Quantity Comparison Questions for Bank Exams: The Short Answer
Quantity comparison questions give two quantities (Quantity I and Quantity II), each a small arithmetic problem, a value or an equation, and ask which is greater, whether they are equal, or whether the relation cannot be established. The fastest method is to solve each quantity only as far as needed to compare, and when a quantity has more than one possible value (such as two roots of a quadratic), compare every value of Quantity I with every value of Quantity II before choosing.
Key takeaway for bank exams: IBPS PO, SBI PO, RRB PO and Clerk prelims often set 3 to 5 quantity comparison questions, sometimes in place of quadratic equations. Most marks are lost on two traps: forgetting the negative root of x² = k, and choosing "Q1 > Q2" when only some pairs satisfy it. Every example on this page was solved in Python.
Quantity comparison is closely related to our quadratic equation tricks for bank exams and data sufficiency for bank exams.
Quantity Comparison Answer Options (Standard Format)
| Option | Meaning |
|---|---|
| Quantity I > Quantity II | Every value of I is greater than every value of II |
| Quantity I < Quantity II | Every value of I is less than every value of II |
| Quantity I ≥ Quantity II | Every I is greater than or equal to every II, with at least one equality |
| Quantity I ≤ Quantity II | Every I is less than or equal to every II, with at least one equality |
| Quantity I = Quantity II or relation cannot be established | Values are equal, or the comparison changes between pairs |
In IBPS and SBI papers, "equal" and "cannot be established" are usually combined into one option, as above.
How to Solve Quantity Comparison Questions (Step-by-Step)
- Read both quantities first. Decide which one is quicker.
- Solve only until you can compare. If Quantity II is 500 and Quantity I is clearly above 600, stop.
- List all possible values when a quantity is an equation (two roots, ± square roots, a range).
- Compare every pair of I-value and II-value.
- Pick the option that is true for all pairs. If the sign changes between pairs, the relation cannot be established.
Quantity Comparison with Arithmetic (Solved Examples)
Example 1: Quantity I: Cost price of an item sold at ₹960 with 20% profit. Quantity II: ₹780.
CP = 960 ÷ 1.2 = ₹800. Quantity I > Quantity II.
Example 2: Quantity I: SI on ₹5,000 at 8% for 3 years. Quantity II: CI on ₹5,000 at 8% for 2 years.
I = ₹1,200; II = 5,000 × (1.08² − 1) = ₹832. Quantity I > Quantity II.
Example 3: Quantity I: Average of the first 10 prime numbers. Quantity II: 13.
First 10 primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 → sum 129 → average 12.9. Quantity I < Quantity II.
Example 4: Quantity I: Probability of a sum of 7 with two dice. Quantity II: Probability of two heads in two coin tosses.
I = 6/36 = 1/6 ≈ 0.167; II = 1/4 = 0.25. Quantity I < Quantity II.
Example 5: Quantity I: Speed (km/h) of a car that covers 240 km in 3 hours. Quantity II: 22 m/s in km/h.
I = 80; II = 22 × 18/5 = 79.2. Quantity I > Quantity II.
Quantity Comparison with Quadratic Equations (Root Rules)
| Pattern | What to do |
|---|---|
| x² − 7x + 12 = 0 vs y² − 9y + 20 = 0 | Find both roots of each, compare all four pairs |
| x² = 81 | x = +9 or −9 (two values) |
| x = √81 | Only +9 (principal square root) |
| x³ = 27 | Only x = 3 (one real root) |
| Both roots positive, one equation shares a root with the other | Usually ≥ or ≤ |
Example 6: Quantity I: x² − 7x + 12 = 0. Quantity II: y² − 9y + 20 = 0.
x = 3 or 4; y = 4 or 5. Pairs: (3,4) <, (3,5) <, (4,4) =, (4,5) <. Quantity I ≤ Quantity II.
Example 7: Quantity I: x² = 81. Quantity II: y = 9.
x = −9 or 9. (−9 < 9) and (9 = 9). Quantity I ≤ Quantity II. If Quantity I were x = √81, the answer would be "equal".
Example 8: Quantity I: x² − 5x + 6 = 0. Quantity II: y² − 7y + 12 = 0.
x = 2 or 3; y = 3 or 4. Pairs: (2,3) <, (2,4) <, (3,3) =, (3,4) <. Quantity I ≤ Quantity II.
Sign trick for roots: for ax² + bx + c = 0 with a > 0, if b and c are both positive, both roots are negative; if b is negative and c positive, both roots are positive; if c is negative, the roots have opposite signs. This lets you rule out options before solving.
Three-Quantity Comparison (New Pattern in SBI PO and IBPS PO)
Newer papers give three quantities and options such as "I > II > III", "I = III < II" or "None of these". Work out all three, then write them on a number line before reading the options.
Example 9: Quantity I: 25% of 480. Quantity II: 5³. Quantity III: √14,400.
I = 120; II = 125; III = 120. On a number line: I = III < II. Answer: Quantity I = Quantity III < Quantity II.
Example 10: Quantity I: the number of days in 15 weeks. Quantity II: 2⁷ − 20. Quantity III: 11 × 10 − 5.
I = 105; II = 128 − 20 = 108; III = 110 − 5 = 105. Answer: Quantity I = Quantity III < Quantity II.
The same rule about multiple values applies: if one of the three quantities has two possible values, check the order for each value. If the order changes, choose "relation cannot be established" or "none of these", as the options allow.
Quantity Comparison Tricks (Quick Revision Table)
| Situation | Shortcut |
|---|---|
| One quantity is a fixed number | Solve the other only until you can compare |
| Both quantities have two values | Make a 2 × 2 table of comparisons |
| x² = k | Always remember the negative root |
| √k or "positive number" given | Take only the positive value |
| Percentages of different bases | Convert both to actual values (35% of 640 = 224, 40% of 560 = 224) |
| Very close values | Calculate exactly; do not approximate |
Common Mistakes in Quantity Comparison
- Dropping the negative root of x² = k.
- Choosing > when one pair is equal. Then the answer is ≥.
- Approximating close values. 28.27 vs 28 needs exact work.
- Mixing units. Convert m/s and km/h, or months and years, before comparing.
- Using plain average speed. Equal distances need 2xy ÷ (x + y).
Quantity Comparison Questions for Bank Exams (Practice Set with Answers)
- Quantity I: 2x² − 11x + 15 = 0. Quantity II: y² − 8y + 15 = 0. Answer: Quantity I ≤ Quantity II. x = 2.5 or 3; y = 3 or 5.
- Quantity I: Price of a ₹1,200 item after a 10% rise and then a 10% fall. Quantity II: ₹1,180. Answer: Quantity I > Quantity II. 1,200 × 1.1 × 0.9 = 1,188.
- Quantity I: Area of a circle of radius 3 cm (π ≈ 3.14). Quantity II: 28 cm². Answer: Quantity I > Quantity II. 9π ≈ 28.27.
- Quantity I: Number of ways to choose 2 items from 5. Quantity II: 10. Answer: Quantity I = Quantity II. ⁵C₂ = 10.
- Quantity I: Average speed for equal distances at 24 km/h and 36 km/h. Quantity II: 30 km/h. Answer: Quantity I < Quantity II. 2 × 24 × 36 ÷ 60 = 28.8.
- Quantity I: x² + x − 12 = 0. Quantity II: y² − 3y − 4 = 0. Answer: Relation cannot be established. x = −4 or 3; y = −1 or 4; 3 > −1 but 3 < 4.
- Quantity I: 35% of 640. Quantity II: 40% of 560. Answer: Quantity I = Quantity II. Both are 224.
- Quantity I: x² = 49. Quantity II: y = −7. Answer: Quantity I ≥ Quantity II. x = 7 or −7.
- Quantity I: CI on ₹10,000 at 10% for 2 years. Quantity II: ₹2,000. Answer: Quantity I > Quantity II. ₹2,100.
- Quantity I: x³ = 64. Quantity II: y² = 16. Answer: Quantity I ≥ Quantity II. x = 4; y = 4 or −4.
For timed practice, take the IBPS PO Quadratic Equation Mock Test 02 and the IBPS PO Quant Mini Mock Test 04.
Quantity Comparison FAQs
What is quantity comparison in bank exams?
It is a question type where two quantities are given and you decide whether the first is greater than, less than or equal to the second, or whether the relation cannot be established.
When is the relation "cannot be established"?
When the comparison is different for different possible values. For example, if Quantity I can be 3 and Quantity II can be −1 or 4, then 3 > −1 but 3 < 4, so no single relation holds.
How do you solve quantity comparison with quadratic equations?
Find both roots of each equation, list all four pairs, and choose the relation that is true for every pair (>, <, ≥, ≤) or "cannot be established" if it changes.
Does x² = 25 have one value or two?
Two: x = 5 or x = −5. But √25 means only the positive root, 5.
How many quantity comparison questions come in IBPS PO?
When set, usually 3 to 5 questions in the prelims quant section of IBPS PO, SBI PO and RRB PO, often instead of or alongside quadratic equations.
How can I solve quantity comparison faster?
Solve the easier quantity first, then work on the other only until the comparison is clear. Use shortcuts like the root-sign rule and effective rates for CI.
Practice Next
- New quantity comparison tests: IBPS PO Quantity Comparison Mock Test 03 and SBI PO Quantity Comparison Mock Test 02.
- Mock tests: IBPS PO Quadratic Equation Mock Test 02, IBPS PO Quant Mini Mock Test 04, SBI PO Quant Mini Mock Test 04 and IBPS PO Quant Sectional Mock Test 07, plus IBPS PO Quadratic Equation Mock Test 03.
- Related notes: quadratic equation tricks for bank exams, data sufficiency for bank exams, simple and compound interest tricks and probability questions for bank exams.
- Exam details: SBI Clerk 2026 notification.
- Browse all study notes.