Data Sufficiency

A certain football team played x games last season, of which the team won exactly y games. If tied games were not possible, how many games did the team win last season?

(1) If the team had lost two more of its games last season, it would have won 20 percent of its games for the season.

(2) If the team had won three more of its games last season, it would have lost 30 percent of its games for the season.



.... My answer is D, each statement alone is sufficient, but the answer key says it's C, both statements together. You can figure out that the correct number of wins is four, by trial-and-error. I.e. For statement 1, if the team has 4 out of 10 wins, and loses 2 more games, they'd have 2 out of 10 wins (won 20% for the season). Why does the answer key say this isn't sufficient? I can't think of any other way a team could lose two more games and still win exactly 20%, other than when they play exactly 10 games. I know they want you to make a formula, but what's wrong with logical trial and error to show sufficiency?

The answer is indeed C.

Statement I
If the team had lost two more of its games last season, it would have won 20 percent of its games for the season.

20%(x+2) = y

x/5 + 2/5 = y

x+2= 5y

we can have infinite values for both x and y. Insufficient.

Statement II
If the team had won three more of its games last season, it would have lost 30 percent of its games for the season.

y+2 = 70%x

10y+20 = 7x

We can have infinite value for both x and y. Insufficient.

Combining I & II

x+2= 5y
10y+20 = 7x

Solving for above equation we can get unique values for x and y.

Sufficient.

Hence C is the answer.

For statement 1, if the team has 4 out of 10 wins, and loses 2 more games, they'd have 2 out of 10 wins (won 20% for the season). Why does the answer key say this isn't sufficient?

Firstly your interpretation of the question is wrong.
4 wins out of 10, 2 more loses means the value of x has increased by 2
4 wins out 10+2 games played.

2 wins out 8, 2 more loses, 2 wins out of 10 games. 20% of wins.

how about 3 wins out 13 games, 2 more loses, 3 out 15. 20% of wins.

You cannot get 2 solutions for the same variable in the DS questions thats why the statement is insufficient.

Let me know if you have any doubts.

Statement 1: Y-2=20%(X) ----->Insufficient

Statement 2: Y+3=70%(X) ----->Insuficcient

Combined: Sufficient ------>X = 10

Hence C