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Two fractions are inserted between 1/4 and 1/2 so that the [#permalink]
23 Aug 2010, 14:03

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Two fractions are inserted between 1/4 and 1/2 so that the difference between any two successive fractions is the same. Find the sum of the four fractions.

Two fractions are inserted between 1/4 and 1/2 so that the diffrence between any two successive fractions is the same. Find the sum of the four fractions. A.18/12 B.16/12 C.5/2 D.9/19 E.24/32

My ans is 16/12 but OA is 18/12... Can someone please explain the OA.....

As the difference of any two successive fractions is the same then we have evenly spaced set (arithmetic progression). Sum of the terms of AP is \frac{first \ term + last \ term}{2}*(# \ of \ terms) --> sum=\frac{\frac{1}{4}+\frac{1}{2}}{2}*4=(\frac{1}{4}+\frac{1}{2})*2=\frac{3}{2}.

Let the fractions inserted b/w \frac{1}{4} & \frac{1}{2} be \frac{1}{x} and \frac{1}{y}We can easily calculate the value of \frac{1}{x} by:- 2(\frac{1}{x}-\frac{1}{4})=\frac{1}{2}-\frac{1}{x}Solving we get, \frac{1}{x}=\frac{1}{3}Also, \frac{2}{y}=\frac{1}{3}+\frac{1}{2} Solving we get \frac{1}{y}=\frac{5}{12}Hence, the 4 fractions are \frac{1}{4}, \frac{1}{3}, \frac{5}{12} and \frac{1}{2} The required sum is thus:- sum=\frac{1}{4}+ \frac{1}{3}+ \frac{5}{12}+ \frac{1}{2}=\frac{18}{12} _________________

If you shut your door to all errors, truth will be shut out.

Re: Two fractions are inserted between 1/4 and 1/2 so that the [#permalink]
22 Jun 2014, 23:02

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