IrinaOK wrote:

Two missiles are launched simultaneously. Missile 1 launches at a speed of x miles per hour, increasing its speed by a factor of sqrt(x) every 10 minutes (so that after 10 minutes its speed is x*sqrt(x) , after 20 minutes its speed is x*sqrt(x)*x*sqrt(x) , and so forth. Missile 2 launches at a speed of y miles per hour, doubling its speed every 10 minutes. After 1 hour, is the speed of Missile 1 greater than that of Missile 2?

1) x=srt(y)

2) x>8

will post OA later.

M1 in 1 hour: x*root(x) (10 min) *root(x) (20 min) *root(x) (30 min) *root(x) (40 min) *root(x) (50 min) *root(x) (1 hour).

Therefore, M1 will have speed = x*x*x*x = x^4.

M2 in 1 hour: y*2 (10 min) *2 (20 min) *2(30 min) *2(40 min) *2(50 min) *2 (1 hour) = y*2*2*2*2*2*2 = 64y.

We need to compare x^4 and 64 y.

1. x = root(y), x^4 = y^2.

y^2 and 32y. If y = 1, we have 1 and 32.

If y = 100, we have 10000 and 3200.

NOT Suff.

2. x>8. Let it be 9,

9^4 and 32y - Not suff.

3. Together.

y^2 and 32y, since x>8 and x = root (y), minimum y>64.

64^2 and 32*64.

Suff.

C.