Question

A mystery number rounds to 200 when rounded to nearest hundred. The sum of its ditgits is 10. When rounded to the nearest 10, it rounds to a number whose digits have a sum of 5. What is the mystery number

Answer 1

226

Explanation:

Let x = mystery number

If x rounds to the nearest hundred, 150 ≤ x ≤ 249

Therefore, it has 3 digits.

The sum of its digits = 10. Therefore, the combinations are:

1, 5, 4 rounds to 150 (sum of 6)

1, 6, 3 rounds to 160 (sum of 7)

1, 7, 2 rounds to 170 (sum of 8)

1, 8, 1 rounds to 180 (sum of 9)

1, 9, 0 rounds to 190 (sum of 10)

2, 0, 8 rounds to 200 (sum of 2)

2, 1, 7 rounds to 220 (sum of 4)

2, 2, 6 rounds to 230 (sum of 5)

2, 3, 5 rounds to 240 (sum of 6)

2, 4, 4 rounds to 240 (sum of 6)

The only sum of 3 digits that rounds to 5 is 226

Therefore x = 226