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If 3 members are to be selected from a group of x members th

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by GMATinsight » Sun Apr 01, 2018 12:06 am
If 3 members are to be selected from a group of x members then what is the value of x?

1) If team of 3 members is selected from the group of x members then 30 different combinations of 3 members can be formed with 2 specific members never being together on the team
2) There are a total of 35 ways to make team of 3 members out of team of x members.

Source: www.GMATinsight.com

Answer: Option D
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Source: — Data Sufficiency |
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by Vincen » Fri Apr 06, 2018 1:33 am
GMATinsight wrote:If 3 members are to be selected from a group of x members then what is the value of x?

1) If team of 3 members is selected from the group of x members then 30 different combinations of 3 members can be formed with 2 specific members never being together on the team
2) There are a total of 35 ways to make team of 3 members out of team of x members.

Source: www.GMATinsight.com

Answer: Option D
Hi GMATinsight.

This is the way I'd solve this DS question. I hope can help you.

We need to determine if we can find x using each statement. It's not necessary to find the value of x.

(1) If team of 3 members is selected from the group of x members then 30 different combinations of 3 members can be formed with 2 specific members never being together on the team

2 specific members never being together = Total number of combinations - 2 specific members being together.

- Total number of combinations = $$xC3\ .\ $$
- 2 specific members being together = $$(x-2)C1$$ because there are 2 members always together, hence we have to pick one member form x-2.

Hence, we get the equation $$xC3-(x-2)C3=30.$$ Since there are one variable and one equation, we can find the value of x.

SUFFICIENT.

(2) There are a total of 35 ways to make team of 3 members out of team of x members.

From this statement we get: $$xC3=35$$ Again, one equation one variable .

SUFFICIENT.

Therefore, the answer is D

PD: the value of x on each statement is x=7.
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