1/x, 2x, x^2,

Number plugging, and since x is positive, test with x = 1/2 and x = 3

With
x = 1/2, can find that I is correct.

With
x = 3, I find that x^2 > 2x > 1/x.

Therefore for me, I only found I to be correct.

How is that II is also correct ?

jymloke wrote:1/x, 2x, x^2,

Number plugging, and since x is positive, test with x = 1/2 and x = 3

With
x = 1/2, can find that I is correct.

With
x = 3, I find that x^2 > 2x > 1/x.

Therefore for me, I only found I to be correct.

How is that II is also correct ?

II is correct for large fractions.

For example, if x = 9/10, then we get:

81/100 < 10/9 < 18/10

which is true.

Stuart Kovinsky wrote:
II is correct for large fractions.

For example, if x = 9/10, then we get:

81/100 < 10/9 < 18/10

which is true.

Stuart,

How did you know that ? I just tried

three values:

0, 1/2 and 2

What is the algebra behind number 2 ?

Hi Stuart,

I like to understand your thought process when answering this sort of questions.

My initial thought process went like this,
try with x > 1 (integer) , x > 1 (fractions), x < 1(fractions)

I never thought of trying it with bigger fractions. The fractions I tested were

1/2 and 10/9 , integer that I tried was 3, since trying 2 would give 2x == x^2

1/x < 2x

2x - 1/x > 0

2x^2-1 > 0

2x^2 > 1

x^2 > 1/2

x > 1/1.4

x > 10/14

x > 5/7




NICE!!!

lets say x=6/7

X^2 = 36/49

1/X = 7/6

2X = 12/7

and this satisfies the evil statement II :twisted:

jymloke wrote:Hi Stuart,

I like to understand your thought process when answering this sort of questions.

My initial thought process went like this,
try with x > 1 (integer) , x > 1 (fractions), x < 1(fractions)

I never thought of trying it with bigger fractions. The fractions I tested were

1/2 and 10/9 , integer that I tried was 3, since trying 2 would give 2x == x^2

Hi!

We know when comparing 1/x and x^2 that we don't need to try different fractions, since all fractions follow the same rule in this regard. However, when comparing 1/x and 2x, we can't be sure that different fractions will all give the same result.

A good general rule for picking numbers is to think about what types of numbers could give different answers. Going to extremes is often a good way to test things out. So, since I wasn't sure if all fractions would work out the same, I tried both a small one and a big one.

A good general rule for picking numbers is to think about what types of numbers could give different answers. Going to extremes is often a good way to test things out. So, since I wasn't sure if all fractions would work out the same, I tried both a small one and a big one.

Stuart,
I am sure that's why u r a 800 scorer on GMAT

Thanks again for your valuable inputs!

Regards,
Cramya

cramya wrote:
Stuart,
I am sure that's why u r a 800 scorer on GMAT

Thanks again for your valuable inputs!

Cramya, I guess you have a value for Stuart's inputs, but I do not..they are really INVALUABLE!

Got ya!

I used another approach:
in my mind, plot the three functions on a plane and see where they intersect by solving for x:
1/x = 2x
1/x = x^2
2x = x^2

1st: ~ 1/1.4 = 0.7
2nd: 1
3rd: 2

so if 0<x<1, then x^2 is smallest and 1/x intersects 2x at approximately 0.7
and if x > 1, then 1/x is smallest and 2x intersects x^2 at 2