Maths Olympiad Prep

Library / /23 of 213

, 2020

Algebra Difficulty 1.1 Junior Find the answer Canada

Which of the following is equal to a whole number?

Pick one

Solution

Since 99 is close to 100 and 9 is close to 10, the value of 99×999\times9 is approximately equal to 100×10=1000100\times10=1000.

Of the given answers, this means that the integer that is closest to 99×999\times9 is most likely 1000.

Multiplying, we get that the value of 99×999\times9 is 891.
Of the given answers, 99×999\times9 is indeed closest to 1000.

Want a route through all this instead of an archive? The track puts 2,444 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.