If x>3,000, then x/(2x+1) is closest to...

[GMATCHPOINT]

I know it supposed to be an easy one, but i dont understand how OG11 explains it.

from pg 97 ex. 39
answer: For all large values of x, the value of x/(2x+1) is going to be very close to the value of x/2x, which is equal to 1/2.

could you help?

[shamz]

x is greater than 3000...assume its 3001
therefore 2x= 6002
1 is negilible compared to 6002
or anything greater than 6000
hence they they have assumed x/2x i.e 1/2

[GMATCHPOINT]

thanks a lot shamz!

[Scott@TargetTestPrep]

If x > 3000, then the value of (x)/(2x+1) is closest to?

A. 1/6
B. 1/3
C. 10/21
D. 1/2
E. 3/2

Let's say x = 3001; we have:

3001/(6002 + 1), which is about 3,000/6,000 = 1/2.

Answer: D

[Matt@VeritasPrep]

It is the night of the zombie threads tonight!

Just pick a number. Say x = 5000. Then x/(2x + 1) = 5000/10001, which is really close to 5000/10000, or 1/2.

[thucanh711]

Hi there, I think it is a little bit too late to answer your post, but just do it anyway, shall we?

The problem is related to the limit of a function, just in case you want to have a deeper understand.

When the variable x is as great as 3000, adding 1 or not to 2x does not affect its value. In another word, plus one is a subtle change to the variable 2x. Therefore, you can treat 2x + 1 as 2x alone.

As a result: x/2x is merely the same as x/2x+1

This is true only if variable x has a great value, or has an infinite limit.

If x is just about 5, for example, adding 1 to 2x might cause a proper change.

x/2x = 0.5
x/2x+1 = 0.45

Hope that was helpful for you.