Which power is the largest — Number System Aptitude Question
Which power is the largest: Which of the following is the largest? 2⁶⁰, 3⁴⁰, 4³⁰, 5²⁰ Answer and worked solution on CodeKairo.
- Topic: Number System
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 90 seconds
Question
Which of the following is the largest?
2⁶⁰, 3⁴⁰, 4³⁰, 5²⁰
Options
- 2⁶⁰
- 3⁴⁰
- 4³⁰
- 5²⁰
Show the answer and the worked solution
Correct answer: B. 3⁴⁰
Worked solution
- Write each with exponent 20: 2⁶⁰ = (2³)²⁰ = 8²⁰, 3⁴⁰ = (3²)²⁰ = 9²⁰, 4³⁰ = (4³)¹⁰ = 64¹⁰ = 8²⁰, 5²⁰ = 5²⁰.
- Comparing bases 8, 9, 8 and 5 at the same power of 20, the largest is 9²⁰.
- So 3⁴⁰ is the largest.
Answer: 3⁴⁰.
The idea
To compare powers, force a common exponent (usually the HCF of the exponents) and then compare bases. Forcing a common base instead only works when the bases share one.
Shortcut. 4³⁰ is 2⁶⁰ in disguise, so those two tie and neither can be the single answer. Of the rest, 3⁴⁰ = 9²⁰ beats 5²⁰ at the same exponent.
Common trap. 2⁶⁰ — chosen for its large exponent; written with exponent 20 it is 8²⁰, smaller than 3⁴⁰ = 9²⁰.