Question

Find the odd pair out: \[ (12,156),\ (14,210),\ (16,272),\ (18,342),\ (20,420),\ (22,508) \]

• A. \((14,210)\)
• B. \((18,342)\)
• C. \((22,508)\)
• D. \((20,420)\)

Hint:

Whenever ordered pairs are given, test multiplication of consecutive numbers, squares, cubes, or simple algebraic expressions before looking for complex patterns.

Answer 1

The Correct Option is C

Concept: In odd-one-out questions involving ordered pairs, the second number is usually generated from the first number using a mathematical rule. We must identify the common rule satisfied by most pairs and then locate the pair that violates it.

Step 1: Examine the first pair. For \[ (12,156) \] \[ 12\times13=156. \] The pair satisfies: \[ n(n+1). \]

Step 2: Check the remaining pairs. For \[ (14,210): \] \[ 14\times15=210. \] Correct. For \[ (16,272): \] \[ 16\times17=272. \] Correct. For \[ (18,342): \] \[ 18\times19=342. \] Correct. For \[ (20,420): \] \[ 20\times21=420. \] Correct. For \[ (22,508): \] According to the pattern, \[ 22\times23=506. \] But the given value is \[ 508. \] Hence this pair does not follow the established rule.

Step 3: Conclusion. All pairs satisfy \[ n(n+1) \] except \[ (22,508). \] Therefore the odd pair is \[ \boxed{(22,508)}. \]