2021 CSAT, all questions
UPSC Prelims 2021 · CSAT
Question 5: Basic Numeracy
If 3^2019 is divided by 10, then what is the remainder ?
a1
b3
c7
d9
AnswerUPSC’s answer is (c).
The remainder on dividing by 10 is just the units digit. Powers of 3 end in 3, 9, 7, 1 and then repeat every four powers. Divide the exponent by 4: 2019 = 4 × 504 + 3, so 3^2019 ends in the same digit as 3^3 = 27, which is 7. The remainder is 7. Remember: for units-digit or remainder-by-10 questions, find the cycle length first, then reduce the exponent modulo that length.
Why each option is right or wrong
- (a) 1 is the units digit when the exponent is a multiple of 4, such as 3^2020, not 2019.
- (b) 3 is the units digit when the exponent leaves remainder 1 on division by 4; 2019 leaves 3.
- (c) Right: remainder 3 on division by 4 gives the third digit of the cycle, 7.
- (d) 9 is the units digit when the exponent leaves remainder 2 on division by 4.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2021, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.