The Manchester Grammar School Entrance Examination 2014 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.
You have 1 hour for this paper which is worth 80 marks.

The first six questions on this paper are each worth 5 marks.

1. You are given that 47 x 382 = 17954
Use this information to answer the following questions
(a) 17954 ÷ 382 =

(b) 4.7 x 3.82 =

(c) 179.54 ÷ 38.2 =

(d)  94 x 191 =

2. (a) In a triangle, one of the angles is 39°,
the second is 81°, what is the size of the
third angle?

(b) A second triangle is isosceles, and one of its
angles is 48°. What are the TWO possible pairs
of values for the other two angles?

(c) In a third triangle ABC, angle B is two times the
size of angle A and angle C is 40° more than
angle A. What is the size of angle A?

3. Andy has done some research on the internet and found two different companies he could pay for the gas he uses, known as GeOn and HdF. The graph below shows the cost of gas for the two different companies, so Andy can compare the costs.


(a) How much does it cost for 40 units of gas from GeOn?

(b) How much does it cost for 50 units of gas from HdF?

(c) For how many units of gas would the cost from each
company be the same?

(d) If Andy uses 80 units of gas, which company would be
cheaper and by how much?

4. Farmer Burrows owns four chickens, each of which he knows by name.

Anna lays 2 eggs each day
Bethan lays 3 eggs each day
Connie lays 4 eggs each day
but Deborah lays 1 egg every other day, starting on day 1. (ie on day 1, then day 3 etc)

(a) How many eggs are laid on day 1?

(b) How many eggs are laid on day 8?

(c) One chicken is ill on a particular day,
so Farmer Burrows is only able to collect 8 eggs.
Which chicken is ill?

(d) How many eggs were laid in total on all the days 1 to 8,
if no chickens were ill on those days?

5. In an IFTHEN sequence, the next number in the sequence is determined by a rule which depends on the previous number.

So for the following rule      IF the number is odd THEN add 1 to it,
                                                         but IF the number is even THEN add 3 to it

then if the sequence starts with 3, it will continue after 3 as follows
                                      4, 7, 8, 11 and so on.

List the next four numbers after the starting number in each of the following IFTHEN sequences by applying the rules given

(a) IF the number is odd THEN multiply by 2,
but IF the number is even THEN subtract 1.
Starting number of sequence is 3

(b) IF the number is greater than 10,
THEN divide by 2, but IF the number
is less than 10 THEN multiply by 3.
Starting number of sequence is 16

(c) IF the number is prime THEN add 5, but IF the number is not prime
THEN divide by 2.
Starting number of sequence is 11

6. In a set of cuboids, the three measurements, length, width and height are always
in the ratio 5 : 4 : 3
i.e. Ratio of Length : Width : Height = 5 : 4 : 3 for each of the cuboids

(a) Find the length of the first cuboid if the width is 20 cm.

(b) Find the width of the second cuboid if its length is
12 cm more than its height.

(c) Find the height of the third cuboid if its volume is 480 cm³

The remaining longer problems on this paper are each worth 10 marks.

7. The "BACT" of two numbers is found by adding together the common factors of the two numbers. So to find the BACT of 20 and 30 which is written as B(20,30) we would work out
 
and then the BACT of 20 and 30 is B(20,30) = 1 + 2 + 5 + 10 = 18
Using this method

(a) Find the BACT of 10 and 15, written as B(10,15)
  Factors of 10 are

Factors of 15 are
So common factors are

(b) Find the BACT of 24 and 36, written as B(24,36)

(c) For any pair of numbers, what is the smallest value
the BACT could have?

(d) If the BACT of two numbers is 7 and both of the
numbers are less than 15, write down a pair of
possible numbers that you could be using

The BACT of three numbers is worked out in the same
way as for two numbers by adding the common factors
of all three numbers.

(e) What is the BACT of 6, 12 and 30, i.e. B(6,12,30)?

8. A class of students is set a test with 20 questions. A correct answer scores 5 marks, but a wrong answer loses 3 marks. An answer space left blank scores 0 marks.

(a) Adil answers all of the questions, leaving no blank
answer spaces and gets 12 right. What is his score?

(b) Brett answers 6 out of the 20 questions correctly
but leaves 8 answers spaces blank. What is his score?

(c) Caroline answers all the questions and scores 28 marks.
How many questions did she get right?

(d) David unfortunately scored zero. Give TWO
ways in which this could have happened,
other than him leaving all the answer
spaces blank.

(e) Eve got twice as many right as she got wrong and
scored 35. How many answer spaces did she leave
blank?

9. Ayton & Eeport are connected by a railway on which 5 trains run each way every day. For all the journeys in the same direction the trains travel at the same speed and take the same time. At one station, only part of the timetable was displayed as a section had been washed off by the rain.

(a) When does train 5 arrive at Eeport?

(b) When does train 4 leave Eeport to return to Ayton?

(c) Nancy lives in Ceebridge and wants to travel to Ayton but
she misses train 2 by 12 minutes. How long will she have
to wait for the next train?

(d) There is a steep downhill section between two of the towns
on the journey. Between which towns is the slope?
Give a reason for your answer.

10. Each day a shoal of small fish increases in number by 50% but each night a shark eats 300 of them.
So if there are 1000 fish on Monday morning, then there will be 1500 by Monday evening but only 1200 left by Tuesday morning!
Complete the following tables showing the number of fish each morning
(a) 

(b)

(c)

(d) If the number of fish each morning is the same on
each of the four days, how many fish were there on
Monday morning?

(e) Word got round amongst the sharks that there was a good
meal to be had in this part of the sea! During the day there is
still a 50% increase in the number of fish, but if 15 sharks
came each night, eating 300 fish each, complete the table below.

11. The numbers 21 to 29 inclusive are to be written in the spaces below so that each number satisfies the condition given on the line where you have written it, with each number appearing
only once.

(a)  ______  is an even number

(b)  _______  is a factor of 144

(c)  _______  is a power of 3

(d)  ______ is a prime number

(e)  _______  has digits which differ by 1

(f)  _______  has exactly 3 factors

(g)  ______  is a multiple of 7

Your new question!

(i)  _______  has its second digit greater than its first digit


Remember each of the numbers 21 to 29 should appear only once.