Among the numbers 132, 176, 279 and 352, identify the odd number based on divisibility by 11.

Introduction / Context:
This odd one out question is based on divisibility rules and factors. You are given four numbers and asked to find which one does not share a common property with the others. In this case, the key is whether each number is divisible by 11. Recognizing divisibility patterns quickly is a valuable skill in quantitative aptitude tests.

Given Data / Assumptions:
The numbers provided are 132, 176, 279 and 352. We suspect that most numbers may be multiples of 11. We use basic divisibility tests and straightforward division for the small numbers involved. We aim to identify one number that is not divisible by 11 while the others are.

Concept / Approach:
The approach is to check divisibility by 11. A quick rule for divisibility by 11 is to compute the difference between the sum of digits in odd positions and the sum of digits in even positions. If this difference is a multiple of 11, including zero, the number is divisible by 11. Alternatively, for small numbers, direct division is also easy. If three numbers are multiples of 11 and one is not, the non multiple is the odd one out.

Step-by-Step Solution:
Step 1: Check 132. Dividing 132 by 11 gives 132 ÷ 11 = 12. Since the result is an integer, 132 is a multiple of 11. Step 2: Check 176. Dividing 176 by 11 gives 176 ÷ 11 = 16. This is an integer, so 176 is also a multiple of 11. Step 3: Check 352. Dividing 352 by 11 gives 352 ÷ 11 = 32. Since the result is an integer, 352 is a multiple of 11. Step 4: Check 279. Dividing 279 by 11, we get 11 * 25 = 275 with a remainder of 4. Thus 279 is not divisible by 11. Step 5: We can also apply the digit rule to 279. The sum of digits in odd positions from the right is 9 + 2 = 11, and the sum in even positions is 7. The difference is 11 - 7 = 4, which is not a multiple of 11, confirming that it is not divisible. Step 6: Therefore, 132, 176 and 352 are all multiples of 11, while 279 is not. Step 7: Hence, 279 is the odd number in the list.

Verification / Alternative check:
To verify, multiply 11 by 12, 16 and 32 to see that you get 132, 176 and 352 respectively. Then check 11 times 25 which is 275 and 11 times 26 which is 286. Neither equals 279, so there is no integer that multiplies 11 to give 279. This confirms that 279 alone is not a multiple of 11 among the given numbers.

Why Other Options Are Wrong:
132 is not the odd number because it is divisible by 11. 176 is not the odd number because it is also divisible by 11. 352 is not the odd number because it too is a multiple of 11. 279 is the odd number because it is not divisible by 11, unlike the others.

Common Pitfalls:
Learners may sometimes try to look for patterns in the digits or prime factorization of all numbers without first checking simple divisibility rules. Another pitfall is to misapply the rule for divisibility by 11 by adding instead of subtracting the alternating digit sums. To avoid these issues, remember the correct rule and apply it systematically or perform direct division for small numbers.

Final Answer:
The number that is not a multiple of 11 and is therefore the odd one out is 279.