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C
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Difficulty:
75%
(hard)
Question Stats:
50% (01:45) correct
50%
(01:49)
wrong
based on 286
sessions
History
Date
Time
Result
Not Attempted Yet
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) 3
C) 8
D) 9
E) 10
A) 2
B) 3
C) 8
D) 9
E) 10
14 Jan 2016, 02:00
Kudos
Bookmarks
Answer is C.
3^4 + 3^4 + 3^4 .............. so on till we get a number that is a perfect cube. To get a perfect cube, the final number should have a total number of prime factors that are in sets of 3. To get this, we have to add 3^4 - 9 times and then factorize.
3^4(1+1+1+1+1+1+1+1+1)
3^4 (9)
3^4 * 3^2
3^6
2 groups of 3^3 each.
Please note that out of 9 terms of 3^4, the first one was added by the teacher. The question is asking us the number of terms that students added, hence the answer is 8.
This is my understanding of the problem. Please correct me if i'm wrong.
3^4 + 3^4 + 3^4 .............. so on till we get a number that is a perfect cube. To get a perfect cube, the final number should have a total number of prime factors that are in sets of 3. To get this, we have to add 3^4 - 9 times and then factorize.
3^4(1+1+1+1+1+1+1+1+1)
3^4 (9)
3^4 * 3^2
3^6
2 groups of 3^3 each.
Please note that out of 9 terms of 3^4, the first one was added by the teacher. The question is asking us the number of terms that students added, hence the answer is 8.
This is my understanding of the problem. Please correct me if i'm wrong.
14 Jan 2016, 04:01
Kudos
Bookmarks
3^4 = 81
81*X= perfect cube (so rephrasing the question: How many times 81 has to be written for a perfect cube )
or, 3*3*3*3*X= perfect cube
X=9
But teacher has already used up 1 ; remaining 8
Thus C
81*X= perfect cube (so rephrasing the question: How many times 81 has to be written for a perfect cube )
or, 3*3*3*3*X= perfect cube
X=9
But teacher has already used up 1 ; remaining 8
Thus C
