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

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Manager
Joined: 14 Dec 2004
Posts: 115
If x > 3000, then the value of (x)/(2x+1) is closest to? [#permalink]

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10 Apr 2005, 17:44
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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
[Reveal] Spoiler: OA
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10 Apr 2005, 17:56
Within few seconds, I think it is D because you have 3000/6001 --> a bit less but almost equal to 1/2. C was tricky but I think it is too much below the average of 10.5
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10 Apr 2005, 18:36
"D".....10 secs

x/2x+1 ----> 1/(2+1/x) ----> 1/x being quite small....it is closest to 1/2
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Joined: 25 Nov 2004
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Re: how fast can you solve.? [#permalink]

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10 Apr 2005, 23:05
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Yes, it is little tricky. it doesnot take more than 15 seconds.

if x>3000, we can assume that x as not equal or less than 3000. lets suppose x = 3001. then;
(x)/(2x+1) =3001/6003, which is close to 1/2.
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11 Apr 2005, 00:10
If x is > 3000, then 2x+1 is approximately going to be about 2x
so x/2x = 1/2 (D)

It takes less than 15 seconds ! You just have to understand that as numbers gets bigger, a small increment will not make a big difference
Manager
Joined: 12 Jan 2013
Posts: 212
Re: If x > 3000, then the value of (x)/(2x+1) is closest to? [#permalink]

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27 Dec 2013, 11:20
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

I assumed that we could do this:

3001/(2*3001) +1 = 1/(2*1) + 1 ----> answer B

Why can we not "short" the numerator and the value of x in the denominator? Of course, I understand 3001/6003 is almost 1/2 but IMO my reasoning for B should work.. What am I missing?
Math Expert
Joined: 02 Sep 2009
Posts: 44298
Re: If x > 3000, then the value of (x)/(2x+1) is closest to? [#permalink]

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28 Dec 2013, 03:37
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Expert's post
aeglorre wrote:
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

I assumed that we could do this:

3001/(2*3001) +1 = 1/(2*1) + 1 ----> answer B

Why can we not "short" the numerator and the value of x in the denominator? Of course, I understand 3001/6003 is almost 1/2 but IMO my reasoning for B should work.. What am I missing?

$$\frac{x}{2x+1}$$ does not equal to $$\frac{1}{2+1}$$. You cannot reduce numerator and only one term of the denominator by x.

Does this make sense?

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Location: United States
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Re: If x > 3000, then the value of (x)/(2x+1) is closest to? [#permalink]

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07 Jan 2014, 06:05

why not E , 3/2 if x = 3001

then 3001/2x3001 + 1 = 3001/ 6001 + 1 = 0.5 + 1 = 1/2 + 1 = 3/2

though its simple, why iam wrong ?
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Senior Manager
Joined: 25 Mar 2013
Posts: 271
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5
Re: If x > 3000, then the value of (x)/(2x+1) is closest to? [#permalink]

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07 Jan 2014, 06:10
yes know i got it bunnel
we cannot separate denominator when addition is there

so 3001/ 6002 +1 = 3001/6003 = 0.5 = 1/2 Right
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Re: If x > 3000, then the value of (x)/(2x+1) is closest to? [#permalink]

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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.

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Re: If x > 3000, then the value of (x)/(2x+1) is closest to?   [#permalink] 17 Nov 2017, 14:40
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