dvinoth86
Two missiles are launched simultaneously. Missile 1 launches at a speed of x miles per hour, increasing its speed by a factor of √x every 10 minutes (so that after 10 minutes its speed is x√x, after 20 minutes its speed is x2, 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 = √y
(2) x > 8
After 1 hour the speed of Missile 1 will be \(x*(\sqrt{x})^6=x^4\);
After 1 hour the speed of Missile 2 will be \(y*2^6=64y\);
Question: is \(x^4>64y\)
(1) \(x=\sqrt{y}\). Substitute \(x\), the question becomes: is \((\sqrt{y})^4>64y\)? --> is \(y^2>64y\)? or is \(y>64\)? (since y<0 is not possible). We don't know that. Not sufficient.
(2) \(x > 8\). Clearly insufficient, since no info about y.
(1)+(2) From (2) \(x>8\), which according to (1) means \(\sqrt{y}>8\) --> \(y>64\). Exactly what we wanted to know. Sufficient.
Answer: C.
Another way.Question: is \(x^4>64y\)
(1) \(x=\sqrt{y}\) --> \(x^2=y\). Substitute \(y\), the question becomes: is \(x^4>64x^2\)? --> is \(x^2>64\)? or is \(x>8\)? (since x<-8 is not possible). We don't know that. Not sufficient.
(2) \(x > 8\). Clearly insufficient, since no info about y.
(1)+(2) From (1) question became "is \(x>8\)?", and (2) \(x>8\) directly answers it. Sufficient.
Answer: C.
Hope it's clear.