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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