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

[angie]

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I narrowed the choices down to c. 10/21 and d. 1/2.

I chose c. because I thought the answer will always be just a little bit smaller than 1/2, and 10/21 is a little bit smaller than 1/2.

The OA is d. 1/2, and the explanation is that 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.

The answer makes sense to me, but I'm not sure that my thought process would change on another similar problem. How do I logically get to conclusion that 10/21 is too far off, and that although x/(2x+1) is always going to be less than 1/2, it's closer to 1/2 than it is to 10/21?

By the way, I am taking Math Foundations I & II, and have found the I workshop very helpful (haven't taken the II yet).

[Sudhan]

This could be solved like this:-
x/2x+1= 1/2+1/x

Sub for x>3000 put x=3001

1/2+1/3001= 1/3001 can be approxed to negligible for larger values of x

Hence 1/2 (Choice D)

When comparing which is one is greater for multiple fractions. use Brute force method

1/2 10/21

Cross multiply 1*21 2*10
Which means 1/2 >10/21

Hence D

Thanks

[StaceyKoprince]

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