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