If @ = −, % = ×, # = +; then 10 % 2 @ 4 # 3 = ?
- (a)19
- (b)12
- (c)9
- (d)23
Answer
Why
Correct — A.
Rule: replace the symbols, then follow BODMAS: × before + and −.
@ = −, % = ×, # = +, so the expression is
10 × 2 − 4 + 3
Multiply first: 10 × 2 = 20
Then left to right: 20 − 4 = 16, and 16 + 3 = 19 → option (a).
Why the others are wrong
- (b)12 — 12 would need 8 taken off 20, but the expression takes off only 4 and then adds 3. After 10 × 2 = 20 the result is 19.
- (c)9 — 9 is 10 − 4 + 3, the value you get by dropping the % 2. That % means × 2, and the multiplication runs first.
- (d)23 — 23 is 20 + 3: it loses the − 4. The @ stands for minus, so 4 comes off before the 3 goes on.
Concept
A symbol-substitution item has two separate steps. First rewrite the expression with the real signs, then evaluate it by the usual order of operations.
BODMAS puts division and multiplication before addition and subtraction. Addition and subtraction, being of equal rank, are then done left to right.
Here the multiplication already sits at the front, so a straight left-to-right reading also gives 19. That will not always hold: 4 # 3 % 2 is 4 + 3 × 2 = 10, while left to right would give 14.
Key facts
- BODMAS: brackets, orders, division and multiplication, then addition and subtraction.
- Operations of equal rank, such as + and −, are done left to right.
- With @ = −, % = × and # = +, the expression reads 10 × 2 − 4 + 3 = 19.
Study next
Common traps
- Reading % as per cent or as a remainder instead of the × the stem assigns.
- Dropping a term while substituting, which gives 23 (no − 4) or 9 (no × 2).
17 Sep 2025, 12:30, Reasoning Q.24 uses the same % = × and # = +, with $ for −: 18 % 2 $ 3 # 1, keyed 34.
23 Sep 2025, 09:00, Reasoning Q.18 assigns the signs differently (@ = +, # = −, $ = ×) in 8 $ 2 @ 6 # 3, keyed 19.
Related PYQs
No directly related past PYQ was found.