If 11 − 3 = 5, 14 − 5 = 4, then 18 − 6 = ?
- (a)12
- (b)6
- (c)10
- (d)11
Answer
Why
Correct — B.
Rule: a − b means a − 2b (take the second number away twice).
11 − 2 × 3 = 11 − 6 = 5 ✓
14 − 2 × 5 = 14 − 10 = 4 ✓
18 − 2 × 6 = 18 − 12 = 6 → option (b).
Why the others are wrong
- (a)12 — 12 is 18 − 6 done as printed. Ordinary subtraction fails the examples: 11 − 3 is 8, but the question gives 5.
- (c)10 — 10 would mean taking 8 from 18. The rule takes the second number away twice, 2 × 6 = 12, which leaves 6.
- (d)11 — 11 would mean taking 7 from 18. The examples take away twice the second number, and 2 × 6 is 12, not 7.
Concept
When a familiar sign gives unfamiliar results, the worked lines define it. Compare each result with what the sign normally gives.
Here 11 − 3 would be 8 but is 5, three less. 14 − 5 would be 9 but is 4, five less. Each time the shortfall equals the second number, so the sign takes it away twice: a − 2b.
Both worked lines fit a − 2b exactly, and it gives 6, the keyed option. Test a rule on every example before applying it, since a rule fitted to one line can fail the next.
Key facts
- 11 − 2 × 3 = 5 and 14 − 2 × 5 = 4.
- 18 − 2 × 6 = 6.
- The gap between ordinary subtraction and the printed result is the second number.
Study next
Common traps
- Answering 12 by subtracting as printed
- Fitting a rule to the first line and not checking it on the second
Here SSC keeps the minus sign and changes what it does, giving two worked lines to decode it.
Related PYQs
No directly related past PYQ was found.