536
Use bus stop method if needed
2/5 1/2 5/8
 Convert all fractions to the lowest common denominator
 The LCD of 5, 8 & 2 is 40. Always easiest to work by going through the highest of the 3 numbers. So count in 8s
 Revised fractions are as per follows so it now becomes much easier to rank these:
^{16}/_{40} ^{25}/_{40} ^{20}/_{40}
18
Work these questions always with the following approach:
^{3}/_{8} * ^{48}/_{1}
Then simplify to:
^{3}/_{1} * ^{6}/_{1}
Easier to get to the answer of 18
6.7 , 48
Sequence Questions. You should always mark clearly what each sequence is moving up in. So in the first case, its going up in “0.3s”
So the next number will be 6.7
For the second one, the pattern is that the numbers are doubling. So the next number will be 48
The trick with these questions is to analyse the change number on number as the key takeaway
1.009
If not sure, put the numbers in column format like below:
9 & 4
 The way to tackle this question is think of multiples of 36. This would be 1,2,3,4,6,9,12,18,36
 The 2 numbers with a difference of 5 are 9 & 4
a) See below
b) See below
Convert all the cards to the same metric if that helps to evaluate
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
9
Work backwards:
35 – 8 = 27. Divide by 3 = 9
40 metres; 10 wooden trays; 160 nails
The approach:
 There are 2 approaches.
 Work out what it would be for 1 bird table and then multiply up by 10 to get the total for 10 bird tables. However, this approach means that you start to deal in decimals as you would need 0.4 wooden trays per bird table. This can sometimes cause errors down the line
 Therefore, the approach I advocate is HCF.

 Look at the core numbers which is that you have the “requirements” for 4 bird tables and need to work out what is required for 10
 The HCF of 4 & 10 is 2
 Therefore, calculate what is needed for 2. In this case, that would be halving what you need for 4.
 So for 2 you need 8 metres of wood, 2 wooden trays and 32 nails
 Then work out “how many batches of 2s” you need to get for the required 10 tables
 So this is 5 batches
 The answer becomes (5 * 8 metres of wood); (5 * 2 wooden trays) and (5 * 32 nails)

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
30
A classic question on the concept of fractions. If Ravi is left with 12 sweets and this equals 2/5, then you have to calculate what 1/5 equals. This is 12/2 so it equals 6 sweets
Therefore, each 1/5 = 6 sweets. There were therefore 30 sweets to start with in the box
a) 6 Years 4 Months
1998 less 1992 = 6 years
1st Sept less 1st May = 4 months
b) 2007
15th birthday will be 1992 + 15 = 2007
18 minutes slow
 Clock A says 7:05. If it is 12 minutes fast, then the actual time is 6:53.
 Clock B is currently 6:35.
 Therefore, Clock B is 18 minutes slow
a) 11 balloons
 Always best to convert to the same denomination.
 If she has a 4metres, then this is 400cm. Each string 35cm, then the total is 400/35 = 11.4
 Total number of balloons = 11
b) 15cm
 11 balloons would take 11 x 35cm of string
 This is 385cm
 Therefore, 15cm is left over
a) 330 minutes
6 x 55 minutes = 330 minutes
b) £19.80
 330 minutes / 60 = 5 hours 30 minutes
 Per Hour = £3.60.
 Therefore £3.60 x 5.5 hours = £19.80
a) b) c) See below
a) 25%
 Firstly count the number of segments. There are 12 segments
 3 of the segments are shaded
 Therefore in total, 3/12 are shaded = 25%
b) 3/16
 Each Large Triangle is equivalent to 2 small triangles
 There are 3 small triangles shaded out of a total of 16
c) See below
 16 squares altogether
 4/16 = 25% shaded
a) b) See below
a) 8



 If 64 cars in total, then the following equation will be used to calculate the number of red cars
 ^{ 64}/_{1} * ^{45}/_{360. }
 After cross cancellation, this is simplified to:
 64/_{1} * ^{5}/_{40}
 Further cross cancellation:
 8/_{1} * ^{1}/_{1}


b) 3/8
 The key here is to remember that the opposite angles when 2 lines cross, create equal angles
 So given Black and Red are 45º each, this gives 90° in total
 So remaining in the circle is 360 – 90 = 270
 Each angle must therefore be 270/2 = 135
 Every 45 degrees = 1/8th. So 135 = 3/8
Need to work through each person to understand the possible options:
Thomas – Brasted, Westerham or Dunton
Henry – Knockholt or Dunton
Edward – Dunton or Sevenoaks
Gordon – Brasted or Knockholt
a) 87m²
 The area of the lawn is 96m² (12 x 8)
 The patio will take 3 x 3 = 9m²
 Therefore, the remaining area of the lawn is 96 – 9 = 87m²
b) 40m
 The perimeter of the lawn is 2 x (12 + 8) = 40m
a) A & C. Both have a perimeter of 8
b) 4cm²
a) 3.7kg
 Important with these questions to recognise what each marker is worth
 In this case, we start at 3kg and finish at 4kg
 There are 10 markers in between so each marker is 100g….OR 0.1kg
 Baby therefore weights 3.7kg
b) 325g
 Same process as above. Work out each marker
 Each marker is 25g
 So the mouse weighs 325g
c) 142cm on the ruler
 Again recognise what each marker is worth. In this case its 2cm per marker
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
210º
 An equilateral triangle is 60º per inside angle. Therefore, the outside to give a right angle is 30
 In addition , P would be 180 + 3o = 210
a) 8 small boxes in the bottom layer
 Given the height of the cube is 2cm, a total of 3 high can fit in the larger box
 The bottom layer of the larger box would therefore occupy 2 x 5 x 9 = 90cm³
 But some space would be left around the base. Below is an aerial view
b) 24 small boxes
 As mentioned above, 3 layers in total
 Therefore 8 x 3 =24
 A 1 x 1 would be left as empty space as you would not be able to break a small box and fit it into the sides
a) 68cm²
 Firstly we need to count the number of cubes. This is equal to 30
 For the 30 cubes, these can be split as follows:

 There are 12 cubes….the steps if you look from South East to North West angle. 2 sides visible so thats 24 in total
 Next the cubes at the side looking from South West to North East angle. There are 6 visible cubes and in total, 10 surfaces. This is the same on the other side so its 20 visible sides in total
 Finally, 6 cubes have 4 sides showing
 Total therefore is 68 sides showing

b) 3 cubes left
Easier than part a for sure!. 30 cubes in part a and 27 in part b
a) i) A connects to D. This is the easier question of the 3
a) ii) E
For the tab connecting to B, this is through visualisation. If B is folded in , then B will be at the base of the cube as you look at it. The tab that locks with B is E
b) 6
Again visualisation.
b)
Remember the question is asking for the incorrect answer. In this case its b)
10
The simple formula is (5×4)/2
Where 5 represents the number of teams. 4 represents the maximum number of games each team can play against. 2 being the required denominator
8
 Work backwards…..Mean = total of all instances/number of instances
 6 = ? /5
 Rearrange = 6×5 = ?
 ? = 30. Given you know the total of the other days as 22, the missing day is 8
11pence
3p + 1r = 50p
2p + 2r = 56p
Therefore…..
6p + 2r = 100p (x formula 1 by 2)
2p2r = 56p
4p = 44p
=11p
1,3,6,9
 Multiples of 3 being 3,6,9, (12 is not possible to include as the total of the cards is less than 20)
 Odd cards being 1,3,5,7,9,11
 This leaves 1,3,6 & 9 because the total of these is 19 so less than the target total of 20
Alice = £16.50
 If their collective total is £26.50, then use Algebra to solve
 Charlie + 10 + Charlie + 3 + Charlie = £26.50
 3Charlie + 16 = £26.50
 3Charlie = £10.50
 Charlie = £3.50
 So Becky = £6.50
 So Alice = £16.50
a) 72
(5+6) * 6
b) 1/2
(1/2 + 1/2) * 1/2
c) 13
(a+2) * 2 = 30
a+2=15
Therefore, rearrange. a=13
d) 5
So (a+a)*a = 2axa=50
a²=25
a=5
a) 6
(9×4)/6 = 36/6 =6
b) 2
(36×2)/(9×4) = 2
a)i) 1,2,3,4,6
a)ii) No
This is because 1,2,3,4,6 add up to 16 and not 12
b) 6
Because 1+2+3 = 6
c) 2,4,8,16,31,62,124,248
Apply the factor tree approach. So you get :
496 = 248 * 2
248 = 124 * 2
124 = 62 * 2
62 = 31 * 2
Highlighted numbers are Prime Numbers. So 31 x 2 x 2 x 2 x 2 = 496
Therefore, factors of 496 = 2,4,8,16,31,62,124,248
Zara
Follow it logically step by step:
Glen > Florence
Florence > Ahmed > Zara
Oliver < Glen > Zara
Yasmin < Glen
Ahmed > Oliver
Florence < Yasmin
If Florence is less than Yasmin and given Yasmin is greater than Glen and Glen is greater than Zara, Zara is the youngest
6
Where “U” stands for Unknown. So Unknown 1 is “U1” etc
U1+4+17 = U2+U1+5
Rearrange:
21 = u2+5
u2=16
Given this, 5+17+u3 = u2+u3+m
22 = 16 + m
m = 6