The Manchester Grammar School Entrance Examination 2017 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. When we multiply three consecutive numbers as shown below we obtain the following answer

                  17  x  18  x  19  = 5814
Using this result, work out the answers to these four questions

(a)  17 x 18 x 38

(b) 9 x 19 x 34

(c) 170 x 180 x 190

(d)  5814 ÷ 51 ÷ 38

2. (a) The average height of three boys is 1.29 metres.
A fourth boy Stephen, whose height is 1.21 metres,
joins the group. Find the new average height of the
group.

(b) Two more boys, Richard and Nigel, join the group.
The new average height of all six boys in the group
is 1.28 metres. If Richard is 1.26 metres, how tall
is Nigel?

3.In a special code, words are replaced by the product of the whole numbers assigned to the letters. In the code, each letter is given a different number.
For example:- if S = 3, P = 4 and Y = 6 then the word
                                   SPY = 3 x 4 x 6 = 72
Using this same method of creating our special code, work out the answers to the following four questions

(a) If TEE = 20, find the values of T and E, if neither of
the letters has the value 1.

(b) Then with those values for T and E, if
TEA = 70, find the value of A.

(c) Now work out the value of the word SEAT with the
letter values you have, including those in the
example at the start.

(d) Finally, if the value of the word FOAL = 504,
work out the value of the word LOAF.

4. On a taxi journey with one particular taxi company, the fare is worked out using a set starting charge plus a charge for each quarter of a mile travelled (the QMC).
So if the starting charge is £1 and the QMC (charge for each quarter of a mile) is 50p then the total fare for a one mile journey is given by

Total Fare = £1 + 4 x 50p = £3

(a) If the Total Fare for a two and a half mile (2½ mile) journey at another taxi company is £9.60 and the QMC (charge for each quarter of a mile) is 80p,
what is the starting charge?

(b) If the starting charge at a third company is £2.20 and the Total Fare for a 6¼ mile journey is £12.20,
what is the QMC?

5. The firm Owl Blocks makes rectangular wooden blocks in many sizes. For all of their blocks the length of the block is always 2.5 times the width of the block. The height of the blocks isn’t limited in any way.
For example, if the width of a block is 4cm then the length of the block would be 10cm
because 4cm x 2.5 = 10cm


(a) Find the length of a block if its width is 7cm.

(b) Find the width of a different block if its length is 50cm.

(c) Find the length of a third block if the perimeter of one
of its faces measured using its length and width is 42cm.

6. The distance, d, in metres, travelled by any vehicle accelerating at a rate A, in t seconds is given by the formula

  d = A x  t² ÷ 2    or   d = A  x  t  x  t ÷ 2

(a) Find the distance travelled by a car accelerating at a rate
of 8 for 3 seconds.

(b) Find the distance travelled by a space rocket
accelerating at a rate of 20 for 2 minutes.

(c) A motorbike travels 270 metres in 6 seconds.
What is its rate of acceleration?

(d) A truck travels 50 metres while accelerating at a
rate of 4. How long does this take?

7. At “Fryers and Co” a portion of chips costs £1.50, a fish costs £3.50 and a pie costs £2.00. Last Saturday evening, they sold 80 lots of fish and chips, 70 lots of pie and chips and 50 portions of chips on their own.
(a) Work out their total income that evening.

The owner bought two 25 kilogram bags of potatoes which cost £40 each for the chips. He paid £2.00 for each of the fish he sold and £1.20 for each of the pies.

(b) How much did the food that the owner
sold that evening cost him?

The owner employs two staff for the evening, paying them £8 per hour each and they work from 4pm to 11pm. Other materials cost £10 for the whole evening.

(c) What are the TOTAL costs for the evening,
including the food, the staff and the other materials?

(d) How much profit (Income – Total Costs) did the owner
make that Saturday evening?

8. The following table shows the first three rows of a table which has five columns. The values of all the entries on a particular row are the same but they are expressed in different forms.


Without necessarily completing the entire table, write down the entry that would be written in the space in the table denoted by each of the letters
(a)

(b)

(c)

(d)

(e)

9.The “Electric Light Organization” makes many electrical components including Zisters which control the power to any electrical appliance.

Zisters can be put together in two different ways as follows
In an AFFTA, the two values of the Zisters are added, so for example



In a NEXTA, the value has to be worked out by adding fractions as follows


(a) Work out the values of the following combinations of Zisters in these two questions using the methods in the examples above.

(b) Work out the value of this combination of AFFTA  and  NEXTA.

(c) Work out the value of this triple NEXTA by adding three fractions.

(d) If this new triple NEXTA has a value of 3, work out the value of the
missing Zister shown with (?)

(e) Finally, here is a special NEXTA. Showing all your working, calculate its value.
(it is special because its value is not a whole number!)