Subject: General Aptitude · Chapter: Number System · Exam: · Marks: · Difficulty:
Match List I with List II and select the correct answer: List I List II (Product) (Digit in the unit's place) A. (1827) ${ }^{16}$ (1) 1 B. $(2153)^{19}$ (2) 3 C. $(5129)^{21}$ (3) 5 (4) 7 (5) 9 A B C A B C
(a)143
(b)423
(c)145
(d)425
Answer
Answer (as printed): C
Explanation
(A) $7^{4}$ gives unit digit 1. So, $7^{16}=\left(7^{4}\right)^{4}$ gives unit digit 1. $\therefore \quad(1827)^{16}$ gives unit digit 1. So, $A \rightarrow(1)$. (B) $3^{4}$ gives unit digit 1. So, $\left(3^{4}\right)^{4}$ gives unit digit 1. $\therefore \quad 3^{19}=3^{16} \times 3^{3}$ gives unit digit $=(1 \times 7)=7$. ∴ (2153) ${ }^{19}$ gives unit digit 7. So, $B \rightarrow(4)$. (C) $9^{2}$ gives unit digit 1. So, $\left(9^{2}\right)^{10}$ gives unit digit 1. $\therefore 9^{21}=\left(9^{20} \times 9\right)$ gives unit digit $=(1 \times 9)=9$. $\therefore(5129)^{21}$ gives unit digit $=9$. So, $C \rightarrow(5)$. Hence, $A B C$ is the correct result. 145
Explanation as extracted from the printed page; notation may be imperfect.