
1. What is (999 − 99 + 9) ÷ 9?
9199100101109One method is to first work out the value of the expression in the brackets and then divide the result by 9. This gives (999 − 99 + 9) ÷ 9 = 909 ÷ 9 = 101. Alternatively, we can first divide each number in the bracket by 9 and then evaluate the resulting expression. This gives (999 − 99 + 9) ÷ 9 = (111 − 11 + 1) = 101.

2. How many minutes are there in 1/12 of a day?
240120603015There are 24 hours in a day. 24 divided by 12 = 2. And in 2 hours there are 120 minutes. Duh!

3. In my row in the theatre the seats are numbered consecutively from T1 to T50. I am sitting in seat T17 and you are sitting in seat T39. How many seats are there between us?
2322212019The seats between us are numbered from T18 up to T38. So the seats between us are the 38 seats from T1 up to T38, other than the 17 seats from T1 up to T17. So there are 38 − 17 = 21 seats between us...OBVIOUSLY!

4. The number 987,654,321 is multiplied by 9. How many times does the digit 8 occur in the result?
12349Yeah for this one you just have to be real good at long multiplication. Sorry.

5. What is the difference between the smallest 4digit number and the largest 3digit number?
11010010009899The smallest 4digit number is 1000. The largest 3digit number is 999. So their difference is equal to 1000 − 999 = 1. OF COURSE.

6. The diagram shows a square divided into strips of equal width. Three strips are black and two are grey. What fraction of the perimeter of the square is grey?
1/51/44/251/32/5Two sides of the square are wholly black, and 2/5 of two sides are grey. So the length of the perimeter that is grey is equal to 2 × 2/5 = 4/5 of the length of one side. The length of the perimeter is 4 times the length of one side. So the fraction of the perimeter that is grey is the sum shown in the image.

7. What is 2014 − 4102 ?
–2012–2088–2092–2098–2112It is easier to subtract the smaller number, 2014, from the larger number, 4102. Now 4102 − 2014 = 2088 and so 2014 − 4102 = −2088. I MEAN DUH.

8. How many prime numbers are there in the list 1, 12, 123, 1234, 12 345, 123 456 ?
None.1234It is important to remember that we do not regard 1 as a prime number. We see that 12, 1234 and 123 456 are not prime numbers because they are divisible by 2. Also, 123 is not a prime number because it is divisible by 3, and 12 345 is not a prime number because it is divisible by 5. So there are no prime numbers in the list. That one is quite tricksy tbh.

9. Triangles XYZ and PQR are drawn on a square grid. What fraction of the area of triangle XYZ is the area of trianglePQR?
1/47/181/25/181/3Calculate the area of both triangles using the formula: Area = 1/2 (base x height) And then work out the fraction by dividing the area of PQR by XYZ.

10. An equilateral triangle is surrounded by three squares, as shown. What is the value of x?
1518243036We have labeled the diagram to help explain this answer. PR = RS because they are sides of a square, and RS = RT because they are sides of an equilateral triangle. RQ = RT because they are also sides of a square. Therefore RQ = PR. And because RQ and PR are sides of an isosceles triangle, angle RPQ = angle RQP. Right now remember that angles of a triangle totaled equals 180°. And angles of a square are all 90° and angles of an equilateral triable are all 60°. Following? Good. So all the angles at point R must equal 360°. So... Angle PRQ = 360 – (90 + 90 + 60) = 120. Therefore x = (360 – 120) / 2 = 30. WOOO WE DID IT.

11. The first two terms of a sequence are 1 and 2. Each of the following terms in the sequence is the sum of all the terms which come before it in the sequence. Which of these is not a term in the sequence?
624487296Another tricksy one this. The third term of the sequence is 1 + 2 = 3, the fourth term is 1 + 2 + 3 = 6, the fifth term is 1 + 2 + 3 + 6 = 12, and so on. So the sequence begins 1, 2, 3, 6, 12, 24, 48, 96 The trick is spotting that from the 4th term onwards each term is just double the previous term. Therefore 72 does not appear.

12. In the division calculation 952 473 ÷ 18, which two adjacent digits should be swapped in order to increase the result by 100?
9 and 55 and 22 and 44 and 77 and 3If after division by 18 the number has to be increased by 100, then before the division it needs to be increased by 18 × 100 = 1800. So we need to find two adjacent digits in the number 952 473 which when swapped increase it by 1800. If 952 473 is increased by 1800 it becomes 952 473 + 1 800 = 954 273. We obtain 954 273 from 952 473 by swapping the adjacent digits 2 and 4. C'MON you got that one right?