Problem Solving

42. 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


My thinking was that the number 3000 didn't matter. So I made the 3000=3, and x=4.

4 4
___ _____
=
2(4) +1 9


4/9 is slightly less than half. I looked over the answer choices and thought that 10/21 (also slightly less than half) would be the closest. However, the correct answer is 1/2.

Where did I go wrong on this one?

Please advise.

Thank,

When you use a small value for X the +1 makes a huge difference. If x = 1, the value would be 1/3. However, when x is very large, the +1 has very little effect. 3000/6001 is very close to 1/2. 3,000,000/6,000,001 is even closer to 1/2.

the notation should be precise x/(2x+1)
We take notice of two things that x is huge, x>3000 and our nominator and denominator values are different by rate of 2x plus 1, where 1 is not significant number. So if we cancel 1 in denominator we get x/2x OR 1/2

answer D

quaktar0004 wrote:42. 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


My thinking was that the number 3000 didn't matter. So I made the 3000=3, and x=4.

4 4
___ _____
=
2(4) +1 9


4/9 is slightly less than half. I looked over the answer choices and thought that 10/21 (also slightly less than half) would be the closest. However, the correct answer is 1/2.

Where did I go wrong on this one?

Please advise.

Thank,