Latest Elitmus Aptitude Question SOLUTION: a,b,c are in gp. log a + log b + log c / log 6 = 6 b-a is the perfect cube . then what will be a+b+c

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(#M40164388) ELITMUS Numerical Ability question elitmus 16/4/17 Keep an EYE

a,b,c are in gp. log a + log b + log c / log 6 = 6
b-a is the perfect cube . then what will be a+b+c

Asked In Elitmus Deepak Bharty (7 years ago)

Solved nitu kumari Read Solution (2)

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Read Solution (2) :

nitu kumari  (7 years ago) Best Solution

since a,b,c are in geometric sequence so,
if a=m then,
b=mn and
c= mn^2
therefor,
m*mn*mn^2= m^3*n^3 = (mn)^3
now acording to question,
log a+log b+log c/log 6=6
so,
logabc/log6=6
log abc=6 log6
abc = 6^6

now
since, abc=(mn)^3
put the value of abc ,
6^6= (mn)^3
mn= 6*6=36=b
now acccording to question b-a=Perfect cube
so a=9=m, as (b-a) =27 that is perfect cube of 3.
therefor n=4
therefor c=144
so a+b+c=9+36+144=189 ans.

Is this solution Helpfull? Yes (13) | No (3)  

chirag  (5 years ago)

Ans is 189.

Let the three numbers in gp be:
a/r,a,ar
then
3loga/log6=6
loga=2*log6
a=36;

now no b - a is a perfect cube i.e

36-36/r = cube;
nearest perfect cube is 27;
so 36-36/r=27 => r=4,

so no. are 36/4+36+36*4 = 189

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