7386038 is divisible by

### Concept & Strategy To find the correct divisor for a large number, apply basic divisibility rules one by one based on the given options, starting with the simplest rules (like 4) and moving to sums (like 3 and 9) or alternating sums (like 11). ### Step-by-Step Solution Let us test the number 7386038 against each option: * **Option (b) Check for 4:** A number is divisible by 4 if its last two digits are divisible by 4. The last two digits are 38. $38 / 4 = 9.5$. Not divisible by 4. * **Option (a) Check for 3 & Option (c) Check for 9:** A number is divisible by 3 or 9 if the sum of its digits is a multiple of 3 or 9. Sum: $7 + 3 + 8 + 6 + 0 + 3 + 8 = 35$. 35 is neither a multiple of 3 nor 9. * **Option (d) Check for 11:** Difference between sum of digits in odd and even positions. Odd places sum (right to left): $8 + 0 + 8 + 7 = 23$. Even places sum (right to left): $3 + 6 + 3 = 12$. Difference: $23 - 12 = 11$. Since the difference is 11, the number is divisible by 11. ### Exam Strategy & Shortcut Always check the rule for 4 first because it only requires looking at the last two digits, taking less than two seconds. If you check 3 and it fails (sum is 35), you can instantly eliminate 9 as well, because any number divisible by 9 MUST be divisible by 3. This dual-elimination saves significant time. ### Common Pitfall Test-takers often recalculate the digit sum for 9 after already finding it for 3. Remember the hierarchical nature of multiples: if it fails the 3 test, do not waste time testing the 9 test. ### Final Answer Therefore, the correct answer is **11**.