Maths Olympiad Prep

Track / Stage 4 / 273 of 340 #533 of 1964

Problem 533

AMC 12 late, AIME early
Number theory Difficulty 4.9 Find the answer

14. (12 points) The six-digit number 20□15□20 \square 15 \square is divisible by 72. What is this six-digit number?

A number or a short expression. Spacing, $ signs and \frac vs / are all fine.

Official solution

【Solution】Solution: If the six-digit number 20□15□20 \square 15 \square can be divided by 72, then the six-digit number 20□15□20 \square 15 \square can be divided by 8,

then 15 口 can be divided by 8,
so 口 =2=2. Then the six-digit number 20□15□20 \square 15 \square can be divided by 9, so 2+0+2+0+ 口 +1+5+2=10++1+5+2=10+ 口 can be divided by 9, so 口 =8=8,

so this six-digit number is 208152,
Answer: This six-digit number is 208152.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.