20

For how many three-digit numbers can you subtract 297 and obtain a second three-digit number which is the original three-digit number reversed?

A. 5

B. 10

C. 20

D. 40

E. 60

Answer

E. 60

SOLUTIOn

Suppose that ‘pqr’ is a three-digit number whose digits are reversed when 297 is subtracted.Since ‘pqr’ represents the number 100p + 10q + r and ‘rqp’ represents 100r + 10q + p, we have 100p + 10q + r − 297 = 100r + 10q + p. This equation can be rearranged to give 99p − 99r = 297 and hence we have p − r = 3. Since we know that ‘rqp’ is a three-digitnumber, r ≠ 0. Therefore there are six possibilities for the pair (p, r), namely (4, 1), (5, 2),(6, 3), (7, 4), (8, 5) and (9, 6). The middle digit, q, can be any one of the 10 digits. Thereforethe number of possible values for the original three-digit number is 6 × 10 = 60.

Our Classes

Where do you hold your classes?
We hold our classes online or on-site on Saturdays at our branch in Pimlico Academy, London.
You can find our timetable here.
What do you need to start learning online?
For lessons you only need a computer or phone with a microphone, camera and Internet access. Wherever you are - in London, Nottingham, New York or Bali - online lessons will be at hand.
When can I take the trial lesson?
You can get acquainted with the school at any time convenient for you. To do this, just leave a request and sign up for a lesson.
What should I expect from the trial lesson?
The trial lesson is a 30-minute online session designed to get a sense of how your child approaches mathematical thinking and problem solving. (In practice, it often runs a bit longer if the student is engaged!)

We typically explore a range of fun and challenging problems drawn from competitions. We adapt the difficulty based on how the student responds, aiming to make it both accessible and stimulating.

After the session, we’ll have a quick conversation with the parent to share observations and suggest a personalised path forward.
I can't attend class, what should I do?
It is OK, it happens! Students have the opportunity to cancel a lesson up to 8 hours before the scheduled time without loss of payment. So you can reschedule it for a convenient time, and the teacher will have the opportunity to
I don't have much free time, will I have time to study?
Learning can take place at your own pace. We will select a convenient schedule and at any time we will help you change the schedule, take a break or adjust the program.
How long is one lesson?
All classes last 1 hour.
Hear from some of our amazing students who already achieved incredible results with us!
"Olympiad Maths Lessons helped me a lot to get the Gold medal in Junior Maths Challenge"
St. Paul's Student

Contact us

...or ask us anything

Ask about our courses and offerings, and we will help you choose what works best for you.

Thank you! Your submission has been received!
Oops! Something went wrong while submitting the form.