2022 CSAT, all questions
UPSC Prelims 2022 · CSAT
Question 9: Basic Numeracy
Which number amongst 2^40, 3^21, 4^18 and 8^12 is the smallest?
a2^40
b3^21
c4^18
d8^12
AnswerUPSC’s answer is (b).
Bring the numbers to a common base or compare directly. 4^18 = 2^36 and 8^12 = 2^36, so these two are equal, and 2^40 is larger than both. For 3^21, write it as (3^7)^3 = 2187^3 and 2^36 as (2^12)^3 = 4096^3. Since 2187 is below 4096, 3^21 is smaller than 2^36. So 3^21 is the smallest. Rewriting exponents with a common power is the quickest route.
Why each option is right or wrong
- (a) 2^40 is the largest of the four.
- (b) Correct: 3^21 = 2187^3, below 4096^3 = 2^36.
- (c) 4^18 = 2^36, which is larger than 3^21.
- (d) 8^12 = 2^36, equal to 4^18 and larger than 3^21.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2022, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.