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.
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j_shreyans
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Last edited by sanju09 on Thu Jul 02, 2015 4:28 am, edited 1 time in total.
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Since, there are no ties, so we need the value of x, and the number of losses (x - y) made by the team, in order to answer y. Let's inspect the statements one by one:j_shreyans wrote: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.
(1) 2 more losses means 2 fewer wins, that's (y - 2) wins out of x games is equivalent to 20 percent of x. We get single equation in 2 variables suggesting multiple options for x and y. Hence, insufficient. Go for BCE
(2) 3 more wins means 3 fewer losses, that's (x - y - 3) losses out of x games is equivalent to 30 percent of x. We get single equation in 2 variables suggesting multiple options for x and y. Hence, insufficient. Go for CE now.
Taken together, [spoiler]we can get both x and y; hence SUFFICIENT.
Take C[/spoiler]
The mind is everything. What you think you become. -Lord Buddha
Sanjeev K Saxena
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Statement 1: Losing 2 more games = winning 20%j_shreyans wrote: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.
y-2 = 0.2x
The equation above has an infinite number of solutions.
INSUFFICIENT.
Statement 2: Winning 3 more games = losing 30% = winning 70%
y+3 = 0.7x
The equation above has an infinite number of solutions.
INSUFFICIENT,
Statements 1 and 2 together:
Since we have 2 variables and 2 distinct linear equations, we can solve for x and y.
SUFFICIENT.
The correct answer is C.
If this were a PS question that we needed to solve, we could divide the first equation by the second:
(y-2)/(y+3) = 0.2/0.7
(y-2)/(y+3) = 2/7
7y-14 = 2y+6
5y = 20
y = 4.
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Target question: How many games did the team win last season?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.
REPHRASED target question: What is the value of y?
Given: The team played x games and won exactly y games
Statement 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.
So, winning 2 fewer games results in 20% wins
In other words, y - 2 = 20% of x
Simplify to get: y - 2 = 0.2x
Cannot solve this 2-variable linear equation for y, so statement 1 is NOT SUFFICIENT
Statement 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.
Lose 30% = Win 70%
So, winning 3 more games results in 70% wins
In other words, y + 3 = 70% of x
Simplify to get: y + 3 = 0.7x
Cannot solve this 2-variable linear equation for y, so statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined:
We have . . .
y - 2 = 0.2x
y + 3 = 0.7x
We have 2 variables and 2 distinct linear equations.
We can solve this system for y
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer = C
Cheers,
Brent
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