Part V — Quantitative Aptitude: Arithmetic & Algebra

Chapter 5: Number Series, Simplification, Quadratic Equations & Arithmetic

5.1 Number Series and Approximation/Simplification

Number series questions require identifying the pattern governing a sequence (arithmetic, geometric, or a mixed/alternating pattern) to find a missing or next term — a Prelims staple, typically appearing as a dedicated set. Approximation and simplification questions test quick estimation of complex expressions and precise order-of-operations calculation respectively.

5.2 Quadratic Equations (Inequalities-Type)

Quadratic equation questions present two equations (in variables x and y) and ask the candidate to determine the relationship between x and y (x > y, x < y, x ≥ y, x ≤ y, x = y, or relationship cannot be established) after solving both equations.

5.3 Profit, Loss, Simple & Compound Interest

Profit and loss: Profit % = (Profit/Cost Price) × 100. Simple Interest = (Principal × Rate × Time)/100. Compound Interest = Principal × [(1 + Rate/100)ᵀ − 1].

5.4 Time, Work, Speed, and Distance

Time and work problems use the "work per unit time" concept (1/n for a task taking n days) to combine multiple workers' rates. Time, speed, and distance: Speed = Distance/Time, with relative-speed concepts for problems involving two moving bodies (same or opposite direction).

5.5 Probability and Permutation-Combination

Probability = (Favourable outcomes)/(Total possible outcomes). Permutations (nPr) count arrangements where order matters; combinations (nCr) count selections where order does not matter — both frequently tested via committee-selection or card-drawing scenarios.

5.6 Practice Set — Arithmetic & Algebra (20 MCQs)

1. In the number series 7, 14, 28, 56, ?, what is the next term?
   (a) 84 (b) 100 (c) 112 (d) 120
2. In the number series 3, 8, 15, 24, 35, ?, what is the pattern (differences 5,7,9,11, next 13) and next term?
   (a) 46 (b) 48 (c) 50 (d) 52
3. Simplify: 45% of 280 + 30% of 150.
   (a) 156 (b) 161 (c) 171 (d) 181
4. Quadratic: Equation I: x² − 7x + 12 = 0. Equation II: y² − 9y + 20 = 0. What is the relationship between x and y?
   (a) x > y always (b) x < y always (c) x ≥ y for some solution pairs and x < y for others; relationship cannot be uniquely established (d) x = y always
5. A shopkeeper buys an item for ₹960 and sells it for ₹1200. What is the profit percentage?
   (a) 20% (b) 22% (c) 25% (d) 30%
6. Find the compound interest on ₹12,000 at 10% per annum for 2 years, compounded annually.
   (a) ₹2400 (b) ₹2500 (c) ₹2520 (d) ₹2600
7. A and B together can complete a task in 8 days. A alone can complete it in 12 days. In how many days can B alone complete it?
   (a) 20 days (b) 22 days (c) 24 days (d) 26 days
8. Two trains 120 m and 180 m long, moving in the same direction at 54 km/h and 36 km/h respectively, take how much time to cross each other?
   (a) 50 seconds (b) 55 seconds (c) 60 seconds (d) 65 seconds
9. A bag contains 4 red and 6 blue balls. What is the probability of drawing a red ball?
   (a) 2/5 (b) 3/5 (c) 1/2 (d) 1/3
10. In how many ways can a committee of 3 be selected from 6 people (order does not matter)?
    (a) 15 (b) 18 (c) 20 (d) 24
11. In how many ways can 3 people be arranged in a row from a group of 5 (order matters)?
    (a) 40 (b) 50 (c) 60 (d) 70
12. Find the simple interest on ₹8000 at 9% per annum for 3 years.
    (a) ₹2080 (b) ₹2160 (c) ₹2260 (d) ₹2360
13. Solve for x: 4x² − 16 = 0.
    (a) x = ±2 (b) x = ±4 (c) x = ±8 (d) x = ±1
14. In the series 2, 3, 5, 8, 13, ?, what is the pattern (Fibonacci-style, each term = sum of previous two) and next term?
    (a) 18 (b) 19 (c) 20 (d) 21
15. A car travels at 72 km/h. What is its speed in metres per second?
    (a) 18 m/s (b) 20 m/s (c) 22 m/s (d) 24 m/s
16. Two dice are rolled together. What is the probability of getting a sum of 7?
    (a) 1/6 (b) 1/9 (c) 1/12 (d) 1/4
17. Approximate the value of: 19.8% of 601 + 30.2% of 199.
    (a) 175 (b) 180 (c) 185 (d) 190
18. Quadratic: Equation I: x² = 25. Equation II: y² − 3y − 10 = 0. What is the relationship between x and y?
    (a) A unique relationship cannot be established, since x = ±5 and y = 5 or −2, giving multiple possible x-y comparisons (b) x > y always (c) x < y always (d) x = y always
19. Find the ratio in which a shopkeeper must mix rice at ₹30/kg and ₹50/kg to get a mixture worth ₹35/kg.
    (a) 1:3 (b) 3:1 (c) 1:1 (d) 2:3
20. A sum of ₹15,000 amounts to ₹19,500 in 3 years at simple interest. What is the annual rate of interest?
    (a) 8% (b) 9% (c) 10% (d) 12%

Answer Key

1.(c)

2.(b)

3.(c)

4.(c)

5.(c)

6.(c)

7.(c)

8.(c)

9.(a)

10.(c)

11.(c)

12.(b)

13.(a)

14.(d)

15.(b)

16.(a)

17.(b)

18.(a)

19.(b) 20.(c)