Competition problem — Algebra — Maths Olympiad Prep

Library / /95 of 168

Algebra Difficulty 1.9 Junior Find the answer

If $3 \times 3 \times 5 \times 5 \times 7 \times 9 = 3 \times 3 \times 7 \times n \times n$ , what is a possible value of $n$ ?

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

Since $3 \times 3 \times 5 \times 5 \times 7 \times 9 = 3 \times 3 \times 7 \times n \times n$ , then $n \times n = \frac{3 \times 3 \times 5 \times 5 \times 7 \times 9}{3 \times 3 \times 7} = 5 \times 5 \times 9 = 5 \times 5 \times 3 \times 3$ . Since $n \times n = 5 \times 5 \times 3 \times 3$ , then a possible value for $n$ is $n = 5 \times 3 = 15$ .

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: Omni-MATH, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.