World Maths Day: Year 5 maths question adults cant solve

They are three maths questions designed for year 5 students: How hard could they be?

The answer is – very hard.

Liam Kerr, head of global marketing at 3P Learning, a mathematical software solutions company, had his team come up with three questions designed for Year 5 students.

However, he said the maths problems have left many adults stumped, in particular the third question about “three friends and the missing $1”.

Mr Kerr said the most common difficulty adults have, comes down to the wording of the three questions.

“They are more word play than maths questions and that’s what parents and adults get caught out on,” Mr Kerr told news.com.au.

He said adults have a more strategic and methodical approach when it comes to solving maths questions, whereas students are more critical thinkers.

“They know how to approach it better because they’re seeing it more often in class,” Mr Kerr said.

“But these questions are about word play and understanding what’s being asked and getting to the chase.”

Want to give it a go? Scroll down for the questions. The answers can be found at the bottom of the page, but no cheating.

1. The pencil and the pen

Stacey buys a pen and a pencil. It costs $1.20 in total. The pen costs $1 more than the

pencil. How much did she pay for the pencil?

2. Ants on a cake

There is a group of ants on a giant cake. Every hour, the ant group doubles in size. If it

takes 48 hours for the ants to fully cover the entire cake, how long would it take the ants

to cover half the cake?

3. Three friends and the missing $1

Three friends booked a hotel room for the night. When they got to the hotel, they paid a $30 fee and went to their room.

The concierge brings up their bags and gives them back $5 because the hotel was having a special discount. The three friends decided to keep $1 each and give the concierge a $2 tip.

However, when they sat down to total their expenses, they could not explain the following:

Each one of them had paid $10 for hotel fee. Each got back $1, which meant they paid $9. They gave the concierge a $2 tip.

3 × $9 = $27

$27 + $2 = $29

What happened to the last dollar?

Answers

1. 10 cents

If the pen costs $1.00 more than the pencil and the total is $1.20, then the pencil must

cost 10 cents and the pen must cost $1.10.

2. 47 hours

The ants would cover half the size of the cake after 47 hours. The group of ants double in size every hour. This means that on any hour, the size of ants was half the size the

hour before. So if the ants cover the entire cake on the 48th hour, it means the ants covered half of the cake on the 47th hour.

3. And for the toughest of them all.

The temptation is to think that the calculation should focus on the amount each friend

paid in the end. But the key is to think about where the money is. The friends each have

$1, the concierge has $2 and there is $25 remaining. So $1 + $1 + $1 +

$2 + $25 = $30. If we think through how much each friend paid, it’s $8.33 not

$9.00 because the payment became $25, rather than $30.

Explainer: This last question is all about “ordering and logic”.

“This question is tricky because the intuitive approach is to think that the calculation should focus on the amount each friend paid in the end, rather than to consider where the money actually is,” Mr Kerr said.

“Most people find it hard not to think this way and fall down this maths rabbit hole that if each friend paid $10, they got back $1 which equals $9 each. Altogether this is $27. If we add the $2 for the concierge, we end up with $29.”

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“But, If we pause to think through how much each friend actually paid, they really paid $8.33 not $9 because the payment to the hotel became $25 post-refund, rather than the original $30. “Then you add on the $1 they each got back from the hotel, which gives you $9.33 each – which means the friends ended up with $28 ($9.33 x 3) and an additional $2 for the concierge.

“The three friends now each have $1, the concierge has $2 and $25 is with the hotel. $1 + $1 + $1 + $2 + $25 = $30.”

World Maths Day kicks off on Wednesday, March 23 and runs for 48 hours. You can register at www.worldmathsday.com

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