Use operations and order of operations to complete quantitative puzzles - CogAT Grades 3 Plus

In the equation $2 \times (a + 5) - 3 = b \times 4 + 1$ , if $a = 7$ and the equation is true, what is the value of $3b - 2$ ?
Answer: 13 Substituting a = 7: 2 × (7 + 5) - 3 = b × 4 + 1, so 2 × 12 - 3 = 4b + 1, which gives 24 - 3 = 4b + 1, so 21 = 4b + 1, therefore 20 = 4b, and b = 5. Then 3b - 2 = 3(5) - 2 = 15 - 2 = 13. Choice A (10) would result if students incorrectly found b = 4. Choice C (16) would result from calculation errors in finding b = 6. Choice D (19) would result from finding b = 7.