Question

A sports team played 100 games last season. Did this team win at least half of the games it played last season? (1) The team won 60% of its first 65 games last season. (2) The team won 60% of its last 65 games last season.

Answer 1

Answer:

Insufficient data.

Step-by-step explanation:

Given,

Total number of games = 100,

(1) The team won 60% of its first 65 games last season.

So, the number of winning games in 65 games = 60% of 65

$=\frac{60\times 65}{100}$

$=13\times 3 = 39$

But we do not know about the data for last 35 games,

Thus, the data is insufficient.

(2) The team won 60% of its last 65 games last season.

So, the number of winning games in last 65 games = 60% of 65 =39,

Thus, the total winning games = 45 + 45 = 90,

But we do not know about the data for first 35 games,

Thus, the data is insufficient.

When we combined both (1) and (2) statements,

we found that the maximum number of games won by the team = 39 + 39 = 78,

But there is a overlap of 30 games,

i.e. an unknown number will be subtract from 78 to find the exact number of winning games.

Hence, even after combining statements (1) and (2),

The data is insufficient.