If 3 + 4 = 19 and 2 + 5 = 17, what is 1 + 6 = ?

Correct — B.
Rule: a + b means (a × b) + (a + b), the product plus the sum.

3 + 4 → 3 × 4 + (3 + 4) = 12 + 7 = 19 ✓
2 + 5 → 2 × 5 + (2 + 5) = 10 + 7 = 17 ✓

1 + 6 → 1 × 6 + (1 + 6)
= 6 + 7 = 13 → option (b).

Why the others are wrong

• (a)
  15 — 15 continues 19 → 17 with another drop of 2. The drop is not fixed: the products fall 12 → 10 → 6, so the results fall 19 → 17 → 13.
• (c)
  12 — 12 is 1 × 6 + 6, adding the second number instead of the sum. That version fails the first example: 3 × 4 + 4 = 16, not 19.
• (d)
  11 — 11 needs 1 × 6 + 5. Both examples add the full sum of the two numbers, and 1 + 6 = 7, so the amount added is 7, not 5.

In a hidden-operation item the printed sign means nothing; the examples define it. Test a rule on every example before applying it.

Here all three pairs have the same sum, 7. So the results differ only through the product: 12, 10 and 6.

Adding 7 to each product gives 19, 17 and 13. The same rule can be written (a + 1)(b + 1) − 1: 4 × 5 − 1 = 19.

Key facts

• 3 × 4 + 7 = 19 and 2 × 5 + 7 = 17: both examples add the sum 7.
• a × b + a + b equals (a + 1)(b + 1) − 1.
• For 1 and 6 the rule gives 1 × 6 + 7 = 13.

Common traps

• Continuing the answers as a series 19, 17, 15 instead of finding the rule
• Fitting a rule to the first example and never testing it on the second

No directly related past PYQ was found.