If # = +, @ = ×, % = −, then (5 # 2) @ 3 % 4 = ?
- (a)20
- (b)17
- (c)18
- (d)21
Answer
Why
Correct — B.
Rule: swap # → +, @ → ×, % → −, and keep the brackets.
(5 # 2) @ 3 % 4 becomes (5 + 2) × 3 − 4
Bracket: 5 + 2 = 7
Multiply: 7 × 3 = 21
Subtract: 21 − 4 = 17 → option (b).
Why the others are wrong
- (a)20 — 20 comes out of neither reading. Brackets first gives 21 − 4 = 17, and dropping the bracket gives 5 + 2 × 3 − 4 = 7.
- (c)18 — 18 would need the last step to subtract 3. The % stands before 4, so the step is 21 − 4 = 17.
- (d)21 — 21 stops at (5 + 2) × 3 and drops the last step. The % 4 still applies as minus 4, giving 17.
Concept
Here each symbol stands for one ordinary sign, so the item tests order of operations more than decoding.
The bracket around 5 # 2 forces the addition first. Without it, multiplication would come first: 5 + 2 × 3 − 4 = 7.
So swap the symbols, keep the brackets exactly where they are, and work outwards: bracket, then ×, then −.
Key facts
- In this item # is +, @ is × and % is −.
- Brackets are worked before × and ÷.
- (5 + 2) × 3 − 4 = 17, while 5 + 2 × 3 − 4 = 7.
Study next
Common traps
- Dropping the brackets after swapping symbols, which gives 5 + 2 × 3 − 4 = 7.
- Stopping at 7 × 3 = 21 and missing the % 4.
18 Sep 2025, 12:30, Reasoning Q.7 turns the task round and asks for the signs: 16 # 4 @ 2 = 62 holds with # as × and @ as −, since 16 × 4 − 2 = 62.
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