Quantity comparison for SBI PO

Quantity comparison gives you two quantities, usually called Quantity I and Quantity II, and asks how they compare. Each quantity is a mini word problem: a percentage, a quadratic root, an interest amount, a train's speed, a probability. You solve both and compare.

It looks simple, and most of the time it is. The marks are lost in two places: a quantity with two possible values, where people compare only one of them, and unit mismatches, where one quantity is in km/h and the other in m/s. This guide covers the option logic, worked examples across the topics that SBI PO-style papers draw on, and a practice set.

The usual options

A typical option set looks like this:

1. Quantity I > Quantity II
2. Quantity I < Quantity II
3. Quantity I ≥ Quantity II
4. Quantity I ≤ Quantity II
5. Quantity I = Quantity II, or no relation can be established

Papers differ in how they word the last option; some split "equal" and "no relation" into separate choices. Read the options once at the start of the set.

The option logic

When each quantity has one value, the comparison is direct. When a quantity has two or more values (roots of a quadratic, x² = 49), compare every value of one with every value of the other.

Why "≥" and not "=". If I can be 3 or 4 and II is 3, then I is sometimes equal and sometimes greater. It is never smaller, so "I ≥ II" is the only statement that is true for every case.

The method

1. Solve Quantity I completely. Write down every possible value.
2. Solve Quantity II completely, in the same units.
3. Compare using the table above.

Worked examples

Example 1. Percentages.
I: 25% of 480
II: 3/8 of 320

• I = 120. II = 320 ÷ 8 × 3 = 120.
• I = II.

Example 2. Quadratic root against a number.
I: x, where x² − 7x + 12 = 0
II: 3

• (x − 3)(x − 4) = 0, so x = 3 or 4.
• 3 = 3 and 4 > 3. Never smaller.
• I ≥ II.

Example 3. Interest.
I: Simple interest on ₹5,000 at 10% a year for 3 years
II: Compound interest on ₹5,000 at 10% a year for 2 years, compounded annually

• I = 5,000 × 10 × 3 ÷ 100 = 1,500.
• II = 5,000 × (1.21 − 1) = 1,050.
• I > II.

Example 4. Units.
I: Speed in km/h of a 180 m train that crosses a pole in 9 seconds
II: 70 km/h

• I = 180 ÷ 9 = 20 m/s. Multiply by 18/5: 72 km/h.
• I > II. If you compared 20 with 70 without converting, you would get it wrong.

Example 5. Probability.
I: Probability of a total of 8 when two dice are thrown
II: Probability of a head when one coin is tossed

• I: (2,6), (3,5), (4,4), (5,3), (6,2) gives 5 of 36 outcomes, about 0.14.
• II = 0.5.
• I < II.

Example 6. Mixture.
I: Litres of water after 6 litres of water are added to 60 litres of a mixture with milk and water in the ratio 7 : 3
II: 25 litres

• Water at the start = 3/10 × 60 = 18. After adding: 24.
• I < II.

Example 7. Ages.
I: A's present age, if A is three times as old as B and in 10 years will be twice as old as B
II: 30 years

• A = 3B and 3B + 10 = 2(B + 10), so B = 10 and A = 30.
• I = II.

Example 8. Arrangements and selections.
I: Number of ways to arrange the letters of BANK
II: Number of ways to choose 2 people from 7

• I = 4! = 24, since all four letters are different.
• II = 7C2 = (7 × 6) ÷ 2 = 21.
• I > II.

Example 9. Two values on one side.
I: x, where x² = 49
II: y, where y³ = 343

• x = 7 or −7. A cube has only one real root, so y = 7.
• 7 = 7 and −7 < 7. Never greater.
• I ≤ II.

Example 10. Work.
I: Days A and B take together, if A alone takes 12 days and B alone takes 18 days
II: 7 days

• Together they do 1/12 + 1/18 = 3/36 + 2/36 = 5/36 of the job a day, so they take 36/5 = 7.2 days.
• I > II. Estimating "a bit over 7" would be risky here, because the gap is only 0.2 days. When the quantities are close, finish the calculation.

Speed tips

• Estimate before solving. If one quantity is obviously far larger (a probability against a speed of 40), you may not need the exact value.
• Convert units first. km/h and m/s (× 18/5 or × 5/18), months and years, percentage and fraction.
• Factorise, don't use the formula, for quadratics with small integer roots. It is faster and less error-prone.
• Sign check for quadratics. If all the coefficients are positive, any real roots are negative. That alone often settles a comparison with a positive number.

Practice set

1. I: 40% of 650. II: 5/8 of 400.
2. I: y, where y² − 9y + 20 = 0. II: 5.
3. I: The average of 12, 18 and 24. II: √324.
4. I: x, where x² − x − 12 = 0. II: 2.
5. I: Compound interest on ₹8,000 at 10% a year for 2 years, compounded annually. II: Simple interest on ₹8,000 at 10.5% a year for 2 years.
6. I: Speed in km/h of a person who walks 1.5 km in 18 minutes. II: 1.5 m/s expressed in km/h.

Answers:

1. I > II. 260 against 250.
2. I ≤ II. y = 4 or 5; 4 < 5 and 5 = 5.
3. I = II. 18 and 18.
4. No relation. x = 4 or −3; 4 > 2 but −3 < 2.
5. I = II. I = 8,000 × 0.21 = 1,680. II = 8,000 × 10.5 × 2 ÷ 100 = 1,680.
6. I < II. I: 1.5 km in 0.3 h = 5 km/h. II: 1.5 × 18/5 = 5.4 km/h.

What to do next

• Do ten quantity comparison questions a day for a week, writing every possible value before comparing.
• Revise quadratic comparisons, which uses the same root logic.
• Brush up the arithmetic behind these questions: simple and compound interest and time, work and speed.