Question
Which is the odd one out based on a divisibility test?
154, 286, 363, 474, 572, 682
The correct answer is
474
Odd One Out Using Divisibility Test
The question asks us to find the number that is different from the others based on a divisibility test. We need to examine the given numbers: 154, 286, 363, 474, 572, 682.
Divisibility Rule Test
Let's test the divisibility rule for 11, which states that a number is divisible by 11 if the alternating sum of its digits is divisible by 11.
- For 154: $(1 - 5 + 4) = 0$. Since 0 is divisible by 11, 154 is divisible by 11.
- For 286: $(2 - 8 + 6) = 0$. Since 0 is divisible by 11, 286 is divisible by 11.
- For 363: $(3 - 6 + 3) = 0$. Since 0 is divisible by 11, 363 is divisible by 11.
- For 474: $(4 - 7 + 4) = 1$. Since 1 is not divisible by 11, 474 is not divisible by 11.
- For 572: $(5 - 7 + 2) = 0$. Since 0 is divisible by 11, 572 is divisible by 11.
- For 682: $(6 - 8 + 2) = 0$. Since 0 is divisible by 11, 682 is divisible by 11.
Identifying the Odd Number
All the numbers except 474 are divisible by 11. Therefore, 474 is the odd one out based on the divisibility test for 11.
Conclusion on Odd Number
The number 474 is the odd one out because it is the only number in the list that is not divisible by 11.
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Important Questions from Number System (Notes)
- Which number system uses only digits 0 and 1?
- The sum of the digits of a 2-digit number is 12. When the digits of the number are interchanged, the number becomes 15 more than twice the original number. The original number is:
- What is the least number which, when divided by 7, 12 and 15 leaves 1 as the remainder in each case?
- If $\frac{1}{9!} + \frac{1}{10!} = \frac{x}{11!}$, then the value of x is:
- What will be the output, if we compute the 9's complement of the decimal number 782.54?
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