sugar. £1.10 per kg. Therefore 500/1000 = 1/2 so 1/2 * £1.10 = 55p
750g of flour. £1.12 per kg. Therefore 750/1000 * 112/1. Think of HCF though. The HCF of 750 *& 1000 is 250. Therefore, given you know what 1000g (1kg) costs, you can work out 250g.
This would be £1.12/4 = 28p per 250g
So 750g of flour = 28p * 3 = 84p
5,575
Work backwards and reverse the signage to get to the starting point
5745 +67 – 237
£18
50 calls @ 17p per call = £8.50. Plus £9.50 for the fixed charge
11, 12.5
With sequences, its vital to look at the change number on number. So 5 up to 6.5 is +1.5. Then 6.5 to 8 is +1.5 etc
The pattern becomes clear. So 9.5 +1.5 = 11. 11+1.5 = 12.5
20
Calculate the Right hand side first which gives 12. Then re arrange. Take “8” over to the right hand side from left so it becomes a positive. So 12 + 8 = 20.
14,002
10,034 + 3,968. Write in Column format to ensure you align digits correctly
a) 555
Given 6*37 answer and 9*37, 15 * 37 will be these 2 answers added together
b) 888
(9*37 + 3*37) * 2
c) 499.5
(9*37)*3 = 999.
999/2
d) 962
(6*37) * 4 = 888. So this is 24 lots of 37. To get another 2 lots of 37, you take 1/3 of the answer for 6 * 37.
So 222/3 = 74. Then 888 + 74
a) 20
W 10 – 5 =X + 5 = Y * 2= 10 + 10 = Zoe
b) 2
Work backwards: Zoe calls out 4. Take away 10 as she added 10 to the number. This gives minus 6. Therefore, Yana must have had minus 3. Xanthe must have had 2.
c) 6.5
If Yana whispers 3, she was originally given 1.5. Xanthe must have had 6.5 from Wendy
d) 0
e) 9
f) 16
For these styles of questions, its vital to SENSE CHECK your answer. Its relatively easy to go back to your workings and ensure what you have done is correct
a) 20 minutes 20 seconds
In total its 19 minutes and 80 seconds = 20 minutes 20 seconds
b) 5 minutes 5 seconds
(20 minutes 20 seconds)/ 4 . If not sure, do the minutes first which is 5 minutes average. Then do the seconds which is 5 seconds average
c) 6 minutes 14 seconds
Range is the difference between the highest and lowest times. (8 minutes 17 seconds) less (2 minutes 3 seconds) = 6 minutes 14 seconds
36 & 64
Think of all the square numbers over 64….
81,100,121,144,169
36 + 64 = 100
a)0.569
Move decimal 2 places to the left when going smaller.
b) 2.007
1997 + 10
Write it out as a maths operations question per above
5,632
Simple addition question
850g
Total Mass = 2.5kg.
Try and convert to the same metric to work through the calculation. So 2,500g
2 Bags of Carrots = 250g x 2
1 Cabbage = 750g
Total of Carrots + Cabbage = 1,250g . Plus 4oog for shopping bag = 1,650g in total
Therefore, Potatoes = 2,500g – 1,650g = 850g