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

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372

2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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