[P6] Problem Sum No. 5: Sum of Digits

A certain two-digit number is 3 times the sum of its digits.

What is this number?

  • Asked by Mark Heng
  • Date: 26 May 2013
  • Source: www.algebra.com; adapted, P6

This type of problem sum certainly looks tricky — doesn’t seem like there are many clues. And it is tempting to think of one general method to solve it: Algebra!

Parents, was algebra the first thing that came to your mind? Do you think there could be simpler ways to tackle this P6-level Maths question? I use the example sum above from algebra.com to illustrate my point…

About Algebra

If I’m not mistaken, algebra will be taught in Primary 6. It will come as easy to some students and tough for others. Algebra represents a radically different way of looking at representing and solving Maths problem sums — some techniques need to be understood to do it correctly.

I shall not go in depth here, since you can readily learn online from a wide range of resources. For starters, you can explore www.algebra.com, the website I found the problem sum on. And the die-hard Maths fan can always look up Wikipedia for the serious stuff.

For all we know, the “enlightened” might even start to question why they had to struggle with models in their earlier years 🙂

Observe First, Then Tackle

This point bears repeating. As I’ve said before, pay attention to analysis and don’t complicate the issue. Being clear about what is being asked can allow you to skip steps intelligently.

Don’t over-complicate things; simple can be better.

Sometimes, logical steps are all that are required to solve a Maths problem. Look first, then apply the correct methods.

Answer Sheet

Click below to reveal the Answer Sheet. You can also download the PDF file for offline reading and printing.

First, let’s look at how logical reasoning can be applied to arrive at the answer without much fuss. While this is not a common approach and may be harder to express as a written solution, I show it ahead of two other methods to draw your attention to a new possibility.

Click here to open and view the Answer Sheet, Page 1

Second comes the trial-and-error approach. This is what my 10-year-old nephew used when I asked him the same question. Again, a quick and simple way to get to the answer. Last but not least, I include the algebraic solution, with a slight twist.

Click here to open and view the Answer Sheet, Page 2

Click hereto get the Answer Sheet PDF file. To save it, right-click for options.

The Answer Sheet is annotated in a specific but consistent way, as I’ve explained here.

Have Your Say

Do you have Maths problems to share or need answers to? Why not send them to No Problem Sums and let me have a go at them?

Click hereto send me your problem sums.

I’ll try my best to work them out and present their solutions in that familiar format you see on this website. Whether it’s algebra-type sums like the one we just went through or other Primary-level Maths questions, help us expand our library of worked examples. Teasers and puzzles are welcome too!

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