Bart wrote the number 1015 as a sum of numbers using only the digit 7. He used a 7 a total of 10 times, including using the number 77 three times, as shown. Now he wants to write the number 2023 as a sum of numbers using only the digit 7, using a 7 a total of 19 times. How many times will the number 77 occur in the sum?
A 2 B 3 C 4 D 5 E 6
E
First note that 777 × 3 = 2331 > 2023 and hence the maximum number of times the number 777 could appear in the sum is 2. If there were no 777s in the sum, the maximum value that could be obtained using the digit 7 exactly 19 times is 9 × 77 + 7 = 700, which is too small. Similarly, if there was only one 777 in the sum, the maximum value that could be obtained using the digit 7 exactly 19 times is 777 + 8 × 77 = 1393, which is also too small. Therefore the number 777 is required twice. Now note that 2023 − 2 × 777 = 469 and that 469 = 6 × 77 + 7. Therefore the sum Bart should write would consist of 777 twice, 77 six times and a single 7, which does consist of the digit 7 a total of 19 times.
Be up-to-date with our recent updates, new problems and answers!
Ask about our courses and offerings, and we will help you choose what works best for you.
