If @ = +, # = −, $ = ×, & = ÷; 8 $ 2 @ 6 # 3 = ?
- (a)19
- (b)17
- (c)13
- (d)14
Answer
Why
Correct — A.
Rule: replace each symbol, then apply BODMAS.
8 $ 2 @ 6 # 3
= 8 × 2 + 6 − 3
Multiply first: 8 × 2 = 16
16 + 6 = 22
22 − 3 = 19 → option (a).
Why the others are wrong
- (b)17 — 17 is 8 + 2 × 6 − 3, reading $ as + and @ as ×. The stem fixes $ = × and @ = +, so the expression is 8 × 2 + 6 − 3.
- (c)13 — 13 is 8 × 2 − 6 + 3, with @ and # swapped. The stem makes @ addition and # subtraction: 16 + 6 − 3 = 19.
- (d)14 — 14 does not come from 8 × 2 + 6 − 3 whether you work left to right or by BODMAS: both give 19.
Concept
Symbol-substitution items are a translation job first and arithmetic second. Rewrite the whole expression with the real operators, then apply the normal order of operations: division and multiplication before addition and subtraction.
The stem defines four symbols but the expression uses three. & (÷) does not appear in it.
Here BODMAS and plain left-to-right working agree, because the multiplication already sits first. They part company when × or ÷ comes after + or −, so write the translated expression out before you calculate.
Key facts
- In this item @ = +, # = −, $ = × and & = ÷.
- 8 × 2 + 6 − 3 = 19.
- Multiplication and division are done before addition and subtraction.
Study next
Common traps
- Swapping the meanings of @ and #, which gives 13.
- Carrying the meaning of @ from another item: at 12 Sep 2025, 09:00, Reasoning Q.25 the same @ stands for −.
The same substitution task is set at 12 Sep 2025, 09:00, Reasoning Q.25 (# = ×, @ = −, $ = +: 9 × 2 − 3 + 1 = 16) and 23 Sep 2025, 16:00, Reasoning Q.20 (10 × 2 − 4 + 3 = 19).
Related PYQs
No directly related past PYQ was found.