Quantitative Ability: arithmetic templates that repeat
Quantitative Ability on IPMAT Rohtak tests Class 8–10 arithmetic and its application, not competitive-mathematics theory. The section rewards translating a short word problem into one clean equation or ratio faster than the clock allows, so reliable handling of standard templates matters more than exotic tricks.
What is actually tested
- Ratio–percentage bridge: 12.5% = 1/8, 16.66% = 1/6, 33.33% = 1/3, 37.5% = 3/8. Successive changes of +20% and −20% give a net −4%, never 0%.
- Time and work: set total work = LCM of the given days, convert every worker into units per day, then add or subtract rates.
- Pipes and cisterns use the same model with one negative rate.
- Averages and mixtures: alligation gives the ratio of quantities as the cross-differences around the mean.
- Number properties: divisibility rules for 3, 9 and 11; unit-digit cyclicity of 2, 3, 7 and 8 (period 4); remainders handled by splitting the divisor into coprime factors.
- Interest and growth: CI = P(1+r)^n; over two years the CI–SI gap equals P(r/100)².
Worked example
A finishes a job in 12 days, B in 18. They work together for 4 days, then A leaves. How long does B need to finish alone? Take total work = LCM(12, 18) = 36 units. A = 3 units/day, B = 2 units/day. Together = 5 units/day, so 4 days give 20 units. Remaining = 16 units, done by B at 2/day → 8 days. Check: 20 + 16 = 36.
Traps that cost marks
- Average speed over equal distances is the harmonic mean 2xy/(x+y), not (x+y)/2.
- Percentage points confused with percentage change in data tables.
- Silent unit switches: minutes to hours, cm to m, lakh to crore.
- Assuming an integer answer when the question says "approximately".
- Burning four minutes on one problem: with negative marking, answer only after eliminating two options.