Number System — Set #1 | Practice

{"setId":"b52dce34-f73a-4898-b677-ffab340a2143","setTitle":"UPSC CSAT Practice Questions","topicName":"Number System","topicSlug":"number-system","setNumber":1,"totalQuestions":10,"questions":[{"id":"c609318e-51f8-426c-bc86-c83c8b85764b","order":1,"statement":"In a certain system, some mathematical operations are coded using symbols: P@Q means P+Q, P$Q means P-Q, P#Q means P x Q, P&Q means (P x Q)^2. What is the value of (8&4)@6$17#5 as per this system?","options":{"A":"935","B":"985","C":"945","D":"925"},"correctOption":"C","solution":"Replacing symbols with operations: (8&4)@6$17#5 = (8x4)^2 + 6 - 17x5 = (32)^2 + 6 - 85 = 1024 + 6 - 85 = 945."},{"id":"ae103360-d00d-45c5-9982-cd6112fd6c10","order":2,"statement":"If 'A' stands for '-', 'B' stands for '+', 'C' stands for 'x', 'D' stands for '/division', find the value of: (525 A 25 B 50 C 100 D 5 A 60) / (125 B 25 D 5 A 50)","options":{"A":"16","B":"18","C":"28","D":"20"},"correctOption":"B","solution":"Substituting the symbols: (525-25+50x100/5-60) / (125+25/5-50) = (525-25+1000-60) / (125+5-50) = 1440/80 = 18."},{"id":"a9d5d0c9-b9cc-436a-a75a-0b35a6956c93","order":3,"statement":"What is the difference between the digits that occupy the fourth position from the right and the third position from the left when all the digits of the number 92581473 are rearranged in ascending order?","options":{"A":"1","B":"3","C":"2","D":"4"},"correctOption":"C","solution":"Arranging the digits of 92581473 in ascending order gives 12345789. The fourth digit from the right is 5, and the third digit from the left is 3. The difference is 5-3 = 2."},{"id":"4f1ebc1d-cc54-4776-b459-4dfde48271b3","order":4,"statement":"Find the sum of all the prime numbers between 21 and 60.","options":{"A":"301","B":"331","C":"352","D":"363"},"correctOption":"D","solution":"The prime numbers between 21 and 60 are: 23, 29, 31, 37, 41, 43, 47, 53, 59. Their sum = 23+29+31+37+41+43+47+53+59 = 363."},{"id":"d6d59fe1-be4a-4bb5-b142-a7164e7b0190","order":5,"statement":"The product of the 1st natural number, 2nd whole number, and 3rd prime number is?","options":{"A":"5","B":"3","C":"7","D":"0"},"correctOption":"A","solution":"1st natural number = 1, 2nd whole number = 1, 3rd prime number = 5. Product = 1 x 1 x 5 = 5."},{"id":"80d8df76-67a8-45ad-ae5e-f547e908f889","order":6,"statement":"The ratio of a two-digit natural number to a number formed by reversing its digits is 8:14. The number of such pairs is","options":{"A":"3","B":"6","C":"8","D":"4"},"correctOption":"D","solution":"Let the number be (10a+b) and its reverse be (10b+a). Given (10a+b)/(10b+a) = 8/14, so 70a+7b = 40b+4a, giving 66a = 33b, so b = 2a. Possible (a,b) pairs: (1,2), (2,4), (3,6), (4,8) - i.e., numbers 12/21, 24/42, 36/63, 48/84. So there are 4 such pairs."},{"id":"86176da5-6faf-4be4-9bee-b2d96bcafe81","order":7,"statement":"What is the difference between the place values of 9 in the number 3982597?","options":{"A":"89910","B":"899910","C":"899990","D":"890000"},"correctOption":"B","solution":"The digit 9 appears twice: once at the lakh's place (value 900000) and once at the ten's place (value 90). The difference between the place values = 900000-90 = 899910."},{"id":"e270c467-1b2c-4e5b-b1ae-50d4ac5c80c3","order":8,"statement":"A certain two-digit number is four times the sum of its digits. If 27 is added to it, the digits are reversed. Find the number.","options":{"A":"63","B":"36","C":"72","D":"27"},"correctOption":"B","solution":"Let the number be 10x+y. Given 10x+y = 4(x+y), which simplifies to 2x = y. Also 10x+y+27 = 10y+x, which simplifies to x+3 = y. Comparing both, x=3 and y=6, so the number is 36."},{"id":"08aa5eac-58be-4887-8c1d-26b46fa2d894","order":9,"statement":"In a two digit number, the sum of the two digits is 8. If 18 is added to the number, its digits are reversed. Find the number.","options":{"A":"26","B":"18","C":"44","D":"35"},"correctOption":"D","solution":"Let the number be 10x+y, with x+y=8. Given 10x+y+18 = 10y+x, which simplifies to y-x=2. Solving both equations gives x=3 and y=5, so the number is 35."},{"id":"492dc22a-ec4b-4790-a106-58aaa8b59989","order":10,"statement":"Which of the following groups has the maximum and minimum number of prime numbers respectively?","options":{"A":"20-30 & 80-90","B":"1-10 & 60-70","C":"11-20 & 90-100","D":"80-90 & 70-80"},"correctOption":"C","solution":"Counting primes in each decade: 1-10 has 4 (2,3,5,7), 11-20 has 4 (11,13,17,19), 21-30 has 2, 31-40 has 2, 41-50 has 3, 51-60 has 2, 61-70 has 2, 71-80 has 3, 81-90 has 2, 90-100 has 1 (97). Groups 1-10 and 11-20 tie for maximum (4 primes), while 90-100 has the minimum (1 prime). Since the question asks for one group covering both extremes, 11-20 (max) and 90-100 (min) is the matching pair."}]}