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

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New post 26 Sep 2019, 14:42
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EMPOWERgmat DS Series:
Block 1, Question 3

For every 7 basketballs in a gym, there are 3 soccer balls. What is the total number of basketballs and soccer balls in the gym?

1) The difference between the number of basketballs and soccer balls in the gym is 24.
2) The number of basketballs in the gym is between 36 and 55.


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For every 7 basketballs in a gym, there are 3 soccer balls  [#permalink]

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New post Updated on: 28 Sep 2019, 19:54
EMPOWERgmatRichC wrote:
EMPOWERgmat DS Series:
Block 1, Question 3

For every 7 basketballs in a gym, there are 3 soccer balls. What is the total number of basketballs and soccer balls in the gym?

1) The difference between the number of basketballs and soccer balls in the gym is 24.
2) The number of basketballs in the gym is between 36 and 55.


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Share your explanation! The GMAT Club member with the most verified Kudos in total on the 5 question SC Block 1 question pack will win an $85 EMPOWERgmat tuition credit, which will entitle the winner to a full month of complete access to the EMPOWERgmat system. Even if you're not sure about your answer or your rationale, share your explanation to help boost your learning and earn a chance to win.

To be eligible, your explanation must be submitted within the 48 hour window after this post was created and should explain your reasoning why the answer you chose is correct

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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

Originally posted by Kinshook on 26 Sep 2019, 18:21.
Last edited by Kinshook on 28 Sep 2019, 19:54, edited 1 time in total.
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For every 7 basketballs in a gym, there are 3 soccer balls  [#permalink]

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New post 26 Sep 2019, 21:32
2
2) The number of basketballs in the gym is between 36 and 55.
Basketballs = 7x = 49
x=7
Total balls = 10x = 70
SUFFICIENT

@Kinshook

Posted from my mobile device[/quote]
Isn't the same case possible for
Basketball =6x=42
x=6
Total Balls= 10x=60
EMPOWERgmat Instructor
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For every 7 basketballs in a gym, there are 3 soccer balls  [#permalink]

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New post 28 Sep 2019, 15:26
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:

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For every 7 basketballs in a gym, there are 3 soccer balls   [#permalink] 28 Sep 2019, 15:26
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