AAPL wrote:Source: Official Guide
In each game of a certain tournament, a contestant either loses 3 points or gain 2 points. If Pat had 100 points at the beginning of the tournament, how many games did Pat play in the tournament?
(1) At the end of the tournament, Pat had 104 points.
(2) Pat played fewer than 10 games.
Here is an algebraic way to combine the two statements:
Let G = a game that results in a 2-point gain and L = a game that results in a 3-point loss.
Statement 1:
Since the played games yield a total of 4 points beyond the intital 100 points, we get:
2G - 3L = 4
2G =
4 + 3L
Note:
Since the expression in blue is equal to an even integer -- 2G -- L must be EVEN.
Statement 2:
Since fewer than 10 games are played, we get:
G+L < 10
G < 10 - L
2G < 20 - 2L
Substituting 2G = 4+3L into 2G < 20-2L, we get:
4 + 3L < 20 - 2L
5L < 16
L < 3.2
Implication:
L must an even nonnegative integer less than 3, with the result that L=0 or L=2.
If we substitute L=0 into 2G = 4+3L, we get:
2G = 4
G = 2.
In this case, L+G = 0+2 = 2, implying that the number of games = 2.
If we substitute L=2 into 2G = 4+3L, we get:
2G = 4 + (3*2)
2G = 10
G=5.
In this case, L+G = 2+5 = 7, implying that the number of games = 7.
Since the number of games can be different values, the two statements combined are INSUFFICIENT.
The correct answer is
E.
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