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closest value of X

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by pemdas » Thu Dec 29, 2011 1:44 pm
x is +ve real number
1/2 +1=3/2 which is closest to e
kishokbabu wrote: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
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by neelgandham » Thu Dec 29, 2011 1:49 pm
X > 3000, then the value of X / 2X +1 is closest to
Assumption: X / 2X +1 = X /(2X +1)
The value of X / (2X +1) is less than 1 and close to 1/2. So, we can eliminate Option A, B, and E. 10/21 is close to 1/2. So we got to choose between 10/21 and 1/2.
a)1/6 - Eliminated
b)1/3 - Eliminated
c)10/21
d)1/2
e)3/2 - Eliminated.

Let Answer = 10/21. Multiply numerator and denominator with 400, Answer = 4000/8400
Let Answer = 1/2. Multiply numerator and denominator with 4000, Answer = 4000/8000
If x = 4000, X / (2X +1) = 4000/8001, which is closer to 4000/8000 than it is to 4000/8400.
So, D is the answer.
Last edited by neelgandham on Thu Dec 29, 2011 2:05 pm, edited 1 time in total.
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by pemdas » Thu Dec 29, 2011 1:58 pm
Nil, it's not clear in the (2x+1) denom

also considering x>3000, if (2x+1) is denom, we use big number theorem and ballpark to 1/2 right away
Last edited by pemdas on Thu Dec 29, 2011 2:04 pm, edited 1 time in total.
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by neelgandham » Thu Dec 29, 2011 2:04 pm
pemdas wrote:Nil, it's not clear in the (2x+1) denom
But a question If X > 3000, then the value of (X/2X) +1 is closest to doesn't make sense because it literally says if X > 3000, then the value of 3/2 is closest to ?. I do apologize for not putting up the assumption note. I edited the post now
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by pemdas » Thu Dec 29, 2011 2:06 pm
yea, i know
other posts are easy too
did you read my last sec edit about ballpark
see MasterGMAT course CAT is impossible to finish in time at all if not for ballparking used with some good 5-6 questions
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by neelgandham » Thu Dec 29, 2011 2:10 pm
Agreed on the difficulty level and the ballparking too. It was just an assumption and I have edited the post accordingly.
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by LalaB » Fri Dec 30, 2011 12:56 am
my approach-

x=3001

then X / (2X +1)=3001/(2*3001+1)=3001/6003 (6003 is close to 6002) so we have 3001/6002 =1/2 :)
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by kishokbabu » Fri Dec 30, 2011 2:42 am
This approach is good and easy.

Thanks lalaB.
LalaB wrote:my approach-

x=3001

then X / (2X +1)=3001/(2*3001+1)=3001/6003 (6003 is close to 6002) so we have 3001/6002 =1/2 :)
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by Abhishek009 » Fri Dec 30, 2011 6:34 am
kishokbabu wrote: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
X > 3000 , take any value of X > 3000 , say X = 4000

Now check -

X / 2X +1 => 4000 / 8001

So the value is close to half ...
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by pemdas » Fri Dec 30, 2011 8:09 am
x/(2x+1), compare 10/21 and 17/35

17/35 : 10/21= 51/50

1/50 accrual with 7 numbers and for 3000/6001 this will be much greater and continue close to 1/2 as x>3000 and not x<3000
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