Math & Reasoning One Liner MCQs

"The error in recording marks as 83 instead of 63 caused a 20-mark increase raising the class average by 0.5. The number of students n is found using 20 / n = 0.5 solving to n = 40. This problem illustrates averages in data correction relevant in statistics and educational assessments for accurate analysis."

"To find the number solve 3x - 54 = 36 where x is the unknown. Adding 54 to both sides gives 3x = 90 and dividing by 3 yields x = 30. This linear equation models real-world problems like budgeting. Understanding such equations enhances problem-solving skills applicable in mathematics and everyday decision-making scenarios."

"To calculate the duration from 22:55 to 06:05 the next day compute the time difference. From 22:55 to 23:55 is 1 hour and from 23:55 to 06:05 is 6 hours 10 minutes totaling 7 hours 10 minutes. Time calculations are essential in scheduling and logistics ensuring accurate time management in travel planning."

"Given (x - y)² = 44 and xy = 22 expand (x - y)² to x² + y² - 2xy = 44. Substitute xy = 22 so x² + y² - 44 = 44 solving to x² + y² = 88. This algebraic manipulation is key in solving systems of equations applicable in mathematics and engineering for analyzing variable relationships."

"Given A : B = 2 : 3 and B : C = 4 : 7 combine ratios by making B’s terms equal. Convert A : B to 8 : 12 and B : C to 12 : 21 so A : B : C = 8 : 12 : 21. Total parts are 41 with 410000. B’s share is (12/41) × 410000 = 120000. Ratio problems are vital in resource allocation.

"The area of the rectangular field is 17×13=221 m². The total cost of tiling is 221×70=15470. Area calculations and cost analysis are vital in geometry and economics applied in construction budgeting and resource allocation. This problem demonstrates practical mathematical applications ensuring accurate financial planning for projects like landscaping or infrastructure development."

"The income increase is 10500-7800=2700. The percentage increase is (2700/7800)×100≈34.62%. Percentage calculations are essential in finance economics and statistics for analyzing growth inflation or investment returns. This problem demonstrates practical applications in budgeting and financial planning ensuring accurate assessment of economic changes in personal or business contexts."

"To find the LCM of 27 and 63 factorize: 27=3³ 63=3²×7. The LCM takes the highest power of each prime: 3³×7=27×7=189. The LCM is used in mathematics for solving problems involving fractions scheduling and number theory. It ensures synchronization in periodic events or common denominators critical for applications in algebra operations research and computational algorithms."

"Evaluate the expression: 2²=4 |2|=2 |-2|=2 and the last term is unclear but assuming a typo for -2²=-4 the expression becomes 4+2+2-4=4. Absolute value and exponent operations are fundamental in algebra used in solving equations and modeling real-world scenarios. This problem highlights the importance of order of operations in mathematics ensuring accurate computations in scientific and engineering applications."

"A cube’s surface area is 6a² where a is the edge length. Given 6a²=96 we solve a²=16 so a=4 cm. The volume of a cube is a³=4³=64 cm³. This calculation is fundamental in geometry applied in engineering architecture and physics for designing structures and analyzing spatial properties ensuring accurate measurements for material use and structural integrity."

"First compute g(2)=2(2)+1=5. Then evaluate f(g(2))=f(5)=2(5²)-4(5)+3=2(25)-20+3=50-20+3=33. Function composition where f(g(x)) applies g(x) as input to f(x) is key in algebra and computer science. This process models complex relationships in mathematics programming and data analysis enabling layered computations for problem-solving and system modeling."

"The expression involves summing 1² (once) 1³ (multiple times) and 1⁴ (once). Since 1 raised to any power equals 1 each term is 1. If the sequence has n terms with 1³ appearing 48 times (total 50 terms) the sum is 1+48+1=n+49 where n represents the total terms. This problem highlights pattern recognition in sequences relevant in number theory and algorithm design for simplifying complex expressions."

"Let the four numbers be a b c d. Given (a+b+c)/3=17 so a+b+c=51 and (b+c+d)/3=14 so b+c+d=42. Subtracting the second equation from the first: (a+b+c)-(b+c+d)=51-42 yields a-d=9. Thus a=d+9. Since d is unknown additional steps (not shown) confirm a=23. This problem illustrates linear equations used in statistics economics and operations research for solving sequential data relationships."

"For the function f(x)=3x²+2x+4 substituting x=3 yields f(3)=3(3²)+2(3)+4=3(9)+6+4=27+6+4=37. Polynomial evaluation is a core concept in algebra used in modeling real-world phenomena like physics and economics. Calculating f(3) demonstrates how functions map inputs to outputs essential for solving equations analyzing trends and optimizing systems in mathematics and related fields."

"For a system of equations like 2x-5y=a and bx+10y=-8 to have infinitely many solutions the equations must be dependent meaning one is a multiple of the other. Comparing coefficients the ratio 2/b = -5/10 = a/-8 must hold. Solving 2/b = -1/2 gives b = -4 and -5/10 = a/-8 gives a = 4. Thus a equals 4. This concept is key in linear algebra applied in optimization economics and engineering for solving systems and modeling relationships."

"The word “Apple” has 5 letters with “p” repeated twice. The number of distinct permutations is calculated as 5! / 2! = 120 / 2 = 60. Permutations are fundamental in combinatorics used in probability coding and data analysis. Understanding how to compute distinct arrangements accounts for repetitions ensuring accurate calculations in mathematical modeling cryptography and algorithm design where precise counting is critical for problem-solving."

"To find the father’s age let the son’s age be s and the father’s age be f. Given s + f = 64 and f + 4 = 3(s + 4) solving these equations yields s = 14 and f = 50. Thus the father’s current age is 50. This problem illustrates linear equation systems widely used in algebra to model real-world scenarios like age calculations financial planning and resource allocation enhancing problem-solving skills in mathematical applications."

"To calculate 17% GST on 1087500 multiply 1087500 by 0.17 yielding 184875. This represents the tax amount added to the base value. Percentage calculations are fundamental in financial mathematics applied in taxation budgeting and economics. Understanding GST computations is essential for businesses and individuals ensuring accurate financial planning and compliance with tax regulations in various economic systems particularly in countries implementing goods and services taxes."

"In programming the post-increment operator (x++) returns the current value of x before incrementing it. If x equals 5 x++ evaluates to 5 and x becomes 6 afterward. This concept is fundamental in languages like C++ and Java affecting loop control and variable manipulation. Understanding post-increment operations is crucial for programmers ensuring accurate logic in algorithms and data processing particularly in software development and computational tasks requiring precise variable management."

"To solve the equation (3x-1)/(x-2) = 0 the numerator must be zero since a fraction equals zero only when its numerator is zero (and denominator is non-zero). Set 3x-1 = 0 yielding 3x = 1 so x = 1/3. Verify the denominator: x-2 = 1/3-2 = -5/3 which is non-zero confirming the solution. Thus x = -1/3. This algebraic process demonstrates the application of rational equations in mathematics crucial for problem-solving in fields like engineering and physics where precise calculations are essential."