chetan2u wrote:
A teacher writes \(3^4\) on the board and asks a student to come and add one more term of \(3^4\) to existing term, such that it now becomes \(3^4+3^4\). The teacher asks other students to repeat the step one after another till the total on board becomes a cube of a positive integer. How many students added the term to the series?
A) 2
B) 10
C) 8
D) 3
E) 9
OA and OE on Sun, 17th Jan 2016
SOLUTION:-
It has been correctly found by all of you, who have tried....
all methods are correct.
the CONCEPT is:-
since we are talking of sum of 3^4, the first cube too will be of 3 or its power..
whenever we add another 3^4 to itself, it is nothing but a multiplication table of 3^4..
so it goes like 1*3^4, 2*3^4, 3*3^4, 4*3^4... and so on..
as we see the sum is always a multiple of 3^4 and therefore the cube will be something to do with 3..cube of 3 is already smaller to 3^4 , the next would be cube of 3^2...
so what is required is 9*3^4..
thus total 9 are required, out of which ONE is already written by the teacher..
so our answer is 9-1=8..
C
_________________