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the median of set R

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the median of set R

by sanju09 » Fri May 07, 2010 3:05 am
a, b, and c are integers and a < b < c. S is the set of all integers from a to b, inclusive. Q is the set of all integers from b to c, inclusive. The median of set S is (3/4) b. The median of set Q is (7/8) c. If R is the set of all integers from a to c, inclusive, what fraction of c is the median of set R?
(A) 3/8
(B) 11/16
(C) 5/7
(D) 3/4
(E) 4/5
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by liferocks » Fri May 07, 2010 4:13 am
median of Q
a+(b-a)/2=3/4b
or a/2=b/4
or a=b/2

median of S
b+(c-b)/2=7/8c
or b/2=3/8c
or b=3/4c
so a=3/8c

median of set R is a+(c-a)/2=3/8c+c/2-3/16c=(6+8-3)c/16=11/16C

Ans option B
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by sanju09 » Fri May 07, 2010 4:32 am
liferocks wrote:median of Q
a+(b-a)/2=3/4b
or a/2=b/4
or a=b/2

median of S
b+(c-b)/2=7/8c
or b/2=3/8c
or b=3/4c
so a=3/8c

median of set R is a+(c-a)/2=3/8c+c/2-3/16c=(6+8-3)c/16=11/16C

Ans option B
you seem to be killing everything, becoming the top first responder very soon. B is right, a detailed explanation is still missing.
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
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The Princeton Review - Manya Abroad
Lucknow-226001

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