What approximate value should come in place of (?) in the following question?

Concept

In an "approximate value" simplification, replace every decimal by the nearest convenient whole number, then evaluate the expression using the normal order of operations (brackets and powers first, then multiply/divide, then add/subtract). The aim is the option closest to the true value, not an exact figure.

Application

1. Round each term: 2511.99 ≈ 2512, 26.992 ≈ 272 = 729, 138.99 ≈ 139, 360.08 ÷ 3.99 ≈ 360 ÷ 4 = 90, 9.99 ≈ 10, and √1368 ≈ √1369 = 37.

2. Evaluate the right-hand bracket: 729 − 139 − 90 = 500.

3. Divide by 10: 500 ÷ 10 = 50. So the whole right-hand side equals 50.

4. Set up the left-hand side: (2512 − ?) ÷ 37 = 50, hence 2512 − ? = 50 × 37 = 1850.

5. Solve for ?: ? = 2512 − 1850 = 662.

Cross-check

Using the unrounded numbers, the right-hand side is about 49.97 and √1368 ≈ 36.99, giving ? ≈ 2511.99 − 49.97 × 36.99 ≈ 663.7, which rounds to the nearest option, 662. The estimate is confirmed.