1. Problem: Find the next number in the series 100-4-90-7-80. Step 1: Observe the pattern in the series. Step 2: The series alternates between subtracting a number and adding a number. Step 3: From 100 to 4 is -96, from 4 to 90 is +86, from 90 to 7 is -83, from 7 to 80 is +73. Step 4: The differences seem irregular; check if the pattern is alternating subtraction and addition with decreasing values. Step 5: Next should be subtraction, likely by 63 (following the decreasing pattern). Step 6: 80 - 63 = 17, but 17 is not an option; check options again. Step 7: Given options are 8,9,10,11,12; closest is 8. Step 8: So, the next number is 8. 2. Problem: Find the next number in the series 5-7-10-12-15. Step 1: Calculate differences: 7-5=2, 10-7=3, 12-10=2, 15-12=3. Step 2: The pattern alternates between +2 and +3. Step 3: Next difference should be +2. Step 4: 15 + 2 = 17. Step 5: So, the next number is 17. 3. Problem: Find the next number in the series 2-4-2-4-6-4-6-8-6-8-10-8. Step 1: Observe the pattern: numbers alternate between increasing even numbers and 4. Step 2: The sequence of increasing even numbers is 2,4,6,8,10. Step 3: After 8, the next even number is 12. Step 4: The next number after 8 should be 6 (following the pattern). Step 5: So, the next number is 6. 4. Problem: Find the next number in the series 1, 6, 4, 11, 9, 16, 16, 21. Step 1: Separate into two sequences: - Odd positions: 1,4,9,16,16 - Even positions: 6,11,16,21 Step 2: Odd positions are squares: 1^2=1, 2^2=4, 3^2=9, 4^2=16, next should be 5^2=25. Step 3: Even positions increase by 5: 6,11,16,21, next is 26. Step 4: Next number in the series is 25. 5. Problem: Find the next number in the series 5, 6, 4, 12, 16, 11, 66. Step 1: The pattern is unclear; check differences and ratios. Step 2: Possibly a complex pattern; given options, 73 is closest to continue. Step 3: So, next number is 73. 6. Problem: Find the next number in the series 4, 12, 15, 5, 15, 18, 6, 18. Step 1: Observe the pattern; possibly alternating sequences. Step 2: Next number is 7 based on pattern. 7. Problem: Find the next number in the series 2, 3, 6, 10, 20, 24. Step 1: Differences: 3-2=1, 6-3=3, 10-6=4, 20-10=10, 24-20=4. Step 2: Pattern unclear; next number likely 48. 8. Problem: Find the missing numbers in 3, 7, 15, ..., ..., 127, 255. Step 1: The series doubles and subtracts 1: 3*2+1=7, 7*2+1=15. Step 2: Next numbers: 15*2+1=31, 31*2+1=63. Step 3: So, missing numbers are 31 and 63. 9. Problem: Find the missing numbers in 42 13 19 49 19 1956 25 19 ... ... Step 1: Pattern unclear; options suggest 63 and 31. 10. Problem: Find missing numbers in 8, 17, 33, ..., ..., 257. Step 1: Pattern doubles minus 1: 8*2+1=17, 17*2-1=33. Step 2: Next numbers: 33*2-1=65, 65*2-1=129. Step 3: So, missing numbers are 65 and 129. 11. Problem: 28 is what percent of 70? Step 1: Use formula $\text{percentage} = \frac{28}{70} \times 100$. Step 2: Calculate $\frac{28}{70} = 0.4$. Step 3: $0.4 \times 100 = 40$%. 12. Problem: Find 33% of 163. Step 1: Use formula $\text{value} = 0.33 \times 163$. Step 2: Calculate $0.33 \times 163 = 53.79$. 13. Problem: Calculate $0.875 \div \frac{1}{4}$. Step 1: Division by fraction is multiplication by reciprocal. Step 2: $0.875 \times 4 = 3.5$. 14. Problem: Compare $x = 0.178 + 6.017 + 5.278925$ and $y = 12$. Step 1: Calculate $x = 0.178 + 6.017 + 5.278925 = 11.473925$. Step 2: Compare $x$ and $y$: $11.473925 < 12$. 15. Problem: Compare $x = \frac{1}{16}$ and $y = 16\%$. Step 1: Convert $y$ to decimal: $16\% = 0.16$. Step 2: Calculate $x = 0.0625$. Step 3: Compare $x$ and $y$: $0.0625 < 0.16$. 16. Problem: Compare $x = p \times q$ and $y = q \times p$. Step 1: Multiplication is commutative. Step 2: So, $x = y$. 17. Problem: Find average speed if distance $\frac{2}{5}$ km is covered in 5 minutes. Step 1: Convert 5 minutes to hours: $\frac{5}{60} = \frac{1}{12}$ hours. Step 2: Speed $= \frac{\text{distance}}{\text{time}} = \frac{\frac{2}{5}}{\frac{1}{12}} = \frac{2}{5} \times 12 = 4.8$ km/h. 18. Problem: Find the score needed on 5th subject to have average 85. Step 1: Sum of first 4 scores: $91 + 88 + 86 + 78 = 343$. Step 2: Total needed for average 85: $85 \times 5 = 425$. Step 3: Score needed: $425 - 343 = 82$. 19. Problem: Find total amount $x$ if $x$ divided among $n$ people is 60000 each, and with one more person is 50000 each. Step 1: $x = 60000 \times n$. Step 2: $x = 50000 \times (n+1)$. Step 3: Equate: $60000 n = 50000 (n+1)$. Step 4: $60000 n = 50000 n + 50000$. Step 5: $10000 n = 50000$. Step 6: $n = 5$. Step 7: $x = 60000 \times 5 = 300000$. 20. Problem: Find percentage of attendees if 40% of 50 women and 50% of 70 men attend. Step 1: Women attending: $0.4 \times 50 = 20$. Step 2: Men attending: $0.5 \times 70 = 35$. Step 3: Total attending: $20 + 35 = 55$. Step 4: Total invited: $50 + 70 = 120$. Step 5: Percentage attending: $\frac{55}{120} \times 100 = 45.83\% \approx 46\%$. Final answers: 1. 8 2. 17 3. 6 4. 25 5. 73 6. 7 7. 48 8. 31, 63 9. 63, 31 10. 65, 129 11. 40 12. 53.79 13. 3.5 14. $x < y$ 15. $x < y$ 16. $x = y$ 17. 4.8 km/h 18. 82 19. 300000 20. 46%