Try this beautiful problem from Algebra about unit digit from AMC-8, 2014.

## Unit digit | AMC-8, 2014|Problem 22

A $2$-digit number is such that the product of the digits plus the sum of the digits is equal to the number. What is the unit digit of the number?

- 7
- 9
- 5

**Key Concepts**

Algebra

Multiplication

integer

## Check the Answer

But try the problem first…

Answer:$9$

AMC-8, 2014 problem 22

Challenges and Thrills in Pre College Mathematics

## Try with Hints

First hint

Let the ones digit place be y and ten’s place be x

Therefore the number be \(10x+y\)

Can you now finish the problem ……….

Second Hint

Given that the product of the digits plus the sum of the digits is equal to the number

can you finish the problem……..

Final Step

Let the ones digit place be y and ten’s place be x

Therefore the number be \(10x+y\)

Now the product of the digits=\(xy\)

Given that the product of the digits plus the sum of the digits is equal to the number

Therefore \(10x+y=(x\times y)+(x+y)\)

\(\Rightarrow 9x=xy\)

\(\Rightarrow y=9\)

Therefore the unit digit =\(y\)=9

## Other useful links

- https://www.cheenta.com/area-of-isosceles-triangle-amc-8-2005-problem-23/
- https://www.youtube.com/watch?v=dLHUPDQzc2Q

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