Number Systems
Number Systems is a Aptitude concept from the MPSC syllabus, tested in 4 past MPSC questions across 4 exam years between 2016 and 2021. Below are those real questions with their correct answers and explanations, plus the concepts worth being comfortable with first.
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क्रमाणिकेतील विसंगत संख्या दर्शवणारा पर्याय निवडा 2, 4, 3.5, 6.5, 5.0, 9.0, 6.5, 12.5, 8.0, 14, ... Select the option that indicates the number that is odd in the series 2, 4, 3.5, 6.5, 5.0, 9.0, 6.5, 12.5, 8.0, 14, ...
The series is two series interleaved. Odd places: 2, 3.5, 5.0, 6.5, 8.0 (adding 1.5). Even places: 4, 6.5, 9.0, ?, 14 (adding 2.5), so the fourth even term should be 11.5. The number that breaks the pattern is 12.5.
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.
जर एका संख्येच्या दुपटीपेक्षा 3 ने लहान असलेली संख्या ही त्या संख्येच्या तिपटीपेक्षा 2 ने अधिक असणाऱ्या संख्येइतकी असेल, तर त्या संख्येच्या पाचपटीपेक्षा 5 ने लहान असलेली संख्या निवडा. If 3 less than twice a certain number is equal to 2 more than 3 times the number, then select the option that is 5 less than 5 times the number.
Let the number be x. Equation: 2x - 3 = 3x + 2, solving gives x = -5. Then 5x - 5 = 5(-5) - 5 = -30.