GMAT Data Sufficiency-- Challenging

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Okay gang,

Here is another one that I've written for my website-- nostressprep.com. It's a challenging one.
So start your clocks and give it a shot!



Can a space program create a mission team so that there are fewer than 700 possible teams?

(1) The program can choose from 13 different candidates.
(2) If the program increased the number of those selected to the mission team by 5, the number of possible teams would not change.

[Maciek]

Hi!

IMO C

Let X be the number of possible mission teams.
Let n be the total number of candidates.
Let r be the number of candidates in the mission team
X < 700 ?


(1) n = 13
Since we do not know the number of candidates in the mission team, we can check
whether threshold value of r is fewer than 13.
nCr = n!/(r!*(n - r)!) = (r first objects of n!)/r!
X = 13Cr
let us plug in numbers:
r = 2
13*12/2 = 78 < 700
r = 4
13*12*11*10/(4*3*2*1) = 13*11*5 > 700
Statement (1) ALONE is INSUFFICIENT

13*12*11/3*2*1
(2) if r increased by 5 then X would not change
we know that nCr = nCx, where x = n - r
if x - r = 5 then X will not change
Statement (2) ALONE is INSUFFICIENT

(1)&(2)
nCr = nCx, where x = n - r
13Cr = 13Cx, where x = 13 - r
x - r = 5
5 + r = 13 - r
r = 4
x = 9
lets check
13C4 = 13*12*11*10/(4*3*2*1) = 13*11*5
13C9 = 13*12*11*10*9*8*7*6*5/(9*8*7*6*5*4*3*2*1) = 13*12*11*10/(4*3*2*1) = 13*11*5
Hence, X > 700
Statements (1)&(2) both are TOGETHER SUFFICIENT

Hope it helps!
Best,
Maciek