A total of 2,000 t-shirts was divided among a soccer team, two basebal

Question

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 .

anudeep133 · Answer

Solution:

Statement1 : T + B = 5/7(B + S) ==> T - 2B/7 - 5S/7 = 0 and T + 2B + S = 2000
We have three variables and two equations. Insufficient.

Statement2 : S=B+400 and T=B-400 ==> T + 2B + S = 2000 ==> B+400+2B+B-400 = 2000 ==> B=500 and T=100
Sufficient

Option B

BrentGMATPrepNow · Answer

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 = 2000 
This 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 - 400 
 Baseball team received 400 more shirts than the track team :  B = T + 400 
We also have the equation:  S + 2B + T = 2000 
This 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

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

This is a value question for which we have four unknowns: the soccer shirts, baseball team A shirts, baseball team B shirts, and track team shirts. Statement (1) doesn’t allow us to solve for these four unknowns.

For (2), we’re given the relationship between one unknown (the soccer team) and the other three unknowns. That would allow us to choose a variable for the soccer team t-shirts, and write the other unknowns with that same variable. We don’t even have to do any math to see that this is sufficient! If we wanted to try this out algebraically, we could pick “x” for the number of shirts given out to the soccer team. Since a total of 2,000 shirts were given out, x + x + (x + 400) + (x – 400) = 2,000. We have a linear equation with a single variable, so we know this choice is sufficient according to the “n equations, n variable” rule.

The answer is (B)

IanStewart · Answer

There's clearly something wrong with the question, because if, as Statement 1 tells us, the ratio of track+baseball to soccer+baseball is 5 to 7, then track+baseball combined received 5/12 of all the shirts, but 2000 is not divisible by 12. I imagine the fraction is meant to be "3/7", which would make the two statements consistent.

Assuming the fraction in Statement 1 is 3/7, we learn that track and baseball combined received 600 shirts, and soccer and baseball combined received 1400 shirts. But we can't extract the baseball shirts from these numbers, so Statement 1 is not sufficient. I'd caution though to anyone producing equations here that on real GMAT questions, you should not just be counting equations and unknowns and moving on (you shouldn't say 'I have 3 unknowns but only 2 equations so I can't solve'). There are questions we can answer using only Statement 1 -- for example, we can tell that track and baseball combined received 600 shirts, or that soccer received 800 more shirts than track. We just can't answer the specific question asked here.

Statement 2 is sufficient since it tells us that the soccer and track team combined received the same number of shirts as the two baseball teams combined, so the two baseball teams received 1000 shirts, one got 500, and the track team got 100, or you can see that algebraically.

A total of 2,000 t-shirts was divided among a soccer team, two basebal

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