Elementary Mathematics and Reasoning
Scope
Elementary Mathematics and Reasoning tests numerical accuracy and logical analysis rather than advanced mathematics. Recurring topics are percentages, ratio, averages, time and work, speed and distance, simple and compound interest, series, coding, blood relations, directions, syllogism and seating arrangement.
Core rules
- Percentage change = (change ÷ original) × 100. Successive percentage changes are not additive.
- Time and work: if A finishes in x days and B in y days, together they finish in xy/(x+y) days.
- Speed = distance ÷ time; convert km/h to m/s by multiplying by 5/18.
- Simple interest = P × R × T ÷ 100; compound interest = P[(1 + R/100)^T − 1].
- Average = sum of terms ÷ number of terms.
- In syllogism, draw minimal Venn diagrams and do not assume extra relations.
Worked example
A can complete a work in 12 days and B in 18 days. Together they complete 1/12 + 1/18 = 5/36 of the work per day. The time taken is 36/5 = 7.2 days, i.e. 7 days and 4.8 hours. The trap is to average 12 and 18 and answer 15 days; that is wrong because rates, not times, add.
Traps
Check units before calculating speed or interest. Do not add successive percentages directly. In reasoning, avoid assumptions not stated in the question. In blood relations, draw a family tree rather than guessing.