HCF
HCF is a Aptitude concept from the MPSC syllabus, tested in 4 past MPSC questions (2017, 2018, 2022). Below are those real questions with their correct answers and explanations, plus the concepts worth being comfortable with first.
📅 Today's Daily Challenge
Five fresh MPSC questions, the same for everyone today — free, no signup.
Asked in
What you need to know first
Real questions that test this
102 सेमी, 136 सेमी, 153 सेमी व 289 सेमी लांबी असलेल्या चार कांबी आहेत. सगळ्या कांबीचे समान कमाल लांबीचे तुकडे केले. सर्व कांबीच्या एकूण तुकड्यांची संख्या दर्शवणारा पर्याय निवडा. There are four metal rods of lengths 102 cm, 136 cm, 153 cm and 289 cm each. They are all cut into parts having equal maximum length. Select the option showing the total number of parts of all the rods.
First, find the HCF of the rod lengths (102, 136, 153, 289) to get the maximum length of equal parts, which is 17 cm. Then divide each rod's length by 17 and sum the number of parts to get the total.
3 मी, 5 मी 10 सेमी, 12 मी 90 सेमी अशी लांबी असलेले कापडाचे तीन तुकडे अचूक मोजण्यासाठी जास्तीत जास्त मोठ्या मापाची मोजपट्टी किती लांबीची असायला हवी, हे शोधाइ. Find the greatest possible length of a scale that can be used to measure exactly, three pieces of cloth of the following lengths : 3 m, 5 m 10 cm, 12 m 90 cm
Convert all measurements into the same unit (centimetres): 3 m = 300 cm, 5 m 10 cm = 510 cm, 12 m 90 cm = 1290 cm. The greatest possible length of the scale is the HCF of 300, 510, and 1290, which is 30 cm.
सहा घंटा सुरवातीला एकत्र वाजतात. आणि अनुक्रमे 2, 4, 6, 8, 10 आणि 12 सेकंदांनी वाजतात. 30 मिनिटांमध्ये त्या किती वेळा एकत्र वाजतील ? Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together ?
First find the LCM of intervals: LCM(2, 4, 6, 8, 10, 12) = 120 seconds = 2 minutes. In 30 minutes, the number of times they toll together = (30 / 2) + 1 = 16 times (including the initial simultaneous toll at 0 minutes).
रिना, टिना आणि हिना यांनी एकाच वेळी एकाच दिशेने एकाच बिंदूपासून वर्तुळाकार क्रीडांगणाभोवती धावायला सुरुवात केली. एक फेरीत रिनाने 70 सेकंदात, टिनेने 105 सेकंदात आणि हिनाने 175 सेकंदात पूर्ण केली. त्या तिघी किती वेळेने पुन्हा प्रारंभिक बिंदूजवळ भेटतील ? Rina, Tina and Hina are starting at the same time from the same point in the same direction to run around the circular playground. Rina completes a round in 70 seconds, Tina in 105 seconds and Hina in 175 seconds. After how much time will they meet again at the starting point ?
Find the LCM of the times taken to complete one round: LCM(70, 105, 175). Prime factors: 70 = 2*5*7, 105 = 3*5*7, 175 = 5*5*7. LCM = 2*3*5*5*7 = 1050 seconds. Convert to minutes: 1050 / 60 = 17.5 minutes = 17 minutes 30 seconds.