2019 · Q40
What is the natural number n for which 3^9 + 3^12 + 3^15 + 3^n is a perfect cube of an integer?
general-mental-abilityquantitative-aptitude
- A10
- B11
- C13
- D14
Explanation
Factor out 3^9: the sum equals 3^9 x (1 + 3^3 + 3^5 + 3^6) = 3^9 x (1 + 27 + 243 + 729) = 3^9 x 1000 = 27^3 x 10^3 = 270^3, a perfect cube. The 3^5 term comes from n = 14. Hence D.