Practice Number Theory MCQs for KPPSC Assistant (BS-16) Mathematics — topic-wise sets with solved answers.
Q1. There are four prime numbers written in ascending order of magnitude. The product of the first three is 7429 and of the last three is 12673. Find the fourth number?
Answer: 29
Explanation: 7429 = 17×19×23 and 12673 = 19×23×29; the fourth (largest) number is 29.
Q2. Find the greatest number of four digits which when divided by 10, 15, 21 and 28 leaves 4, 9, 15 and 22 as remainders respectively?
Answer: 9654
Explanation: Each divisor exceeds its remainder by 6; LCM(10,15,21,28) = 420; largest 4-digit multiple = 9660; answer = 9660 − 6 = 9654.
Q3. What is the least number which when divided by 8, 12, 18 and 24 leaves the remainders 4, 8, 14 and 20 respectively?
Answer: 68
Explanation: Each remainder is 4 less than its divisor, so the answer = LCM(8,12,18,24)−4 = 72−4 = 68.
Q4. LCM of 87 and 145 is_______?
Answer: 435
Explanation: 87 = 3×29, 145 = 5×29; LCM = 3×5×29 = 435. Show the calculation clearly when solving similar quantitative items.
Q5. Find the greatest number which will divide 25, 73 and 97 as so to leave the same remainder in each case?
Answer: 24
Explanation: The required number is the GCD of the differences: GCD(73−25, 97−73) = GCD(48,24) = 24.
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