Choose the odd number out: 22, 33, 66, 99, 121, 279, 594.

Introduction / Context:
Multiples of a particular integer (here 11) often dominate such sets. Identifying the one number that is not a multiple isolates the odd term cleanly.

Given Data / Assumptions:

• Multiples of 11: 22 (=11*2), 33 (=11*3), 66 (=11*6), 99 (=11*9), 121 (=11*11), 594 (=11*54)
• 279 / 11 = 25.363… (not an integer)

Concept / Approach:
Check divisibility by 11 for each entry. Basic factoring or quick division confirms membership in the set of multiples of 11.

Step-by-Step Solution:
Compute 279 ÷ 11 = 25.363… ⇒ not divisibleAll others divide evenly by 11Therefore, 279 is the odd number out

Verification / Alternative check:
Use the 11-divisibility test (alternating sum of digits): for 279, (2 − 7 + 9) = 4 ≠ 0 mod 11; for 594, (5 − 9 + 4) = 0 ⇒ divisible by 11.

Why Other Options Are Wrong:
33/121/594 are multiples of 11 and thus belong to the main group.

Common Pitfalls:
Assuming 121 is special (it is 11^2 yet still a multiple of 11 and fits the rule).

Final Answer:
279