Question

1. I am a three-digit number. My tens digit is 3 more than my

ones digits. If you round me to the nearest ten and subtract
320, the estimated difference is 150. What number am I?

2. I am a three-digit number. All my digits are odd numbers.
My ones digits is 4 more than the hundreds digits. My tens
digits is the greatest of the three digits. If you round me to
the nearest hundred and subtract 100, the estimated
difference is 300. What number am I?​

Answer 1

1. 474

2. 397

Explanation:

1. If the three-digit number is xyz, then y = z + 3.

When rounded to the nearest ten and reduced by 320, the result is 150. 150 + 320 = 470, so x = 4. y = 6 if z ≥ 5, and y = 7 if z < 5.

So the number is either 463 or 474. 463 doesn't round to 470, so the answer is 474.

2. If the three-digit number is xyz, then z = x + 4. y is the largest of the three digits; since all the digits are odd, y is either 5, 7, or 9. So z is either 5 or 7, and x is either 1 or 3.

When rounded to the nearest hundred and reduced by 100, the result is 300. 100 + 300 = 400, and y > 5, so xyz is rounded up to 400, which means x = 3. So z = 7 and y = 9.

The answer is 397.