Divisibility Rules
Divisibility Rules is a Aptitude concept from the MPSC syllabus, tested in 4 past MPSC questions across 4 exam years between 2018 and 2025. Below are those real questions with their correct answers and explanations, plus the concepts worth being comfortable with first.
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P या नैसर्गिक संख्येल्या 11 ने गुणून त्यात 33 ही संख्या मिळवली. या बेरजेला 9 ने भागले आणि बाकी शून्य मिळाली. दिलेल्या अटींचे समाधान करणारी P ची सर्वात लहान किंमत निवडा.
11P + 33 must be divisible by 9 with zero remainder. Testing natural numbers in order: P=1 gives 44 (not divisible), P=3 gives 66 (not divisible), P=6 gives 11(6)+33 = 99, and 99 / 9 = 11 exactly. So P=6 is the smallest value that satisfies the condition.
खालील संख्येपैकी किती संख्यांना 273 ने भाग जात नाही ? 546, 1156, 3003, 3564, 5733, 3822, 9605, 8736 How many of the following numbers are not divisible by 273 ? 546, 1156, 3003, 3564, 5733, 3822, 9605, 8736
To check divisibility by 273, we can check divisibility by its coprime factors 3 and 91 (or 3, 7, and 13). Testing each number helps identify how many are not divisible, resulting in the correct count of 2 numbers.
2, 3, 5, 6, 7 आणि 9 या अंकांपासून 5 ने भाग जाणारी आणि कोणतीही अंक पुन्हा न येता, अशा तीन अंकी किती संख्या तयार होऊ शकतील ? How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9 which are divisible by 5 and none of the digits is repeated ?
A 3-digit number is divisible by 5 if its unit's digit is 5. Given digits: 2, 3, 5, 6, 7, 9. Unit place can only be filled by '5' (1 way). The remaining 2 places can be filled from the remaining 5 digits (2, 3, 6, 7, 9) in 5P2 = 5 * 4 = 20 ways. Total numbers = 1 * 20 = 20.
दोन संख्यांचा लसावि हा त्यांच्या मसाविच्या 45 पट आहे. जर एक संख्या 125 असून त्यांच्या मसावि आणि लसाविची बेरीज 1150 आहे, तर दुसरी संख्या _______ . The LCM of two numbers is 45 times their HCF. If one of the number is 125 and sum of their HCF and LCM is 1150, then the other number is _______ .
Given LCM = 45 * HCF and LCM + HCF = 1150, we get 46 * HCF = 1150, so HCF = 25 and LCM = 1125. Using Product = LCM * HCF, second number = (25 * 1125) / 125 = 225.