Try this beautiful problem from Algebra about unit digit from AMC-8, 2014.
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?
Algebra
Multiplication
integer
Answer:$9$
AMC-8, 2014 problem 22
Challenges and Thrills in Pre College Mathematics
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 ..........
Given that the product of the digits plus the sum of the digits is equal to the number
can you finish the problem........
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
AMC - AIME Boot Camp... for brilliant students.
Use our exclusive one-on-one plus group class system to prepare for Math Olympiad
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's M.Stat Entrance. They ranked within the first 50 in the entire country in these entrances. I.S.I. M.Stat Entrance
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's B.Stat Entrance and Chennai Mathematical Institute's B.Sc. Math Entrance. They ranked within the first 200 in the entire country in these entrances. Most of these students attended the problem solving workshops regularly, which happen 5 days every week. CMI B.Sc. Math Entrance […]
In 2025, 8 students from Cheenta Academy cracked the prestigious Regional Math Olympiad. In this post, we will share some of their success stories and learning strategies. The Regional Mathematics Olympiad (RMO) and the Indian National Mathematics Olympiad (INMO) are two most important mathematics contests in India.These two contests are for the students who are […]
Cheenta Academy proudly celebrates the success of 27 current and former students who qualified for the Indian Olympiad Qualifier in Mathematics (IOQM) 2025, advancing to the next stage — RMO. This accomplishment highlights their perseverance and Cheenta’s ongoing mission to nurture mathematical excellence and research-oriented learning.