The Number System is the foundational chapter for IPMAT Quantitative Aptitude, tested in both IPMAT Indore and JIPMAT. Mastering this chapter ensures you never leave easy marks on the table. This guide covers divisibility rules, LCM/HCF, remainders (cyclicity), factors, and 50+ practice concepts for IPMAT 2027.
IPMAT Number System u2014 Importance
| Parameter | IPMAT Indore | JIPMAT |
|---|---|---|
| Section | Quantitative Ability (QA) | Quantitative Aptitude |
| Total QA Questions | 40 (IPMAT Indore SA) + 20 MCQ | 40 MCQ |
| Number System Qs | 4u20136 | 3u20135 |
| Difficulty | Medium-High | Medium |
Divisibility Rules (Must Know)
| Divisor | Rule | Example |
|---|---|---|
| 2 | Last digit is 0, 2, 4, 6, or 8 | 246 u00f7 2 u2713 |
| 3 | Sum of digits divisible by 3 | 123: 1+2+3=6 u2713 |
| 4 | Last 2 digits divisible by 4 | 1324: 24u00f74=6 u2713 |
| 5 | Last digit is 0 or 5 | 145 u00f7 5 u2713 |
| 6 | Divisible by both 2 and 3 | 132 u00f7 6 u2713 |
| 7 | Double last digit, subtract from rest; repeat | 343: 34-6=28 u2713 |
| 8 | Last 3 digits divisible by 8 | 1000 u00f7 8 u2713 |
| 9 | Sum of digits divisible by 9 | 729: 7+2+9=18 u2713 |
| 11 | Alternating sum of digits divisible by 11 | 121: 1-2+1=0 u2713 |
LCM and HCF u2014 Formulas and Applications
Key relationships:
- HCF u00d7 LCM = Product of two numbers (only for 2 numbers)
- HCF divides LCM always
- HCF of fractions = HCF of numerators / LCM of denominators
- LCM of fractions = LCM of numerators / HCF of denominators
Application types in IPMAT:
- Two runners on a circular track u2014 time to meet = LCM of individual lap times
- Bells ringing at different intervals u2014 time to ring together again = LCM
- Finding the largest tile that fits a floor = HCF of floor dimensions
Number of Factors u2014 IPMAT Favourite
For N = pu2081^a u00d7 pu2082^b u00d7 pu2083^c …, Total factors = (a+1)(b+1)(c+1)
| Number | Prime Factorisation | Number of Factors |
|---|---|---|
| 36 | 2u00b2 u00d7 3u00b2 | (2+1)(2+1) = 9 |
| 120 | 2u00b3 u00d7 3 u00d7 5 | (3+1)(1+1)(1+1) = 16 |
| 360 | 2u00b3 u00d7 3u00b2 u00d7 5 | (3+1)(2+1)(1+1) = 24 |
Unit Digit Cyclicity u2014 IPMAT Must-Know
| Base | Cycle of Unit Digits | Cycle Length |
|---|---|---|
| 2 | 2, 4, 8, 6, 2, 4, 8, 6… | 4 |
| 3 | 3, 9, 7, 1, 3, 9, 7, 1… | 4 |
| 7 | 7, 9, 3, 1, 7, 9, 3, 1… | 4 |
| 8 | 8, 4, 2, 6, 8, 4, 2, 6… | 4 |
| 4 | 4, 6, 4, 6… | 2 |
| 9 | 9, 1, 9, 1… | 2 |
| 0, 1, 5, 6 | Always same unit digit | 1 |
Method: For 7^53, divide 53 by cycle length 4 u2192 remainder 1 u2192 unit digit of 7^1 = 7
Remainder Theorem Shortcuts
- Fermat’s Little Theorem: a^(p-1) u2261 1 (mod p) where p is prime and gcd(a,p)=1
- Wilson’s Theorem: (p-1)! u2261 -1 (mod p) for prime p
- Chinese Remainder Theorem: Used when dividing by two coprime numbers
Practice Quiz u2014 IPMAT Number System
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FAQ
Is Number System important for IPMAT Rohtak?
Yes. IPMAT Rohtak tests Quantitative Aptitude with similar topics u2014 divisibility, LCM/HCF, remainders, factors. The difficulty level is similar to JIPMAT. Number System problems appear in both MCQ and Integer Type sections.
How many questions are there in IPMAT Indore Quantitative section?
IPMAT Indore has two QA sections: 40 Short Answer (integer type) questions and 20 MCQ questions. The Short Answer section is particularly challenging. Number System topics appear in both sections. Target 75% accuracy in Number System to secure a good rank.
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