Bunuel wrote:
A total of 2,000 t-shirts was divided among a soccer team, two baseball teams, and a track team. How many shirts did the track team receive?
(1) The track team and one of the baseball teams together received 5/7 as many shirts as the other baseball teams and the soccer team combined; and the two baseball teams each received the same number of shirts.
(2) Each baseball team received 400 fewer shirts than the soccer team and 400 more than the track team.
Kudos for a correct solution.
My thought process: at first glance, I want to assign variables for the 3 types of teams. HOWEVER, I'm concerned that it may be possible for each baseball team receives a DIFFERENT number of shirts, in which case I'll have to use 2 variables like B1 and B2. So, before I go any further with this line of reasoning, I SCAN the two statements to see that they both indicate that each baseball team receives the SAME number of shirts.
Great! I can assign my variables as follows:
Let S = the number of shirts the soccer team received
Let B = the number of shirts that EACH baseball team received
Let T = the number of shirts the track team received
Target question: Find the value of T. Since the TOTAL number of shirts is 2000, we already have have the equation:
S + 2B + T = 2000(1) The track team and one of the baseball teams together received 5/7 as many shirts as the other baseball teams and the soccer team combined; and the two baseball teams each received the same number of shirts.We can write the equation:
T + B = 5/7(B + S)We also have the equation:
S + 2B + T = 2000This gives us 2 equations with 3 variables, which
we cannot solve for T.
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
(2) Each baseball team received 400 fewer shirts than the soccer team and 400 more than the track team.We can write 2 equations here:
Baseball team received 400 fewer shirts than the soccer team:
B = S - 400Baseball team received 400 more shirts than the track team:
B = T + 400We also have the equation:
S + 2B + T = 2000This gives us 3 equations with 3 variables, which
we COULD solve for T.
Since we COULD answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent