Arithmetic
101, 103, 105, 107, 109, 111.
Exactly one of the following numbers is not prime. Which is it?
111
Amrita thinks of a number. She doubles it, adds 9, divides her answer by 3 and finally subtracts 1. She obtains the same number she originally thought of. What was Amrita’s number?
6
The angles of a quadrilateral are in the ratio
3 : 4 : 5 : 6.
What is the difference between the largest angle and the smallest angle?
600
One half of one third of one quarter of one fifth of a number is 2. What is the number?
240
Four different positive integers have a product of 110. What is the sum of the four integers?
19
The sum of ten consecutive integers is 5. What is the largest of these integers?
5
The lengths of the sides of an equilateral triangle are given by:
x+ 2y, 5y - x and 3x - y.
Which of the following could not be the values of x and y?
(18,12)
(15,10)
(12,8)
(10,6)
(10,6)
A train carriage has 80 seats. On my journey I noticed that all the seats in my carriage were taken and 7 people were standing. At Banbury, 9 people left the carriage, 28 people entered it and all seats were taken. How many people now had no seat?
26
How many two-digit primes have both their digits non-prime?
5
The combined age of Alice and Bob is 39.
The combined age of Bob and Clare is 40.
The combined age of Clare and Dan is 38.
The combined age of Dan and Eve is 44.
The total of all five ages is 105.
Which of the five is the youngest?
Dan
The interior angles of a triangle are
5x + 3y, 3x + 20 and 10y + 30.
where x and y are positive integers.
What is the value of x+ y?
15
A small ink cartridge has enough ink to print 600 pages.
Three small cartridges can print as many pages as two medium cartridges.
Three medium cartridges can print as many pages as two large cartridges.
How many pages can be printed using a large cartridge?
1350 pages
How many integers are greater than 20+18 and also less than 20 * 18?
321
For what value of x is 64x equal to 5125 ?
7.5
In the triangles PQR and STU,
∠RPQ = 2 × ∠UST
∠PRQ = 2 × ∠SUT
∠RQP = 1 /5 × ∠UTS
How large is ∠UTS ?
1000
A group of 42 children all play tennis or football, or both sports. The same number play tennis as play just football. Twice as many play both tennis and football as play just tennis. How many of the children play football?
35
The number "tu" is the two-digit number with "u" units digit and "t" tens digit.
The digits a and b are distinct, and non-zero.
What is the largest possible value of "ab"-"ba"?
72
The product of two positive integers is equal to twice their sum. This product is also equal to six times the difference between the two integers. What is the sum of these two integers?
9
PQRS is a square.
Point T lies on PQ so that PT : TQ = 1:2.
Point U lies SR on so that SU : UR = 1: 2.
The perimeter of PTUS is 40 cm.
What is the area of PTUS?
75 cm2
Gill is now 27 and has moved into a new flat. She has four pictures to hang in a horizontal row on a wall which is 4800 mm wide. The pictures are identical in size and are 420 mm wide. Gill hangs the first two pictures so that one is on the extreme left of the wall and one is on the extreme right of the wall. She wants to hang the remaining two pictures so that all four pictures are equally spaced. How far should Gill place the centre of each of the two remaining pictures from a vertical line down the centre of the wall?
730 mm