Hey everyone, I have two questions I'm stuck on:
If x is positive, which of the following could be the correct ordering of 1/x, 2x, and x^2?
I. x^2 < 2x < 1/x
II. x^2 < 1/x < 2x
III. 2x < x^2 < 1/x
From my testing of numbers, statement I is fine. But the answer is both statements I and II. Could someone explain to me how statement II might hold true? I've tried fractions, whole numbers...can't figure it out, and it's driving me nuts
and second:
For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100) + 1, then p is:
A – between 2 and 10
B – between 10 and 20
C – between 20 and 30
D – between 30 and 40
E – greater than 40
I have no idea how to approach this second one...
If x is positive, which of the following could be the correct ordering of 1/x, 2x, and x^2?
I. x^2 < 2x < 1/x
II. x^2 < 1/x < 2x
III. 2x < x^2 < 1/x
From my testing of numbers, statement I is fine. But the answer is both statements I and II. Could someone explain to me how statement II might hold true? I've tried fractions, whole numbers...can't figure it out, and it's driving me nuts
and second:
For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100) + 1, then p is:
A – between 2 and 10
B – between 10 and 20
C – between 20 and 30
D – between 30 and 40
E – greater than 40
I have no idea how to approach this second one...
