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OG PS Supplement Q# 42

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by GMATMadeEasy » Mon May 30, 2011 1:32 pm
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

Could someone explain how to choose between C and D ? The best way to handle such questions please.

OA is D
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by SoCan » Mon May 30, 2011 1:51 pm
As x becomes larger, the +1 in the denominator becomes less and less significant, and the limit of the expression is 1/2.

x/(2x+1) = 10/21 when x=10. Since x>3000, we know the expression is much closing to 1/2.
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by smackmartine » Mon May 30, 2011 2:55 pm
IMO D

x/(2x + 1) can be rewritten as 1/ (2+1/x)

as value of x > 3000, x can be very large value.

As we increase the value of "x" the the value of "1/x" comes closer to zero and at a very large value , "1/x" tends to zero.

So, 1/ (2+1/x) at "x" tends to a very large value is equal to 1/(2+0) , i.e 1/2
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by deep.amangmat » Mon May 30, 2011 8:39 pm
@smackmartine: This explanation seems like how one would explain the concepts of "limits" .. are you from India.[/quote]
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by sivaelectric » Mon May 30, 2011 8:58 pm
I also suppose that D is the closest answer :). I calculated with the value of 3001. Is my approach ok.
If I am wrong correct me :), If my post helped let me know by clicking the Thanks button ;).

Chitra Sivasankar Arunagiri
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by hrushi_gmat » Tue May 31, 2011 1:26 am
x/2x+1 when x = 3000 is 3000/6001


1/2 = 1000/2000 = 3000/6000
10/21 = 1000/2100 = 3000/6300

Therefore 1/2 is more close to x/2x+1 when x is > 3000
As x will increase beyond 3000 x/2x+1 will be approx. = x/2x = 1/2
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by manpsingh87 » Tue May 31, 2011 1:43 am
GMATMadeEasy 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

Could someone explain how to choose between C and D ? The best way to handle such questions please.
OA is D
x/(2x + 1); can be re written as;
1/2(2x/2x+1);
1/2{2x+(1-1)/2x+1};
1/2{2x+1/2x+1-1/2x+1);
1/2(1-1/2x+1);
now as x>3000;
therefore 1/2x+1; will assume very small value and 1-1/2x+1 will approximate be equal to 1;
hence answer will be 1/2(1)=1/2 hence D
O Excellence... my search for you is on... you can be far.. but not beyond my reach!
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