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# Two fractions are inserted between 1/4 and 1/2 so that the

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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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Difficulty:

25% (low)

Question Stats:

74% (02:41) correct 25% (01:22) wrong based on 55 sessions
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.

A. 18/12
B. 16/12
C. 5/2
D. 9/19
E. 24/32

[Reveal] Spoiler:
My ans is 16/12
but OA is 18/12...
Can someone please explain the OA.....
[Reveal] Spoiler: OA
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Kudos [?]: 15812 [3] , given: 1572

Re: fractions.... [#permalink]  23 Aug 2010, 14:23
3
KUDOS
Expert's post
harithakishore wrote:
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}.

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Kudos [?]: 10 [2] , given: 49

Re: fractions.... [#permalink]  05 May 2013, 19:14
2
KUDOS
Hi Bunuel...

Can we solve it like in following procedure...

Let a/b and c/d two fraction..so the sequence 1/2,a/b,c/d,1/4

As given- 1/2-a/b=c/d-1/4=>a/b+c/d=3/4
Question ask us to find 1/2+a/b+c/d+1/4=>1/2+3/4+1/4=3/2 ans....

Rgds
Prasannajeet
Math Expert
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Posts: 15206
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Kudos [?]: 15812 [0], given: 1572

Re: fractions.... [#permalink]  05 May 2013, 22:02
Expert's post
prasannajeet wrote:
Hi Bunuel...

Can we solve it like in following procedure...

Let a/b and c/d two fraction..so the sequence 1/2,a/b,c/d,1/4

As given- 1/2-a/b=c/d-1/4=>a/b+c/d=3/4
Question ask us to find 1/2+a/b+c/d+1/4=>1/2+3/4+1/4=3/2 ans....

Rgds
Prasannajeet

Yes, that's correct.
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Re: fractions.... [#permalink]  05 May 2013, 22:02
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}
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Re: Two fractions are inserted between 1/4 and 1/2 so that the [#permalink]  25 May 2013, 04:45
Think of this as 4 points on the number line...

(1/4).....(X).....(Y).....(1/2)

OR

(3/12)....(X).....(Y).....(6/12)

You can easily see that X & Y should be 4/12 and 5/12 respectively. Add and you'll get the sum as 3/2.
Re: Two fractions are inserted between 1/4 and 1/2 so that the   [#permalink] 25 May 2013, 04:45
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