Find the odd number out in the sequence: 835, 734, 642, 751, 853, 981, 532 (each is a three-digit number).

Introduction / Context:
Odd-man-out puzzles often hide a digit-wise rule within three-digit numbers. A common pattern uses the middle digit as a function (sum or difference) of the first and last digits. We examine each number to see whether its tens digit equals the difference between its hundreds and units digits.

Given Data / Assumptions:

• Sequence: 835, 734, 642, 751, 853, 981, 532
• Hypothesis: For a valid term, tens digit = hundreds digit − units digit

Concept / Approach:
Check each term digit-wise. If hundreds − units equals the tens digit, it fits the rule. Otherwise it is the outlier. This is faster than seeking arithmetic progressions or sums across the whole numbers.

Step-by-Step Solution:
835: 8 − 5 = 3 ⇒ tens = 3 ✔734: 7 − 4 = 3 ⇒ tens = 3 ✔642: 6 − 2 = 4 ⇒ tens = 4 ✔751: 7 − 1 = 6 ⇒ tens shown is 5 ✖853: 8 − 3 = 5 ⇒ tens = 5 ✔981: 9 − 1 = 8 ⇒ tens = 8 ✔532: 5 − 2 = 3 ⇒ tens = 3 ✔

Verification / Alternative check:
All except 751 satisfy the difference rule exactly; no other hidden constraint (such as sum equality) fits the set as neatly, confirming 751 as the unique mismatch.

Why Other Options Are Wrong:
853/981/532 each obey the pattern tens = hundreds − units and are therefore not odd.

Common Pitfalls:
Trying total sums or prime checks on whole numbers rather than exploring intra-digit rules; overlooking that subtraction order matters (hundreds minus units, not vice versa).

Final Answer:
751