Hardest 11+ Maths Interview Questions and Answers

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11+ interview preparation requires a great deal of thought about a student’s broad life experiences and goals. This article focuses on mental arithmetic and problem solving.

You can find a range of tips and tutorials, as well as dedicated interview questions, in our 11+ Interview Online Course & Question Bank.

Hardest 11+ Maths Interview Questions and Answers: Arithmetic

What do you get if you add 1+2+3+4, all the way up to 10?

This gives 55. You can calculate this by adding the first number and the last, then dividing by 2, then multiplying by the number of values. So here, we would add 1+10 = 11, divide by 2 = 5.5, then multiply by 10 to get 55. 

If I increase a number by 20% I get 72. What was my original number?

The answer is 60. If 72 is 120% of the original number, then 1% is 72/120=0.6. So, 100% (the original number) is 0.6 x 100 = 60. 


Divide 3.5 by 0.7

This gives an answer of 5. You can calculate this as 3.5 ÷ 0.7 = 5, because 0.7 goes into 3.5 exactly five times. You could also do 35 / 7 = 5, as we have multiplied both sides by 10. 

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Hardest 11+ Maths Interview Questions and Answers: Problem Solving

If three books cost £36 in total, how much would 13 books cost?

The answer is £156. Each book costs £36 ÷ 3 = £12. So, 13 books cost 13 x £12 = £156. 

You buy a sweatshirt and a pair of shoes for £150. The shoes cost £100 more than the sweatshirt. How much does each item cost?

The sweatshirt costs £25 and the shoes cost £125. It would be easy to think that the shoes cost £150 and the sweatshirt costs £50 at first, but this doesn’t give you a total of £150. Therefore you need to find two numbers that add up to 150, and are 100 apart. This could be written as
X + y = 150
X – y = 50
Add both to get x = 100

When Tom was 6, Tim was half his age. If Tom is 40 today, how old is Tim?

Tim must be 37. When Tom was 6, Tim was 3 – therefore Tim is 3 years younger than Tim. If Tom is now 40, then Tim is 40 – 3 = 37.

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Hardest 11+ Maths Interview Questions and Answers: Problem Solving (Continued)

If a toy car travels at a speed of 5 meters per second, how far will it travel in 3 minutes and 30 seconds?

To solve this, we first need to convert minutes into seconds since the speed is given in meters per second. 3 minutes and 30 seconds is equal to 210 seconds (3 * 60 seconds + 30 seconds). The distance the car travels can be found by multiplying the speed by the time. So, the car travels 5 m/s * 210 seconds = 1050 meters.

If I have a bag of 180 marbles, 45% of which are red, how many marbles are not red?

First, we find the number of red marbles: 45% of 180 is 81 (45/100 * 180). To find the number of non-red marbles, we subtract the number of red marbles from the total. So, 180 – 81 = 99 marbles are not red.


A rectangular garden has a length of 12 meters and a width of 7 meters. If a gardener wants to build a fence around the garden, how much fencing will he need?

The fencing needed is equal to the perimeter of the rectangle, which can be calculated by the formula 2 * (length + width). So, the gardener needs 2 * (12m + 7m) = 38 meters of fencing.

A container holds 4.5 litres of water. This water is equally poured into cups, each holding 250 millilitres. How many cups can be filled?

This question involves units conversion. First, we need to convert the volume of water in the container from litres to millilitres, since the volume of the cups is given in millilitres. There are 1000 millilitres in 1 litre, so 4.5 litres is equal to 4.5 * 1000 = 4500 millilitres. Then, we divide the total volume of water by the volume of each cup to find the number of cups that can be filled: 4500 ml / 250 ml/cup = 18 cups. So, 18 cups can be filled with 4.5 litres of water.

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