MCQ
Number System MCQ - Practice Questions with Answers
Solve 24 Number System questions for RAS/RPSC preparation.
Practice questions
Q1On a laboratory scale, four concentrations measure 2/5, 3/7, 4/9 and 5/11. The smallest concentration is:
Decimal values are 2/5 = 0.4, 3/7 ≈ 0.429, 4/9 ≈ 0.444 and 5/11 ≈ 0.455. Cross-products confirm the same order: for example 2 × 7 = 14 < 3 × 5 = 15 so 2/5 < 3/7, and similarly each later fraction is larger. Hence the smallest concentration is 2/5.
Q2Four oil drums fill 5/7, 6/11, 8/13 and 9/17 of a tank respectively. By how much does the fullest drum’s fill exceed the emptiest, as a single simplified fraction?
Approximate or cross-compare: 5/7 ≈ 0.714, 6/11 ≈ 0.545, 8/13 ≈ 0.615 and 9/17 ≈ 0.529, so the maximum is 5/7 and the minimum is 9/17. Their difference is (5 × 17 − 9 × 7)/(7 × 17) = (85 − 63)/119 = 22/119, already in lowest terms because 22 and 119 share no common factor greater than 1.
Q3What is the least number greater than 11 which, when reduced by 11, becomes exactly divisible by 16, 24 and 40?
If N − 11 is divisible by 16, 24 and 40, then N − 11 is a common multiple of these three numbers. With 16 = 2^4, 24 = 2^3 × 3 and 40 = 2^3 × 5, LCM(16, 24, 40) = 2^4 × 3 × 5 = 240. Because the question asks for the least N greater than 11, N − 11 must be the least positive common multiple 240, so N = 240 + 11 = 251.
Q4Three automatic packing machines complete one cycle every 24 s, 36 s and 40 s. Starting together, after how many seconds will they next finish a cycle at the same instant?
The next common finishing time is the LCM of 24, 36 and 40. Factorising, 24 = 2³ × 3, 36 = 2² × 3² and 40 = 2³ × 5, so LCM = 2³ × 3² × 5 = 360 s. Hence they next finish together after 360 s.
Q5The digit * in 5*84 must be chosen so that the number is divisible by 3. What is the smallest possible value of *?
A number is divisible by 3 when the sum of its digits is divisible by 3. Here 5 + * + 8 + 4 = 17 + *, so 17 + * must be a multiple of 3. The smallest digit * from 0 to 9 that works is 1, making the sum 18.
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More questions
6A warehouse prints a single verification digit equal to the units place of 13^25 × 17^18 on every outgoing carton. Which digit is printed?
7When identical warehouse crates are packed into cartons of 7, of 8, or of 9, exactly 3 crates remain each time. What is the least number of crates strictly above 200 for which this leftover pattern holds?
8A workshop stamps a serial whose value equals 27^45 + 43^36 − 18^29. What is the units digit of this serial?
9For the pair 54 and 90, the ratio of their LCM to their HCF equals:
10The units digit of 9^58 is:
11A ledger entry records the sum 13^25 + 17^25 + 19^25. Its units digit equals:
12A rectangular courtyard 8.4 m long and 6.3 m wide is to be paved with identical uncut square tiles of the largest possible side. What is that side length?
13Bus tickets numbered from 100 to 250 inclusive are printed. How many of these ticket numbers are divisible by both 4 and 6 but not by 9?
14A warehouse stocks tea in cartons that hold exactly 16 kg, 20 kg or 28 kg. What is the least mass of tea that fills an exact number of cartons of each size?
15The smallest positive integer that leaves a remainder of 4 when divided by 6, a remainder of 6 when divided by 8, and a remainder of 8 when divided by 10 is: