$12345679 \times 72$ is equal to

Concept & Strategy This question relies on recognizing a special numerical pattern. The number $12345679$ (missing the digit 8) multiplied by multiples of $9$ yields a repeating digit sequence. Step-by-Step Solution * The expression is: $$12345679 \times 72$$ * Recognize that $72$ is a multiple of $9$. We can split $72$ into $9 \times 8$: $$12345679 \times (9 \times 8)$$ * Multiply $12345679$ by $9$ first. This is a known mathematical property: $$12345679 \times 9 = 111111111$$ * Now multiply this intermediate result by the remaining factor, $8$: $$111111111 \times 8 = 888888888$$ * Notice that the final result has nine 8s. Exam Strategy & Shortcut If you don't remember the pattern $12345679 \times 9 = 111111111$, you can use the unit digit and digit sum. $9 \times 2 = 18$, so it ends in $8$. Option (b) has nine 8s. Let's count digits: an 8-digit number times a 2-digit number will generally be a 9-digit or 10-digit number. $1.2 \times 10^7 \times 7.2 \times 10^1 \approx 8.6 \times 10^8$, which perfectly aligns with the 9-digit number $888888888$. Option (a) only has eight digits. Common Pitfall The most common mistake is choosing option (a) because students miscount the number of repeating digits. Always verify the order of magnitude or count the length of the expected answer. Final Answer **Therefore, the correct answer is 888888888.**