If 9 * 7 = 32, 13 * 7 = 120 and 17 * 9 = 208, then what is the value of 19 * 11?
2023
If 9 * 7 = 32, 13 * 7 = 120 and 17 * 9 = 208, then what is the value of 19 * 11?
Answer: C. 240 — ConceptTo infer a nonstandard operation, use one invariant that reproduces every given example. The difference-of-squares identity is a2 − b2 = (a − b)(a +…
- A.
180
- B.
220
- C.
240
- D.
More than one of the above
- E.
None of the above
Show answer & explanation
Correct answer: C
Concept
To infer a nonstandard operation, use one invariant that reproduces every given example.
The difference-of-squares identity is a2 − b2 = (a − b)(a + b).
Application
Check 9 and 7: 92 − 72 = (9 − 7)(9 + 7) = 2 × 16 = 32.
Check 13 and 7: 132 − 72 = (13 − 7)(13 + 7) = 6 × 20 = 120.
Check 17 and 9: 172 − 92 = (17 − 9)(17 + 9) = 8 × 26 = 208.
Apply the same rule to 19 and 11: 192 − 112 = (19 − 11)(19 + 11) = 8 × 30 = 240.
Cross-check
Direct squaring gives 361 − 121 = 240, confirming the factored calculation.
Result
Therefore, 19 * 11 = 240.