Multiple choice

The number n is a 2-digit number. When n is divided by 10, the remainder is 9, and when n is divided by 9, the remainder is 8. What is the value of n?

  1. 99

  2. 89

  3. 79

  4. 65

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

n = 10a + b. n mod 10 = 9 implies n ends in 9. n mod 9 = 8 implies n = 9k + 8. Testing 2-digit numbers ending in 9: 19 (19/9=2 R 1), 29 (29/9=3 R 2), 39 (39/9=4 R 3), 49 (49/9=5 R 4), 59 (59/9=6 R 5), 69 (69/9=7 R 6), 79 (79/9=8 R 7), 89 (89/9=9 R 8). 89 fits.

AI explanation

Based on the problem, the number n can be expressed in two ways, which are n = 10a + 9 and n = 9b + 8, where a and b are integers. Since n is a two-digit number, checking the given options reveals that 89 satisfies both conditions. Dividing 89 by 10 leaves a remainder of 9, and dividing 89 by 9 gives a quotient of 9 with a remainder of 8. The value of n is 89.