chetan2u wrote:
AbdurRakib wrote:
Which of the following fractions is closest to \(\frac{1}{2}\)?
A) \(\frac{4}{7}\)
B) \(\frac{5}{9}\)
C) \(\frac{6}{11}\)
D) \(\frac{7}{13}\)
E) \(\frac{9}{16}\)
OG 2017 New Question
Please Explain
Hi,
Do not waste time in calculating..
look at the similarity in all choices- they all EXCEPT E are of type \(\frac{x}{2x-1}\)...
and \(\frac{x}{2x-1}\) for an integer x is always >1/2 and will become lesser in value , that is will keep getting closer to 1/2 with higher VALUE of x..
you can check in two ways-1) for x as 1 or 2 or 3..x=1, \(\frac{x}{2x-1}\) = 1..
x=2, \(\frac{x}{2x-1}\) = 2/3..
x=3, \(\frac{x}{2x-1}\) = 3/5..
so each successive value is smaller than previous one..
2) simplify the term..-
IMPORTANT \(\frac{x}{2x-1}\)=\(\frac{1}{(2x-1)/x}\) = \(\frac{1}{(2x/x-1/x)}\) = \(\frac{1}{(2-1/x)}\)
so the denominator should be closer to 2 so \(2-\frac{1}{x}\) should be close to 2, and therefore x should be MAX to make \(\frac{1}{x}\) less
Therefore, here 7 is the highest value in the four choices so D is the closest to 1/2.
lets see E... It is the TYPE \(\frac{x}{2(x-1)}\)... clearly since 7 and 9 are close to each other but denominator in E is reduced by a larger number,
Can you help me understand this:
2) simplify the term..- IMPORTANT
x2x−1x2x−1=1(2x−1)/x1(2x−1)/x = 1(2x/x−1/x)1(2x/x−1/x) = 1(2−1/x)1(2−1/x)
so the denominator should be closer to 2 so 2−1x2−1x should be close to 2, and therefore x should be MAX to make 1x1x less