Given:For every 7 basketballs in a gym, there are 3 soccer balls.

Asked:What is the total number of basketballs and soccer balls in the gym?

Let basketballs be 7x and soccer balls be 3x.

1) The difference between the number of basketballs and soccer balls in the gym is 24.
7x-3x=4x=24
x=6
Total balls = 7x+3x=10x=60
SUFFICIENT

2) The number of basketballs in the gym is between 36 and 55.
Basketballs = 7x = 42 or 49
x=6 or 7
Total balls = 10x = 60 or 70
NOT SUFFICIENT

IMO A

OFFICIAL EXPLANATION

Hi All,

We're told that for every 7 basketballs in a gym, there are 3 soccer balls. We're asked for the TOTAL number of basketballs and soccer balls in the gym. This question is based on 'ratio math', but you have to be thorough with your thinking to make sure that you've considered all of the possibilities.

1) The difference between the number of basketballs and soccer balls in the gym is 24.

With the information in the prompt, we determine the exact number of basketballs and soccer balls, using Algebra or 'brute force.'

Since the number of basketballs is a multiple of 7, we can refer to that 'unknown' as 7X. In that same way, since we're dealing with a ratio, the number of soccer balls is an equivalent multiple of 3 - which we can refer to as 3X. The difference in those numbers is 24, so...

7X - 3X = 24
4X = 24
X = 6

With the value of X, we now know the total number of basketballs (7x6 = 42) and the total number of soccer balls (3x6 = 18)... for a total of 60 balls.

Using 'brute force', you can 'map out' how the values change as you increase the number of basketballs:
7 basketballs + 3 soccer balls = 10 total; difference = 4
14 basketballs + 6 soccer balls = 20 total; difference = 8
21 basketballs + 9 soccer balls = 30 total; difference = 12
28 basketballs + 12 soccer balls = 40 total; difference = 16
35 basketballs + 15 soccer balls = 50 total; difference = 20
42 basketballs + 18 soccer balls = 60 total; difference = 24

As the number of balls increases, the difference clearly increases, meaning that there's only one way to end up with a difference of 24 --> when the total number of balls = 60.
Fact 1 is SUFFICIENT

2) The number of basketballs in the gym is between 36 and 55.

From the prompt, we know that the number of basketballs is a multiple of 7. There are TWO different multiples of 7 between 36 and 55 though.... 42 and 49

IF....
there are 42 basketballs, then there are 18 soccer balls and the total number of balls is 60
there are 49 basketballs, then there are 21 soccer balls and the total number of balls is 70
Fact 2 is INSUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich
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