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
Selecting 3 members from x =xC3
Selecting 3 when the 2 specific members are together=(x-2)C1... 2 selected from x, the remaining 1 can be selected from remaining x-2.
So cases when the 2 are not together=xC3-(x-2)C1=30...
\(\frac{x(x-1)(x-2)}{6}-(x-2)=30.....(x-2)(x^2-x-6)=180.......(x-2)(x-3)(x+2)=180=4*5*9\)
So x-2=5..x=7
Sufficient


2) There are a total of 35 ways to make team of 3 members out of team of x members.
xC3=35...
\(\frac{x(x-1)(x-2)}{6}=35......x(x-2)(x-1)=5*6*7\)
x=7
Sufficient

D
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Isnt xC3-(x-1)C3=15??

7C3= 35 and 6C3 =20, or am I wrong?

Bunuel,

Is (x-2)C1 correct in chetan2u answer ?