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tough one!!!!!!!!!

Expert replies
by runzun » Thu Aug 04, 2011 10:22 am
--|--|---|---|--
a b c d

in the figure above points a , b , c, d are evenly distributed. if point a equals to 2^17 and point c equals to 4^9, what is the value of point d?

a. 2^19
b.2^17
c.5(2^16)
d.3(2^16)
e.2^16
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Source: — Problem Solving |

by force5 » Thu Aug 04, 2011 10:41 am
you need to understand that "evenly distributed" here means evenly spaced, which means that a,b,c d are in AP.

b-a = c-b
2b= 2^18+2^17

hence b= 3.2^16

common difference will be 2^18-3.2^16
= 2^16

hence d = 2^18+ 2^16 = 5.2^16
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by runzun » Thu Aug 04, 2011 11:14 am
thanks for the reply but can you please explain in detail..
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by force5 » Thu Aug 04, 2011 11:25 am
No problem runzun here it goes.

b-a= c-b
2b=c+a

putting values (c=4^9 = 2^18)

2b= 2^18+2^17
= 2^17(2+1) [taking 2^17 common]
2b= 3.2^17
b= 3.2^17/2
= 3.2^17.2^-1
= 3.2^16 [powers added]
common diff = c-b

2^18-3.2^16
2^16(2^2-3) [ taking 2^16 common]
2^16 (4-3)
2^16

now d will be c+ common difference
2^18+2^16
2^16(2^2+1)
2^16(4+1)
5.2^16

hope it helps....
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by runzun » Thu Aug 04, 2011 11:30 am
thanks ...
it was great help
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