The Manchester Grammar School Entrance Examination 2019 Arithmetic Section B Online Quiz

For each question, show all your working in full, as this will be marked, and then write your answer clearly in the space provided. If you run out of space for an answer use the space provided at the end of this booklet, numbering your answers carefully.
You have 1 hour for this paper which is worth 80 marks.

1. The table below shows the highest and lowest temperatures in °C recorded in six cities around the world on one particular day last year


(a) What is the difference between the highest and lowest
temperatures in Boston?

1.(b) What is the difference between the highest and lowest
temperatures in St Petersburg?

1.(c) Which city has the lowest recorded temperature of all?

1.(d) Which city has the largest difference between its
highest and lowest temperature?

2. The gas meter reading on Andrew’s smart meter in October was 5475 units. Exactly three months later, in January, the reading was 6045 units. M-power charge a fixed amount of £16.20 each month plus 40p for each unit used during the three months between the two readings.

(a) How many units of gas has Andrew used in the three
month period from October to January?

2.(b) Calculate the total amount Andrew has to pay for that three
month period.

2.(c) In fact, M-power also have to add 5% to Andrew’s bill which
is the tax known as VAT. What will be the final bill that Andrew
has to pay for his gas?

3. The “Blast” of a two digit number is obtained as follows:

The Blast of 63 is 216                 because 6 x 6 x 6 = 216
and the Blast of 27 is 128         because 2 x 2 x 2 x 2 x 2 x 2 x 2 = 128

(a) Write down the Blast of the two digit number 34

3.(b) Which two digit number has a Blast of 125

3.(c) Work out another two digit number which has the same Blast as 24

3.(d) A particular two digit number is Blasted and then that answer
is also Blasted. If the final answer is 9, what was the original number?

4. A plant grows during the first month after it is planted. During the second month it grows by half the height it had already reached. During the third month it grows by one third of the height it had reached at the end of the second month. It then grows by one quarter and one fifth of the height reached in the same way in the next two months.
(a) If a plant is 1 metre tall at the end of the first month,
how tall will it be after five months?

4.(b) If a plant grows 90 cm in the third month,
how tall was it after one month?

4.(c) If a plant is 2 metres tall at the end of the first month,
how much will it have grown, in total, by the end of the
fifth month?

5. The table below shows four different makes of car each with four different engine sizes, in litres, and the Insurance Group for each.
For example a Hissan 1.5 car is in Insurance Group B.



The second table shows the monthly insurance payment paid by drivers of different age bands for each of the insurance groups, so a person aged 37 would be in the age band 21 - 45 and so would pay £105 each month for a car in Insurance group C.



(a) How much will a 19 year old pay for a Foxhall 1.5 car
each month?

5.(b) A 30 year old pays £95 for a Hissan car. What is the engine
size of their car , in litres?

5.(c) How much would a 50 year old person save each month by
using a 1.1 Hissan car rather than a 1.9 Hissan car?

5.(d) If a 32 year old pays £95 for a Skoyota car, what would a 20
year old pay for a Jagley car with the same size engine?

6. If the weight of straight bones in the human body depends on the length, radius and density of the bone using the following formula

Weight = Length x Radius x Radius x Density
or  W    = L x R x R x D

then a shin bone of length 40cm, radius 3cm and density 5 would have a weight of 1800g because
                                    W = 40 x 3 x 3 x 5 = 1800
Using this formula,


(a) Work out the weight of a finger bone of length 3cm,
with a radius of 0.5cm and density 2.

6.(b) Work out the density of a forearm of length 30cm,
with a radius of 2cm which weighs 480g.

6.(c) Work out the radius of a thigh bone of length
50cm which has a density of 8 and weighs 3600g.

7. A top international bowler playing in a cricket match bowls a cricket ball at 90 miles per hour.

(a) How many miles would the ball travel in one minute?

7.(b) If a mile is 1760 yards, how many yards would the
ball travel in one minute?

7.(c) How many yards does the ball travel in one second?

7.(d) If the distance the ball travels through the air from the point
where the bowler bowls the ball to the point where it is hit
by the batsman is 22 yards, how long is the ball travelling for?

8. Megaprint make small business cards with names and contact details on, that people can give to clients as part of their work. The total cost of buying the cards they sell is made up of two amounts.
There is a fixed cost that people must pay no matter how many cards they order and this amount is always the same. Then there is a second amount which depends on the number of cards ordered. These two amounts are added together to give the total cost of the order and the graph below shows what the total cost would be for the number of cards ordered.



Using the graph

(a) Write down the total cost of having 100 cards printed.

(b) Andy’s order costs him £16.00. Write down the number
of cards he ordered.

(c) If 200 cards are ordered, using the total cost what is
the cost of one card?

(d) Write down the fixed cost that Megaprint charge for
each order, regardless of the number of cards ordered.

(e) If you exclude the fixed cost, how much is charged for one
card to be printed?

(f) Using the graph, or otherwise, work out the number of cards
for which the total cost would be the same from both companies.

9. A two digit number is called a multisum if it is a multiple of the sum of its digits.

           So 84 is a multisum                      since 8 + 4 = 12
          and 84 is a multiple of 12

(a) Work out and write down the smallest number, greater
than 50, which is a multisum.

(b) Work out and write down the smallest multiple of 7 which
is a multisum.

(c) Work out and write down the only multiple of 9 which is
NOT a multisum.

(d) Work out and write down all the numbers between
20 and 30 which are NOT multisums.

10. A pair of numbers written as a column like this
is known as a VEC.
VECs can be combined together in two different ways, as follows



(a) Work out the value of