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
A particular prism has ten faces. How many edges does it have?
24
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)
(3,2)
(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
Harriet has a square piece of paper. She folds it in half to form a rectangle and then in half again to form a second rectangle (which is not a square). The perimeter of the second rectangle is 30 cm. What is the area of the original square?
144 cm2
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
Farmer Fatima rears chickens and goats. Today she returned from market and said, “I sold 80 animals, and now there are 200 fewer legs on my farm than before!” How many goats did she sell?
20 goats
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
Peter wrote a list of all the numbers that could be produced by changing one digit of the number 200.
How many of the numbers on Peter's list are prime?
None.
203 = 7 * 29
209 = 11 * 19
For any fixed x, which of the following four expressions has the largest value?
(x+1)(x-1)
(x+0.5)(x-0.5)
(x+1/3)(x-1/3)
(x+0.25)(x-0.25)
(x+0.25)(x-0.25)
How many of these four shapes could be the shape of the region where two triangles overlap?
equilateral triangle
square
regular pentagon
regular hexagon
4
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