Numerical Ability: Calculation Discipline over Brute Force
Numerical Ability, also called Quantitative Aptitude, is the most calculation-heavy part of the UIIC Assistant paper. The question mix is predictable: simplification and approximation, number series including wrong-number series, quadratic equations, data interpretation, and arithmetic word problems on percentage, profit and loss, ratio, time and work, speed-distance-time, boats and trains, simple and compound interest, mixtures, ages and pipes.
Speed tools
Learn tables to 20, squares to 30, cubes to 15, and the fraction-to-percentage conversions (1/8 = 12.5%, 1/16 = 6.25%, 1/6 = 16.66%). Use multipliers for successive percentage changes: two successive 10% increases equal 1.1 x 1.1 = 1.21, a 21% rise, not 20%.
Data interpretation
Read the axis labels, units and the base of every percentage before computing. In caselet DI, extract the paragraph into a table first; in pie charts, check whether the values are degrees or absolute numbers.
Approximation
When options are far apart, round each figure to two significant figures. The correct option should be the only one near your estimate, so exact long division is wasted effort.
Worked example
A finishes a job in 12 days and B in 18 days. In one day they complete 1/12 + 1/18 = 3/36 + 2/36 = 5/36 of the work, so together they need 36/5 = 7.2 days, that is 7 days 4 hours 48 minutes.
Traps
Computing exactly inside an approximation question; using the new value instead of the original as the base for a percentage change; applying the simple-interest formula to compound interest for two or more years; and misreading 'X is what percent more than Y', where Y is the base.
Series and quadratics
Check differences, then ratios, then squares and cubes; for wrong-number series, test the pattern on all terms before naming the odd one. In quadratic equations, compare the roots only after factorising both equations.