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

Question

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

Bunuel · Accepted Answer

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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christianbze · Answer

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

PerfectScores · Answer

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

beatthegmat05 · Answer

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.

DoItRight · Answer

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.

TroyfontaineMacon · Answer

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

ALL LOGIC

ScottTargetTestPrep · Answer

Let’s say x = 3001; we have:

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

Answer: D

akshay98 · Answer

Since 1 is negligible in compare to 3000 then we get 3000/6000 = 1/2
{D}

Abhishek009 · Answer

Let  x = 301

So,  \frac{x}{(2x + 1)} = \frac{301}{(2*301 + 1)} = \frac{301}{603}  ~  \frac{301}{602} = \frac{1}{2} , Answer must be (D)

totaltestprepNick · Answer

D https://www.youtube.com/watch?v=93qdMboNxMI Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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My Rewards