grandh01 wrote:If x,y, and n are positive integers,
is (x/y)^n > 1000
1) x=y^3 and n>y
2) x>5y and n> x
oa is B
Target question:
Is (x/y)^n > 1000?
Statement 1: x=y^3 and n>y
At this point, we can take our target question and replace x with
y^3 to get: Is (
y^3/y)^n > 1000?
We can rewrite this as "Is (y^2)^n >1000?"
Since we haven't really restricted the values of n and y, there are several possible cases. Here are two:
case a: y=1 and n=1, in which case (y^2)^n is not greater than 1000.
case a: y=5 and n=10, in which case (y^2)^n is greater than 1000.
So, statement 1 is NOT SUFFICIENT
Statement 2: x>5y and n> x
First take x>5y and divide both sides by x to get x/y > 5 (great, we already have an idea about the value of x/y.)
Next, since x/y > 5, we know that x must be greater than 5. How do we know this? Well, we're told that x, y and n are positive integers. So, the smallest y could be is 1. Since x/y > 5, we know that x must be greater than 5.
Also, since n>x, we know that n must be greater than 5 as well (in fact, we can conclude that n is actually greater than 6, but that doesn't really matter here).
So, we know that x/y > 5 and we know that n>5.
This means that (x/y)^n
must be greater than 1000
So, statement 2 is SUFFICIENT
Answer =
B
Cheers,
Brent
