Among all topics in IBPS PO and SBI Clerk Quantitative Aptitude, Quadratic Equations and Number Series together contribute 10 marks — that's 10 out of 35 questions in Prelims alone (nearly 29%!). What's remarkable is that with the right patterns, most aspirants can score 8-10/10 in these topics with consistent practice. This guide will show you exactly how.
The key insight from analyzing 5 years of IBPS exam papers: There are only 9 Number Series patterns and 4 Quadratic Equation sign combinations that cover 95% of all questions asked. Memorize these and you've essentially unlocked a guaranteed 8-10 marks every time.
Part 1: Quadratic Equations — The Sign Method
The Sign Method is the fastest way to determine the relationship between x and y without actually finding the roots. It works by analyzing the signs of the b and c coefficients in ax² + bx + c = 0.
For a quadratic equation in the form x² + bx + c = 0, the roots' signs follow this universal truth:
| Sign of b (coefficient of x) | Sign of c (constant) | Roots Are | Memory Aid |
|---|---|---|---|
| + (positive) | + (positive) | Both negative (-, -) | Both signs flip |
| - (negative) | + (positive) | Both positive (+, +) | Opposite of b sign |
| + (positive) | - (negative) | One - and one + (smaller, bigger) | Mixed signs |
| - (negative) | - (negative) | One + and one - (bigger, smaller) | Mixed signs, flipped |
Now compare: if x = 3 or 4, and y = -5 or 2, what's the relationship between x and y?
Cases: x=3,y=-5 → x>y; x=3,y=2 → x>y; x=4,y=-5 → x>y; x=4,y=2 → x>y
Conclusion: x > y always.
If the constant terms ('c') are negative in BOTH equations, the roots of one equation will be
mixed signs (one positive, one negative), and so will the other — making definitive comparison
impossible.
Answer in this case: CND (Relationship cannot be determined)
Advanced Quadratic: Coefficient of x² ≠ 1
When the leading coefficient isn't 1 (e.g., 2x² - 11x + 12 = 0), the Sign Method still works but with a modification: multiply the coefficient of x² by the constant, then find factors of that product that sum to the middle coefficient.
Part 2: Number Series — The Complete 9-Pattern Framework
Every Number Series question in competitive exams falls under one of these 9 patterns. Mastering pattern identification — not calculation — is the real skill.
Logic: Constant gap, or gap that itself follows a pattern (+5, +10, +15... OR +2, +4, +6...)
Ex: 12, 19, 28, 39, ? — Gaps are +7, +9, +11 (odd numbers increasing). Next gap: +13.Answer: 39 + 13 = 52
Logic: Each term × some multiplier. ×2 series double. ×2+1 series are "geometric with constant" types.
Ex: 3, 6, 18, 72, ? — Gaps are ×2, ×3, ×4. Next: ×5Answer: 72 × 5 = 360
MOST IMPORTANT PATTERN. Appears in 40%+ of Number Series questions in IBPS PO.
Ex: 8, 4, 4, 6, 12, ?Logic: ×0.5, ×1, ×1.5, ×2... (multiplier increases by 0.5 each time)
Next multiplier: ×2.5 → 12 × 2.5 = 30 ✅
Gaps between terms are prime numbers (2, 3, 5, 7, 11, 13, 17, 19...). Distinguish from "odd number" gaps!
Ex: 10, 12, 15, 20, 27, ?Differences: +2, +3, +5, +7 (primes). Next prime: +11
Answer: 27 + 11 = 38
When 1st differences show no clear pattern, take differences of differences.
Ex: 10, 15, 27, 48, 80, ?1st Differences: 5, 12, 21, 32
2nd Differences: 7, 9, 11 (arithmetic! +2 each time). Next 2nd diff: 13. Next 1st diff: 32+13=45.
Answer: 80 + 45 = 125
Numbers are n² ± k or n³ ± k. Look for rapid growth or numbers near known squares/cubes.
Ex: 126, 217, 344, ?126 = 5³+1, 217 = 6³+1, 344 = 7³+1
Next: 8³+1 = 512+1 = 513 ✅
Produces numbers: 2, 6, 12, 20, 30, 42, 56, 72... (product of consecutive integers)
Ex: 30, 42, 56, ?30 = 5×6, 42 = 6×7, 56 = 7×8. Next: 8×9 = 72
Two separate series are woven together. Identify by alternating positions.
Ex: 60, 10, 55, 12, 50, ?Position 1,3,5: 60, 55, 50 (decreasing by 5). Position 2,4,6: 10, 12, ? (increasing by 2)
Answer: 14
Logic: ×2-1, ×2-2, ×2-3... or ×3+1, ×3-1, ×3+1... (alternating)
Ex: 5, 9, 16, 29, ?5×2-1=9, 9×2-2=16, 16×2-3=29. Next: 29×2-4 = 54
Wrong Number Series — Extended Strategy
For "Wrong Number" questions, identify the pattern first using all terms, then find which term breaks it.
- Step 1: Check for geometric progression (consistent ratio). If one term has wrong ratio, that's the wrong term.
- Step 2: If not GP, check for differences and second differences.
- Step 3: The wrong number is almost always one of the middle 3-4 terms, not the first or last.
- Step 4: Verify your identified pattern gives ALL other terms correctly before finalizing.
Exam Strategy: Solving 5 Series Questions in 5 Minutes
Here's the exact mental process top scorers use:
- 5 seconds: Glance at all terms. Are they growing slowly? (Patterns 1,4,5) or fast? (Patterns 2,3,6)
- 5-10 seconds: Check for obvious square/cube values or alternating pattern.
- 10-15 seconds: Calculate differences if pattern isn't immediately clear.
- 15 seconds: Confirm with one term and write the answer.
FAQ
Q: How many questions from Quadratic Equations appear in IBPS PO?
A: Typically 5 questions in Prelims (one question = find relationship between x and y for a quadratic
pair). With the Sign Method, you can solve all 5 in roughly 3 minutes.
Q: I keep missing Pattern 3 (decimal series). Any tips?
A: Pattern 3 is tricky because the growth sometimes looks irregular. The key identifier: write the ratio
between consecutive terms. If the ratios form a simple arithmetic sequence (0.5, 1, 1.5, 2, 2.5...),
it's Pattern 3. Practice specifically with Ikkish Prep's "Missing Series" module at Hard level.
Q: Should I attempt Number Series before or after other topics?
A: IBPS PO toppers almost universally suggest: Number Series → Simplification → Quadratics (in that
order). Series often has the most "free marks" if you're good at pattern recognition, so building
momentum there first sets the right mindset for the rest of the section.
Start your practice now on Ikkish Prep's Number Series Quiz at Hard level — that's where all 9 patterns appear, ensuring you're ready for everything the exam throws at you.