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

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If x > 3,000, then the value of x/(2x + 1) is closest to  [#permalink]

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New post 16 Jan 2014, 04:48
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If x > 3,000, 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

Problem Solving
Question: 42
Category: Algebra Simplifying algebraic expressions
Page: 67
Difficulty: 600


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Re: If x > 3,000, then the value of x/(2x + 1) is closest to  [#permalink]

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New post 16 Jan 2014, 04:48
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SOLUTION

If x > 3,000, 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

For large enough values of x the value of x/(2x+ 1) will be very close to x/(2x)=1/2 (+1 in the denominator is negligible in this cases).

Answer: D.

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Re: If x > 3,000, then the value of x/(2x + 1) is closest to  [#permalink]

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New post 16 Jan 2014, 06:16
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If x > 3,000, 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 us say x = 3999.5 then 3999.5/(8000)

Now we approximate = 4000/8000 = 1/2
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Re: If x > 3,000, then the value of x/(2x + 1) is closest to  [#permalink]

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New post 16 Jan 2014, 08:39
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1 is very less as compared to 3000 so the effect of adding 1 to denominator is negligible . By approximation we can say that it will be always closest to 1/2. Another way can be differential calculus.
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Re: If x > 3,000, then the value of x/(2x + 1) is closest to  [#permalink]

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New post 16 Jan 2014, 11:24
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You can solve this question within let's say 15seconds.

as \(x > 3000\) you can think of \(x -> infinity\)
and then a little trick will do the magic

\(\frac{x}{2x+1} = \frac{1}{2+1/x}\) by dividing the whole fraction (numerator and denominator on their own) through 'x'.

\(1/x -> 0\) because \(x -> infinity\) you have a solution of \(1/2\)

Thank you GMAT for showing me why 'limit of a function' problems in high-school were important
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Re: If x > 3,000, then the value of x/(2x + 1) is closest to  [#permalink]

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New post 16 Jan 2014, 17:33
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Question ask to approximate x/(2x+1) when x>3000
x/(2x+1), you can ignore the 1 because the value is too small when x>3000.
x/2x. x cancels out
1/2. Answer choice D.
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Re: If x > 3,000, then the value of x/(2x + 1) is closest to  [#permalink]

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New post 22 Jan 2014, 19:15
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This is another logic problem...because \(x>3000\) its clear that adding \(1\) to \(6000\) creating a number like \(\frac{3001}{6002+1}\) is close to \(\frac{3001}{6002}\) or \(\frac{1}{2}\)

Little to no math involved

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Re: If x > 3,000, then the value of x/(2x + 1) is closest to  [#permalink]

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New post 17 Nov 2017, 14:40
cloaked_vessel wrote:
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
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Re: If x > 3,000, then the value of x/(2x + 1) is closest to  [#permalink]

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