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IPMAT Indore 2025 · Question 26 of 90 · Quantitative Ability (MCQ)

IPMAT Indore 2025 — Question 26

Which of the following numbers is divisible by $3^{10} + 2$ ?

A $3^{20} + 4$
B $3^{20} + 8$
C $3^{30} + 2$
D $3^{30} + 8$

Reveal answer

Correct answer

D.

3^{30} + 8

Reveal solution

Let $A = 3^{10}$ , $B = 2$ . Then $A^{3} + B^{3} = 3^{30} + 8$ factors as $(A + B) (A^{2} - A B + B^{2})$ . So $(3^{10} + 2)$ divides $3^{30} + 8$ .

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