algebra

sud21 wrote:If X =1/30+1/31+1/32. Which of the following three statements are true?
I. X> 3/32
II. X=1
III. x =2/31

This is a nice question, since it allows us to answer it without performing the lengthy calculation of adding 1/30+1/31+1/32

I. X > 3/32
Notice that 1/32 is less than 1/30, and 1/32 is less than 1/31
So, 1/32 + 1/32 + 1/32 must be less than 1/30 + 1/31 + 1/32
When we simplify the left-hand-side, we see that 3/32 must be less than 1/30 + 1/31 + 1/32
In other words, 3/32 must be less than X
So, statement I is true

II. X = 1
This one we can estimate quickly.
Since 1/30, 1/31 and 1/31 each equal approximately 0.03, the sum of all three cannot possible equal 1
So, statement II is not true

III. X = 2/31
Notice that, since 1/30 and 1/32 are both close in value to 1/31, we can say that:
1/30 + 1/31 + 1/32 is approximately equal to 1/31 + 1/31 + 1/31
In other words, 1/30 + 1/31 + 1/32 is approximately equal to 3/31
Since 3/31 is 50% greater than 2/31, we cannot say that 1/30 + 1/31 + 1/32 equals 2/32
So, statement III is not true

Cheers,
Brent