📑 Topics on this page (Jump to Topic):
📌 1. BODMAS / VBODMAS
- Order: Bracket → Of (powers/roots) → Division → Multiplication → Addition → Subtraction.
- ÷ and × have equal priority — solve left to right; the same for + and −.
⚠️ Exam Traps:
- First replace the signs, then apply BODMAS — never the other way round.
📌 2. Substitution & Interchange
Example: if '+' means '×', '−' means '÷', '×' means '−', '÷' means '+', then 8 + 2 − 4 × 1 ÷ 3 = 8 × 2 ÷ 4 − 1 + 3 = 4 − 1 + 3 = 6.
💡 Memory Tip: In interchange questions, test each option directly in the equation — the fastest way.
📌 3. Inequality
| Statement | Conclusion |
|---|---|
| A > B ≥ C | A > C ✔ |
| A ≥ B ≥ C | A ≥ C ✔ |
| A > B < C | No relation between A and C |
| A = B > C | A > C ✔ |
- A relation exists only through signs in one direction (>, ≥ or <, ≤); an opposite sign breaks it.
- Either-or: when A ≥ B is fixed but neither A > B nor A = B alone is certain, the answer is 'either I or II'.
📌 4. Practice MCQs
📝 Practice MCQs (prepared by SF Prep — not PYQs)
Q1. If '+' means '×', '−' means '÷', '×' means '−' and '÷' means '+', then 8 + 2 − 4 × 1 ÷ 3 = ? Practice
Correct answer: (B)
8 × 2 ÷ 4 − 1 + 3 = 4 − 1 + 3 = 6.
8 × 2 ÷ 4 − 1 + 3 = 4 − 1 + 3 = 6.
Q2. Simplify: 18 ÷ 3 × 2 + 4 − 1 Practice
Correct answer: (C)
Left to right: 18 ÷ 3 = 6, 6 × 2 = 12, 12 + 4 − 1 = 15.
Left to right: 18 ÷ 3 = 6, 6 × 2 = 12, 12 + 4 − 1 = 15.
Q3. If '×' means '+', '+' means '÷', '÷' means '−' and '−' means '×', then 12 × 6 + 3 ÷ 4 − 2 = ? Practice
Correct answer: (D)
12 + 6 ÷ 3 − 4 × 2 = 12 + 2 − 8 = 6.
12 + 6 ÷ 3 − 4 × 2 = 12 + 2 − 8 = 6.
Q4. Which two signs must be interchanged to make the equation correct? 6 + 4 × 2 − 8 = 18 Practice
Correct answer: (A)
Swap + and ×: 6 × 4 + 2 − 8 = 24 + 2 − 8 = 18 ✔. Others: + ↔ − gives 6, × ↔ − gives −6, the original gives 6.
Swap + and ×: 6 × 4 + 2 − 8 = 24 + 2 − 8 = 18 ✔. Others: + ↔ − gives 6, × ↔ − gives −6, the original gives 6.
Q5. Statement: A > B ≥ C = D. Conclusions: I. A > D II. B ≥ D Practice
Correct answer: (B)
A > B ≥ C = D ⇒ A > D and B ≥ D, both follow.
A > B ≥ C = D ⇒ A > D and B ≥ D, both follow.
Q6. Statement: P < Q > R. Conclusions: I. P < R II. P > R Practice
Correct answer: (C)
Opposite signs give no relation between P and R; they may also be equal, so not even either-or.
Opposite signs give no relation between P and R; they may also be equal, so not even either-or.
Q7. Statement: M ≥ N = O. Conclusions: I. M > O II. M = O Practice
Correct answer: (D)
M ≥ O is certain; neither alone follows but together they cover it ⇒ either-or.
M ≥ O is certain; neither alone follows but together they cover it ⇒ either-or.
Q8. If 'P' means '+', 'Q' '−', 'R' '×', 'S' '÷', then 20 S 4 R 3 P 6 Q 5 = ? Practice
Correct answer: (A)
20 ÷ 4 × 3 + 6 − 5 = 15 + 6 − 5 = 16.
20 ÷ 4 × 3 + 6 − 5 = 15 + 6 − 5 = 16.
Q9. Simplify: 5 + 3 × 4 − 10 ÷ 2 Practice
Correct answer: (B)
5 + 12 − 5 = 12.
5 + 12 − 5 = 12.
Q10. If '÷' means '×' and '×' means '÷', then 36 × 6 ÷ 2 = ? Practice
Correct answer: (C)
36 ÷ 6 × 2 = 6 × 2 = 12.
36 ÷ 6 × 2 = 6 × 2 = 12.
Q11. Statement: A ≤ B < C, D > C. Conclusions: I. D > A II. B < D Practice
Correct answer: (D)
A ≤ B < C < D ⇒ D > A and B < D.
A ≤ B < C < D ⇒ D > A and B < D.
Q12. If 'A' = '+', 'B' = '×', 'C' = '−', 'D' = '÷', then 15 B 2 C 9 D 3 A 4 = ? Practice
Correct answer: (A)
15 × 2 − 9 ÷ 3 + 4 = 30 − 3 + 4 = 31.
15 × 2 − 9 ÷ 3 + 4 = 30 − 3 + 4 = 31.
Q13. Statement: X > Y, Y = Z, Z ≥ W. Conclusions: I. X > W II. Y ≥ W Practice
Correct answer: (B)
X > Y = Z ≥ W ⇒ X > W, Y ≥ W.
X > Y = Z ≥ W ⇒ X > W, Y ≥ W.
Q14. If '+' means '−' and '−' means '+', then 25 + 10 − 5 = ? Practice
Correct answer: (C)
25 − 10 + 5 = 20.
25 − 10 + 5 = 20.
Q15. Simplify: (8 + 4) ÷ 3 × 5 − 2 Practice
Correct answer: (D)
12 ÷ 3 = 4, × 5 = 20, − 2 = 18.
12 ÷ 3 = 4, × 5 = 20, − 2 = 18.
Q16. Statement: K < L ≤ M, N ≥ M. Conclusions: I. N > K II. L ≤ N Practice
Correct answer: (A)
K < L ≤ M ≤ N ⇒ N > K, L ≤ N.
K < L ≤ M ≤ N ⇒ N > K, L ≤ N.
Q17. If '@' means '+', '#' means '−', '$' means '×', then 7 $ 3 # 4 @ 2 = ? Practice
Correct answer: (B)
7 × 3 − 4 + 2 = 21 − 4 + 2 = 19.
7 × 3 − 4 + 2 = 21 − 4 + 2 = 19.
Q18. Statement: E = F > G < H. Conclusions: I. E > G II. F > H Practice
Correct answer: (C)
E = F > G ⇒ E > G follows; F and H are separated by opposite signs ⇒ II does not follow.
E = F > G ⇒ E > G follows; F and H are separated by opposite signs ⇒ II does not follow.
Q19. Simplify: 48 ÷ 8 + 6 × 3 − 4 Practice
Correct answer: (D)
6 + 18 − 4 = 20.
6 + 18 − 4 = 20.
Q20. If '−' means '÷', '+' means '−', '÷' means '×', '×' means '+', then 40 − 8 ÷ 3 + 5 × 2 = ? Practice
Correct answer: (A)
40 ÷ 8 × 3 − 5 + 2 = 15 − 5 + 2 = 12.
40 ÷ 8 × 3 − 5 + 2 = 15 − 5 + 2 = 12.