Arithmetic
Which of the following fractions is closest to 1?
7/8
8/7
9/10
10/11
11/10
10/11
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 rectangle is three times as long as it is high. The area of a square is twelve times the area of the rectangle. What is the ratio of the perimeter of the square to the perimeter of the rectangle?
3:1
In 2014, in Boston, Massachusetts, Eli Bishop set a world record for the greatest number of claps per minute. He achieved 1020 claps in one minute. How many claps is that per second?
17
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)
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?
144cm2
In William Shakespeare's play As You Like It, Rosalind speaks to Orlando about “He that will divide a minute into a thousand parts”. How many seconds is equal to one thousandth of one minute?
0.06
The sum of two numbers a and b is 7 and the difference between them is 2. What is the value of a*b?
45/4
Seven squares are drawn on the sides of a regular heptagon so that they are outside the heptagon. What is the sum of all the angles at the vertices that lie between the squares outside the heptagon.
3600
The range of a list of integers is 20,
and the median is 17.
What is the smallest possible number of integers in the list?
2
Consider the following three statements.
(i) Doubling a positive number always makes it larger.
(ii) Squaring a positive number always makes it larger.
(iii) Taking the positive square root of a positive number always makes it smaller.
Which statements are true?
Only (i)
Which integer n satisfies
3/10 < n/20 < 2/5?
3 or 4 or 5 or 6 or 7
7
A 3 by 3 grid shows nine 1 cm × 1 cm squares and uses 24 cm of wire. What length of wire is required for a similar 20 by 20 grid?
840 cm
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
Jamal writes down a sequence of six integers. The rule he uses is, “after the first three terms, each term is the sum of the three previous terms.” His sequence is —, —, —, 8, 13, 25. What is his first term?
3
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
The distance between Exeter and London is 175 miles.
Sam left Exeter at 10:00 on Tuesday for London. Morgan left London for Exeter at 13:00 the same day.
They travelled on the same road. Up to the time when they met, Sam's average speed was 25 miles per hour, and Morgan's average speed was 35 miles an hour. At what time did Sam and Morgan meet?
14:40