Mathematical operations for RRB Group D

In a mathematical operations question, the usual signs have new meanings. "+" might mean "÷", or the letter A might stand for "×". The sums are easy. What goes wrong is the switching: halfway through, your brain reads "+" as plus again, and you land on a wrong answer that sits neatly among the options.

One rule prevents that. Rewrite the whole expression with the real signs first, then calculate. This guide covers the six forms these questions take, with a worked example of each.

BODMAS, in one line

After rewriting, solve in this order:

1. Brackets.
2. Division and multiplication, left to right, whichever comes first.
3. Addition and subtraction, left to right.

So 16 ÷ 4 × 3 is (16 ÷ 4) × 3 = 12, not 16 ÷ 12. Our BODMAS guide has more practice on the order itself.

The six forms

Worked examples

Example 1 (changed signs): If + means ÷, − means ×, × means + and ÷ means −, find 16 + 4 − 3 × 2 ÷ 1.

• Make a small key first: + → ÷, − → ×, × → +, ÷ → −.
• Rewrite: 16 ÷ 4 × 3 + 2 − 1.
• 16 ÷ 4 = 4, then 4 × 3 = 12.
• 12 + 2 − 1 = 13.

Example 2 (letter-coded signs): If A means +, B means −, C means × and D means ÷, find 18 D 3 C 4 A 6 B 5.

• Rewrite: 18 ÷ 3 × 4 + 6 − 5.
• 18 ÷ 3 = 6, then 6 × 4 = 24.
• 24 + 6 − 5 = 25.

Example 3 (interchange two signs): Which two signs must be interchanged to make 8 + 6 × 2 − 4 = 46 true? (a) + and − (b) + and × (c) × and − (d) none of these

• (a) gives 8 − 6 × 2 + 4 = 8 − 12 + 4 = 0. False.
• (b) gives 8 × 6 + 2 − 4 = 48 + 2 − 4 = 46. True.
• (c) gives 8 + 6 − 2 × 4 = 8 + 6 − 8 = 6. False.
• Answer: (b).

Example 4 (missing signs): Choose the signs that make 12 ? 3 ? 4 = 16 true. (a) ×, ÷ (b) +, − (c) −, + (d) ÷, ×

• (d) 12 ÷ 3 × 4 = 4 × 4 = 16. True.
• (a) 12 × 3 ÷ 4 = 36 ÷ 4 = 9. (b) 12 + 3 − 4 = 11. (c) 12 − 3 + 4 = 13.
• Answer: (d).

Example 5 (made-up operation): If 3 # 4 = 25 and 5 # 12 = 169, find 6 # 8.

• Try simple rules on the first example. 3 + 4 = 7 and 3 × 4 = 12, neither is 25. But 3² + 4² = 9 + 16 = 25.
• Check on the second example: 5² + 12² = 25 + 144 = 169. The rule fits both.
• 6 # 8 = 36 + 64 = 100.

Example 6 (symbol comparisons): A $ B means A is greater than B. A @ B means A is less than B. A & B means A equals B. If P $ Q and Q & R, how are P and R related?

• P > Q and Q = R, so P > R.
• Answer: P $ R.

Common mistakes

• Solving with the normal signs out of habit. Always rewrite on paper first.
• Doing all divisions before all multiplications. They go left to right together.
• In made-up operations, trusting a rule that fits only one example. It must fit every example given.
• In symbol comparisons, chaining two statements that point opposite ways. A > B and C > B tells you nothing about A and C.

Practice set

1. Using the signs in Example 1, find 20 + 5 − 2 × 3 ÷ 4.
2. Which two signs must be interchanged to make 12 − 4 + 2 × 3 = 47 true? (a) + and × (b) − and + (c) − and ×
3. Using the symbols in Example 6, if A @ B and B @ C, how are A and C related?
4. If × means −, − means +, + means ÷ and ÷ means ×, find 10 × 6 − 8 + 2 ÷ 3.
5. Using the letter codes in Example 2, find 40 D 8 A 7 C 2 B 9.
6. In a new question, 2 # 3 = 10 and 4 # 5 = 36. Find 6 # 2.
7. Choose the signs that make 9 ? 3 ? 5 = 8 true. (a) ÷, + (b) ×, − (c) +, ÷ (d) −, ×
8. Using the symbols in Example 6, if X $ Y and Z $ Y, how are X and Z related?

Answers:

1. 7. It becomes 20 ÷ 5 × 2 + 3 − 4 = 4 × 2 + 3 − 4 = 8 + 3 − 4.
2. (c). 12 × 4 + 2 − 3 = 48 + 2 − 3 = 47. Option (a) gives 7 and (b) gives 10.
3. A @ C. A < B and B < C, so A < C.
4. 16. It becomes 10 − 6 + 8 ÷ 2 × 3 = 10 − 6 + 12.
5. 10. It becomes 40 ÷ 8 + 7 × 2 − 9 = 5 + 14 − 9.
6. 48. The rule is a × (a + b): 2 × 5 = 10 and 4 × 9 = 36. So 6 × 8 = 48.
7. (a). 9 ÷ 3 + 5 = 3 + 5 = 8. The others give 22, 9.6 and −6.
8. Cannot be determined. Both X and Z are greater than Y, but they are never compared with each other.

What to do next

• Write the BODMAS order and the "left to right" rule at the top of your rough sheet in every mock.
• Solve 10 questions of this type a day for a week, always writing the rewritten expression before calculating.
• For made-up operations, practise the usual suspects: sum, product, a² + b², (a + b)², a × b + a + b.
• Revise coding–decoding, which trains the same "translate first" habit, and the reasoning plan.