IPMAT Quantitative Aptitude Mastery

Key Concepts

This chapter covers essential arithmetic foundations for IPMAT Quantitative Aptitude: divisibility, HCF/LCM, remainders, ratios, percentages, profit-loss, and simple/compound interest. You need these because most mixed questions reduce to a few standard rules.

You MUST know:

• Divisibility rules (by 2, 3, 4, 5, 6, 8, 9, 10) and how to use them quickly.
• HCF (GCD): largest number dividing given integers; LCM: smallest common multiple.
• Remainders theorem: dividing by a number gives a remainder less than the divisor.
• Number properties: parity (even/odd), squares/cubes parity, remainder patterns.
• Ratios: conversion to fractions/percentages; using unitary method.
• Percentages: increase/decrease; “base × rate/100”.
• Profit/Loss: Profit% = (Profit/CP)×100, Loss% = (Loss/CP)×100, and SP = CP ± Profit/Loss.
• Simple Interest (SI): SI = (P×R×T)/100, Total Amount = P + SI.
• Compound Interest (CI): Amount = P(1+R/100)^T, CI = Amount − P.
• Exam mindset: choose the rule that matches the structure (divisibility vs HCF/LCM vs remainder vs ratio/percent).

Before you continue (check):

Can you find HCF and LCM using prime factorization and then use the remainder rule to solve a “remainder on division” question?

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Key Terms

HCF (Highest Common Factor) - largest number that divides two or more integers exactly.

LCM (Least Common Multiple) - smallest number that is a multiple of two or more integers.

Prime Factorization - writing a number as a product of primes (e.g., 60 = 2^2 × 3 × 5).

Remainder Theorem (Divison Rule) - when A is divided by B, remainder r satisfies: A = B×q + r, with 0 ≤ r CP; Loss - SP CP; Loss means SP < CP. Draw a quick comparison line.

• SI vs CI mix-up: SI grows linearly: Amount = P(1 + R/100 × T). CI grows by compounding: Amount = P(1 + R/100)^T.

Exam-focused tips

• Write formulas first, then substitute values; markers reward correct method even if arithmetic slips.
• For word problems, convert everything to CP/SP/Principal/Rate/Time before calculating.

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Quick Reference

Key formulas/rules

• Divisibility:
• by 2: last digit even
• by 5: last digit 0 or 5
• by 3 or 9: sum of digits divisible by 3 or 9
• by 4: last 2 digits divisible by 4
• by 8: last 3 digits divisible by 8
• Division algorithm: If a