Which of the following numbers is divisible by both 7 and 11 ?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 16,324.
| Understanding/Application |
|
By taking the last digit of the number, doubling it, and then subtracting the doubled number from the remaining number. If the number is evenly divisible by seven, the number is divisible by seven. For a test of divisibility by 11 starts from the right and add every second digit. Now subtract from that total the sum of the remaining digits. The resulting number is divisibly by 11 if and only if the number you started with is divisible by 11. |
|
We will try these ways on each option one by one - Taking Option 1 - 12235 1223 - 5(2) = 1213 12235 is divisible by 7 if 1213 is divisible by 7, applying the same rule again. 121 - 3(2) = 115 Again applying - 11 - 5(2) = 1 Thus, 12235 is not divisible by 7. Taking Option 2 - 16257 1625 - 7(2) = 1611 16257 is divisible by 7 if 1625 is divisible by 7, applying the same rule again. 162 - 5(2) = 152 Applying again - 15 - 2(2) = 11 Thus, the number is not divisible by 7. Taking Option 3 - 16425 1642 - 5(2) = 1632 16425 is divisible by 7 if 1632 is divisible by 7, applying the same rule again. 163 - 2(2) = 159 Applying again - 15 - 2(9) = -3 Thus, it is not divisible by 7. Taking Option 4 - 16324 1632 - 2(4) = 1624 16324 is divisible by 7 if 1624 is divisible by 7, applying the same rule again. 162 - 2(4) = 154 Again applying same - 15 - 2(4) = 7 Thus, the number is divisible by 7 16324 (4 + 3 + 1) - (2 + 6) = 0 Thus, the number is divisible by both 7 and 11. |