In a game played to 100 points, Player A scores 100 points while Player B scores only 65 points in the same time. By how many points can A give B a start in a 100-point game?

Introduction / Context:
Point-advantage (handicap) problems convert performance differences into a fixed start so that two players would finish together if both play to their usual standard. If A scores faster than B, A can give B a head start equal to the deficit B has when A reaches the target score.

Given Data / Assumptions:

• Target score = 100 points.
• In equal playing time, A scores 100 while B scores 65.
• Both maintain constant scoring rates during a game.

Concept / Approach:
When A hits 100, B has 65. The difference 100 − 65 is the sustainable head start B would need so that both would reach 100 simultaneously if they kept the same rates.

Step-by-Step Solution:
A's score at finish = 100 points B's score at the same instant = 65 points Head start for B = 100 − 65 = 35 points

Verification / Alternative check:
If B begins 35 points ahead, then by the time A accumulates 100 points, B will also have effectively accumulated 35 more than his usual 65 in that span, i.e., 100, yielding a simultaneous finish under equal conditions.

Why Other Options Are Wrong:
45, 25, or 55 do not match the exact deficit measured in the same time interval; the data imply precisely 35 points.

Common Pitfalls:
Confusing time handicaps with point handicaps; averaging scores instead of using the direct difference at the target moment; changing the target score incorrectly.

Final Answer:
35