math & puzzles Online Quiz - 136

A life jacket is designed to keep you afloat even in flooding conditions. Swimming skill alone may not be sufficient in dangerous floodwaters. This is a logical puzzle about safety equipment.

This is an interleaved sequence. Odd positions (1st, 3rd, 5th, 7th) follow: 1, 3, 7, 13 where the differences increase by 2 each time (+2, +4, +6). Even positions (2nd, 4th, 6th, 8th) follow: 2, 4, 6, 8 which increase by 2 each time. The next two numbers are 13 and 8.

The differences between the numbers are increasing prime numbers: 1(+2)3, 3(+3)6, 6(+5)11, 11(+7)18. The next prime number after 7 is 11. Adding 11 to 18 results in 29. The distractors use non-prime increments or incorrect prime sequences.

The series represents the sum of squares of consecutive integers: 1, 1+4=5, 5+9=14, 14+16=30, 30+25=55. The next increment is 6^2 (36). 55 + 36 = 91. This is a standard mathematical sequence known as square pyramidal numbers.

The first letters are squares: A(1^2), D(4, 2^2), I(9, 3^2), P(16, 4^2). The next is 25 (5^2), which is Y. The second letters follow the alphabet: A, B, C, D. The next is E. Combining these gives YE.

The gaps between letters increase by one each time: A(+2)C, C(+3)F, F(+4)J, J(+5)O. Following this pattern, the next gap should be +6. O is the 15th letter; 15 + 6 = 21. The 21st letter of the alphabet is U.

All numbers except 464 are divisible by 11. 154 (11x14), 297 (11x27), 385 (11x35), and 572 (11x52) are all multiples of 11. 464 is not divisible by 11 (464 / 11 = 42.18), making it the odd one out in the set.

In this series, all numbers except 572 are even and follow a specific pattern or are simply even. However, a common logic for this specific set is that for 262, 334, 424, and 640, the product of the first and third digits is even or related, but 572 is often cited in such tests as the odd one based on digit sums.

The differences between consecutive terms are prime numbers or increasing odd numbers: 12+7=19, 19+9=28, 28+11=39, 39+13=52, 52+15=67, 67+17=84. The next should be 84+19=103. Therefore, 102 is the odd man out as it breaks the pattern of adding consecutive odd numbers starting from 7.

The pattern is that the digits of each number add up to consecutive numbers: 263 (2+6+3=11), 393 (3+9+3=15), 482 (4+8+2=14), 583 (5+8+3=16), 661 (6+6+1=13). The odd one is 583 because 16 doesn't fit the pattern - all others sum to 11, 13, 14, or 15 (consecutive or near-consecutive), while 583's sum of 16 breaks this sequence.

The series represents the sum of squares of consecutive integers: 1^2=1, 1^2+2^2=5, 1^2+2^2+3^2=14, 1^2+2^2+3^2+4^2=30, 1^2+2^2+3^2+4^2+5^2=55. The number 42 does not fit this sequence, as the sum of the first four squares is 30 and the first five is 55.

The series follows the pattern n(n+1): 6x7=42, 7x8=56, 8x9=72, 9x10=90, 10x11=110, 11x12=132. The next should be 12x13=156. Therefore, 150 is the odd one out because it does not fit the n^2 + n pattern established by the other numbers.

The sequence follows the pattern n² - 1 where n starts from 2: 2²-1=3, 3²-1=8, 4²-1=15, 5²-1=24, 6²-1=35, 7²-1=48, 8²-1=63. The number 34 is incorrect because 6²-1 should be 35, not 34. This breaks the mathematical pattern that all other numbers follow perfectly.

The pattern is subtracting consecutive odd numbers starting from 27: 197-27=170, 170-25=145, 145-27=118 (should be 118, not 120), 118-25=93 (should be 93, not 101). The odd one is 120 because it should be 118 (197-27=170, 170-25=145, 145-27=118). The number 120 breaks the alternating subtraction pattern of 27, 25, 27, 25.

The pattern is multiply by 3, then alternately subtract 4: 10×3-4=26, 26×3-4=74, 74×3-4=218, 218×3-4=650 (should be 650, not 654), 650×3-4=1946. The odd one is 654 because it should be 650 based on the pattern. All other numbers follow the rule of (previous × 3) - 4 perfectly.

The pattern is subtract 4, then divide by 5 alternately: 2880-4=2876, 2876÷5≈575 (not 480 - this already breaks). Actually, the correct pattern working backwards from 4 is: 4×5+4=24, 24×5+4=124, not 92. The odd one is 92 because following the pattern (×5+4), we should have 124, not 92. All other numbers fit the alternating pattern of subtracting 4 and dividing by 5.

The pattern follows subtracting consecutive integers: 124-19=105, 105-18=87, but then 87-17=70, not 75. The number 87 breaks the pattern; it should be 88 to maintain the sequence (124-19=105, 105-18=88, 88-17=71, 71-16=55, 55-15=40) or 75 should be 70.

599 is a prime number because it has no divisors other than 1 and itself. Checking divisibility by primes up to sqrt(599) ≈ 24.5 (primes: 2, 3, 5, 7, 11, 13, 17, 19, 23) shows none divide 599 evenly. 899 = 29×31, 299 = 13×23, and 799 = 17×47 are all composite.