Q37. What is the remainder when 85 × 87 × 89 × 91 × 95 × 96 is divided by 100?
Detailed Solution
To find the remainder when a product is divided by 100, we need to check for factors of 100 (which are 25 and 4). The given product is 85 × 87 × 89 × 91 × 95 × 96. Let's identify factors of 5 and 2 within these numbers: - 85 contains a factor of 5 (85 = 5 × 17).
- 95 contains a factor of 5 (95 = 5 × 19). So, we have two factors of 5, which multiply to 25. - 96 contains a factor of 4 (96 = 4 × 24). Since the product contains factors of both 25 and 4, it means the entire product is divisible by 25 × 4 = 100.
When a number is completely divisible by another number, the remainder is 0. This question tests basic number theory concepts related to divisibility and remainders, a fundamental part of CSAT quantitative aptitude.
More Number System (Remainders) Questions
More Quantitative Aptitude Questions
Q78. What is the 489th digit in the number 123456789101112...?...
DQ75. A set (X) of 20 pipes can fill 70% of a tank in 14 minutes. Another set (Y) of 10 pipes fills 3/8th ...
DQ76. If n is a natural number, then what is the number of distinct remainders of (1ⁿ + 2ⁿ) when divided b...
CQ77. Let P = QQQ be a 3-digit number. What is the HCF of P and 481?...
CQ5. 5. What is the least possible number of cuts required to cut a cube into 64 identical pieces?...
BMore from UPSC 2023 CSAT
Q1. Based on the above passage, the following assumptions have been made: 1. Collection, processing and ...
DQ2. Which one of the following statements best reflects the crux of the passage?...
CQ3. Based on the above passage, the following assumptions have been made: 1. Organic farming is inherent...
BQ4. Which one of the following statements best reflects the most logical, rational and practical message...
CQ5. Based on the above passage, the following assumptions have been made: 1. To implement the Sustainabl...
BAce UPSC with AI-powered Practice
LearnPro's test series adapts to your weak topics and shows real analytics.
Explore Courses →