ABC26GN0365 · Number System

Subject: General Aptitude · Chapter: Number System · Exam: · Marks: · Difficulty:

$\left(3^{25}+3^{26}+3^{27}+3^{28}\right)$ is divisible by
(a)11
(b)16
(c)25
(d)30
Answer
Answer (as printed): D
Explanation
$$\begin{aligned} & \left(3^{25}+3^{26}+3^{27}+3^{28}\right)=3^{25}\left(1+3+3^{2}+3^{3}\right) \\ & =3^{25}(1+3+9+27)=3^{25} \times 40 \\ & =(3 \times 10) \times\left(3^{24} \times 4\right)=30 \times\left(3^{24} \times 4\right), \end{aligned}$$ which is divisible by 30 .

Explanation as extracted from the printed page; notation may be imperfect.

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