Number Classification

Divisible by 4

Among 120, 168, 290, and 380, the number 380 is different because it's the only one that when divided by 10 gives a number (38) that is even but not divisible by 3. Alternatively, 120, 168, and 290 are all divisible by 2 but not all by 4, while 380 is divisible by 4. The exact pattern is unclear but the stated answer is D.

N² + 3

Looking at each pair: 13→21 (add 8), 19→27 (add 8), 15→23 (add 8), but 16→23 (add 7). The first three pairs all follow the pattern of adding 8, while the last pair (16:23) adds only 7, making it the odd one out.

Among 369, 462, 761, and 862, the number 761 is different because it's the only prime number in the group. 369=3×123, 462=2×231, and 862=2×431 are all composite numbers. This makes 761 the odd one out.

Analyzing the pairs: 50=7²+1 with 6=7-1, 65=8²+1 with 7=8-1, 37=6²+1 with 5=6-1. However, 28=5²+3 with 4=5-1. The pair 28:4 doesn't follow the 'n²+1 : n-1' pattern that the other three pairs follow, making it the odd one out.

Looking at the sequences: B (2,8,4,16) follows ×4,÷2,×4. C (1,4,2,8) follows ×4,÷2,×4. D (3,12,6,24) follows ×4,÷2,×4. But A (4,16,24,12) follows ×4, then +8 (not ÷2), breaking the consistent pattern. This makes sequence A the odd one out.

Among 17, 27, 37, and 47, the number 27 is different because it's the only composite number (27=3×9=3³). The other three numbers (17, 37, 47) are all prime numbers, making 27 the odd one out.

Looking at 225=15², 625=25², 1225=35², and 1825. The first three are all perfect squares, but 1825 is not a perfect square (√1825≈42.7). Specifically, 1825=25×73, making it composite and not square. This makes 1825 the odd one out.

The numbers 3, 13, and 23 are all prime numbers (divisible only by 1 and themselves). However, 33 = 3 × 11 is a composite number, making it the odd one out in this sequence.

M : 4M + 3

The sequence follows the pattern n² - 1 for consecutive integers starting from 3: 3²-1=8, 4²-1=15, 5²-1=24, 6²-1=35, 7²-1=50, 8²-1=63, 9²-1=80. The number 50 (7²-1) correctly follows the pattern. However, the question asks for the 'odd' (incorrect) number in the sequence, and 50 actually fits correctly. Looking at the options given, 50 is listed as A and marked correct, but the question is framed oddly.

The numbers 377, 477, and 567 are all divisible by 7 (377 ÷ 7 ≈ 53.86, actually 377 = 13×29 - not divisible by 7). Let me recalculate: 377 factors to 13×29, 477 = 9×53, 567 = 9×63 = 9×9×7, and 982 = 2×491. The clearer pattern is that 377, 477, and 567 are all odd numbers, while 982 is even, making it the odd one out.

The numbers 8, 18, and 32 are all even numbers (divisible by 2). However, 15 is an odd number, making it the odd one out in this set.

The numbers 15, 63, and 143 are all composite odd numbers (15 = 3×5, 63 = 7×9, 143 = 11×13). However, 257 is a prime number (only divisible by 1 and itself), making it the odd one out in this set.