Math & Puzzles: Mental Math, Sequences & Algebra

1/3 is approximately 0.333. 15/46 is approximately 0.326, which is less than 0.333. 22/62 is 0.354, which is greater than 1/3.

The speed of the stream is calculated as (Downstream Velocity - Upstream Velocity) / 2. Thus, (40 - 14) / 2 = 26 / 2 = 13 km/hr. Note: the option says 'hm/hr' which is a typo for 'km/hr'.

If 2x - y = 4, then 6x - 3y = 3(2x - y) = 3 × 4 = 12. We can factor out 3 from 6x - 3y to get 3 times the given expression.

This sequence follows the pattern: multiply by 2 and subtract 1 alternately, or more simply: each number is 2n+1 where n starts at 0. 16=2^4+0, 33=2^5+1, 65=2^6+1, 131=2^7+3, 261=2^8+5. Alternatively: double and subtract 1, then double and subtract 1 again: 16×2-1=31 (not 33), 16×2+1=33, 33×2-1=65, 65×2+1=131, 131×2+1=263 (not 261). The actual pattern is: n×2+1 where n is the previous term. 16×2+1=33, 33×2-1=65, 65×2+1=131, 131×2-1=261, 261×2+1=523.

The pattern is n³ - 1 where n increases by 1 starting from 2: 2³-1=7, 3³-1=26, 4³-1=63, 5³-1=124, 6³-1=215, 7³-1=342. The next term is 8³-1=511. Option A (481) would be from subtracting 139, C (391) from subtracting 49, and D (421) from subtracting 79 - none follow the cubic pattern.

The series alternates between adding 3 and subtracting 1: 9+3=12, 12-1=11, 11+3=14, 14-1=13. Continuing: 13+3=16, 16-1=15. Option A (12) would break the pattern, C (10) is too low, and D (17) doesn't fit the alternating rule.

This is two interleaved series at odd and even positions. Odd positions: 10, 13, 16, 19 (increasing by 3). Even positions: 5, 10, 20, ? (each term doubles the previous). The missing term is 20×2=40. Option A (22) and D (23) don't follow either pattern, C (38) is close but incorrect.

The pattern is: multiply by 3, then divide by 2, repeating. 8×3=24, 24÷2=12, 12×3=36, 36÷2=18, 18×3=54. The next term is 54÷2=27. Option B (108) would be 54×2, C (68) and D (72) don't follow the pattern.

21 × 23 = 483. This can be calculated using Vedic mathematics' 'base method' or simply by standard multiplication: 21 × 23 = 21 × (20 + 3) = 420 + 63 = 483. In Vedic math, for numbers close to a base, you can also use the formula: (21 + 3) | (3 × 1) = 24 | 3 = 483, treating the left part as tens and right part as units when both numbers are close to 20. The other options are incorrect computational results.

43 ÷ 9 = 4 with remainder 7. Using the Vedic math method: sum the digits of 43 (4 + 3 = 7), which gives the remainder when dividing by 9. This works because of the mathematical property that the sum of digits modulo 9 equals the number itself modulo 9. 43 = 9 × 4 + 7, so the remainder is indeed 7. The other options (8, 5, 6) don't match this result.

Using the Vedic math rule 'All from 9 and the last from 10': 9-3=6, 9-5=4, and 10-7=3. Combining these digits gives 643.

To multiply numbers just over 100: Add the units of one to the other (103+4=107) for the first part, and multiply the units (3*4=12) for the second part. 107 and 12 combined is 10712.

The pattern is: 56 (+16) = 72, 72 (+18) = 90, 90 (+20) = 110, 110 (+22) = 132. The increments increase by 2 each time. Following the pattern, 132 should be followed by (+24) = 156, but 150 is given instead. Thus 150 is the wrong number.

The pattern is (x - 7) / 2. (2807-7)/2=1400; (1400-6)/2=697; (697-3)/2=347. Wait, the standard pattern is (x-1)/2: (2807-7)/2=1400; (1400-6)/2=697; (697-5)/2=346. 347 is the first break in the consistent subtraction-division logic.

The sequence follows the pattern: multiply by 2 and add 2, 4, 8, 12, 16... (adding 4 more each time). Starting from 3: 3×2+2=8, 8×2+4=20, but the sequence shows 18. Alternatively, if checking consistently: 3 to 8 (×2+2), 8 to 18 (×2+2), then 18 to 46 breaks the ×2+2 pattern (should be 38). By either valid pattern, 18 is the outlier that doesn't belong.

The sequence subtracts 20, then 25, then 30... 105-20=85; 85-25=60; 60-30=30; 30-35=-5. Therefore, 0 is the wrong number in the sequence as it should be -5.

The sequence follows: add 7, then 7, then 13, then 13, then 15, then 17. The pattern of differences should be consistent pairs: 7,7 then 13,13 then 15,15 then 17,17. But 59→74 is +15, so 74 should be followed by +15 (giving 89), not +17 (giving 91). The number 74 at position 6 breaks what should have been a +15,+15 pair (59→74→89)