Q54. 32^5 + 2^27 is divisible by
Detailed Solution
The given expression is 32^5 + 2^27. First, rewrite 32 as a power of 2: 32 = 2^5. So, 32^5 = (2^5)^5 = 2^(5*5) = 2^25. Now, the expression becomes 2^25 + 2^27. Factor out the common term, which is 2^25: 2^25 + 2^27 = 2^25 + (2^25 * 2^2) = 2^25 (1 + 2^2) = 2^25 (1 + 4) = 2^25 * 5.
To check for divisibility by 10, we need a factor of 10 (which is 2 * 5). We can rewrite 2^25 as 2^24 * 2: = (2^24 * 2) * 5 = 2^24 * (2 * 5) = 2^24 * 10. Since the expression can be written as 2^24 * 10, it is clearly divisible by 10. This question tests basic exponent rules and divisibility properties.
More Number System - Divisibility Questions
More Basic Numeracy Questions
Q5. What is the maximum value of n such that 7 × 343 × 385 × 1000 × 2401 × 77777 is divisible by 35^n ?...
BQ7. P and Q walk along a circular track. They start at 5:00 am. from the same point in opposite directio...
BQ9. A tram overtakes 2 persons X and Y walking at an average speed of 3 km/hr and 4 km/hr in the same di...
CQ10. If N^2 = 12345678987654321, then how many digits does the number N have?...
BQ15. Consider the first 100 natural numbers. How many of them are not divisible by any one of 2, 3, 5, 7 ...
CMore from UPSC 2024 CSAT
Q1. 1. Which of the following statements best reflect the most logical and rational inferences that can ...
BQ2. 2. Based on the above passage, the following assumptions have been made : 1. The food distribution m...
AQ3. 3. Which of the following statements best reflects/reflect the most logical and rational inference/i...
CQ4. 4. Based on the above passage, the following assumptions have been made : 1. Fiscal policies of gove...
DQ5. 5. What is the least possible number of cuts required to cut a cube into 64 identical pieces?...
BAce UPSC with AI-powered Practice
LearnPro's test series adapts to your weak topics and shows real analytics.
Explore Courses →