## Journal Maths Week 2019 Puzzles

1 Which is the smallest value?

a) 67%

b) 2/3

c) 8/13

d) 0.666

- What is one half of two fifths of twenty times three?

a) 12

b) 25

c) 5

d) 14

- A recent Journal report on energy drinks told us that over 26 million litres of energy drinks are consumed in Ireland per year. One product popular with young people is sold in 500 ml cans. Each of these contains 55g of sugar. Suppose someone was to drink one can of this a day for a year, how much sugar would they consume in a year from this source alone?

a) 2.17 kg

b) 3.65 kg

c) 20.075 kg

d) 5.5 kg

- Last Wednesday was 10
^{th}day of the 10^{th}month. 10 multiplied by 10 is one hundred which of course is a square number. How many more times will this happen (the product of the day and the month be a square number) before the end of this year?

a) 1

b) 2

c) 3

d) 4

5. The following shape, equivalent to five squares, was cut out of cardboard to make a box. The perimeter is 72 cm. What is the area of cardboard?

a) 72 cm2

b) 120 cm2

c) 180 cm2

d) 144 cm2

6 Which is the best value?

a) Half a square metre for €10

b) Half a metre squared for €5

c) They are both the same.

d) None of the above

7. My age is four times what it was four years ago minus twice what it will be in four years’ time. What’s my age?

a) 16

b) 18

c) 24

d) 26

8) Which is best value per litre from these special offers of the same product originally marked €4 per litre?

- a) 1 litre for €3:49
- b) 1 litre with 20% off marked price
- c) Three for the price of two
- d) 33% extra free

9. The government increased the carbon tax in the budget by €6 per tonne of carbon dioxide (CO_{2}) released. A petrol car for instance can emit 2.31 kg of carbon dioxide from burning one litre of fuel. How much extra would this cost for a petrol car with a fuel efficiency of 16 km/l driving 10,000 km in a year?

a) €56

b) More than €100

c) €28

d) less than €10

10.

The following maths puzzle went viral in Japan, as most people will fall into the same trap and get the incorrect answer. Can you solve it correctly?

## Journal Maths Week 2019 Puzzles Solutions

**Solutions and explanations**

1 Which is the smallest value?

a) 67%

b) 2/3

c) 8/13

d) 0.666

Answer c) 8/13

We can compare them if we convert all to decimals.

a) 67% is 0.67, b) 2/3 is 0.666 (approximately) c) 8/13 is 0.615 and d) is 0.666

- What is one half of two fifths of twenty times three?

a) 12

b) 25

c) 5

d) 14

Answer a)

Twenty times three is 60

One fifth of 60 is 12

Two fifths of 60 therefore is 24

One half of 24 is 12.

- A recent Journal report on energy drinks told us that over 26 million litres of energy drinks are consumed in Ireland per year. One product popular with young people is sold in 500 ml cans. Each of these contains 55g of sugar. Suppose someone was to drink one can of this a day for a year, how much sugar would they consume in a year from this source alone?

a) 2.17 kg

b) 3.65 kg

c) 20.075 kg

d) 5.5 kg

Answer c)

55 g a day for 365 days would be 55 x 365 = 20,075 g.

There are 1000 grams in 1 kilogram

So that makes 20.075 kg.

- Last Wednesday was 10
^{th}day of the 10^{th}month. 10 multiplied by 10 is one hundred which of course is a square number. How many more times will this happen (the product of the day and the month be a square number) before the end of this year?

a) 1

b) 2

c) 3

d) 4

Answer d) 4:

The dates are 11/11, 3/12 (3×12 = 36 which is the square of 6), 12/12, 27/12 (27×12 =324 which is the square of 18)

5. The following shape, equivalent to five squares, was cut out of cardboard to make a box. The perimeter is 72 cm. What is the area of cardboard?

a) 72 cm2

b) 120 cm2

c) 180 cm2

d) 144 cm2

Answer c) 180

The perimeter is 72 units. There are 12 equal edges on the perimeter.

Therefore each edge is 72/12 = 6 units long.

Each square therefore has an area of 6×6 = 36

There are 5 of these squares so total area is 5 x 36= 180

6 Which is the best value?

a) Half a square metre for €10

b) Half a metre squared for €5

c) They are both the same.

d) None of the above

- c) They are both the same

Half a square metre for €10 is equivalent to a square metre for €20

Half a metre squared is 0.5m x 0.5m = 0.25m^{2} which is a quarter of a square metre which for €5 is also equivalent to €20 per square metre.

7. My age is four times what it was four years ago minus twice what it will be in four years’ time. What’s my age?

a) 16

b) 18

c) 24

d) 26

Answer c)

If we let Y represent my age, then we can convert the word statement into a mathematical statement as follows.

Y = 4 (Y-4) – 2(Y + 4)

Y = 4Y – 16 – (2Y + 8)

Y = 4Y – 16 – 2Y -8

Y = 2Y -24

Subtracting 2Y from each side we get

-Y = -24

Multiplying both sides by -1 we get

Y = 24.

8) Which is best value per litre from these special offers of the same product originally marked €4 per litre?

- a) 1 litre for €3:49
- b) 1 litre with 20% off marked price
- c) Three for the price of two
- d) 33% extra free

Answer: c) Three for the price of two

a) is €3.49 a litre.

b) 20% off marked price is 20% off €4. 20% of €4 is €0.80. So the price is €3.20 per litre

c) Three for the price of two is three litres for €8. Which is 8/3 = €2.67 per litre.

d) 33% extra free is 1.33 litres for €4. This would be 4/1.33 = €3 per litre.

9. The government increased the carbon tax in the budget by €6 per tonne of carbon dioxide (CO_{2}) released. A petrol car for instance can emit 2.31 kg of carbon dioxide from burning one litre of fuel. How much extra would this cost for a petrol car with a fuel efficiency of 16 km/l driving 10,000 km in a year?

a) €56

b) More than €100

c) €28

d) less than €10

Answer d) less that €10

This car, driving 10,000 km at 16 km/l will use 10,000/16 = 625 litres of petrol.

Burning one litre of petrol will emit 2.31 kg of CO_{2}. 625 litres will cause 626×2.31 = 1443.75 kg emissions. That is 1.443 tonnes

If the carbon tax charges and extra €6 per tonne then the extra cost will be

€6×1.443 = €8.66

10.

The following maths puzzle went viral in Japan, as most people will fall into the same trap and get the incorrect answer. Can you solve it correctly?

Answer. 1.

Order of operations is important here. BIMDAS is an acronym that helps us remember the order in which operations should be done so that everyone gets the same answer. It tells us Brackets – Indices (powers) – Multiplication – Division – Addition – Subtraction. In the above statement the division must be done first:

So it becomes 9 – 9 + 1

= 0 + 1

= 1

It is a good idea to use brackets to make it obvious to others what you intend.