Number Series and Logical Patterns

If there are n members and each contributes n paise, total collection = n × n paise = n² paise. Rs. 59.29 = 5929 paise. So n² = 5929, which means n = √5929. Computing: 70² = 4900, 80² = 6400, 77² = (80-3)² = 6400 - 480 + 9 = 5929. Therefore, n = 77 members.

To solve this question, the user must identify the pattern in the given sequence of numbers and use it to predict the next number in the sequence.

Looking at the sequence, we can see that each number is obtained by adding 213 to the previous number. Specifically, the pattern is:

213, 426, 639, 852, 1065, ...

To get the next number in the sequence, we just need to add 213 to the last number in the sequence:

1065 + 213 = 1278

Therefore, the answer is:

The Answer is: B. 1278

This is a sequence of triangular numbers where the difference increases by 1 each time: +2, +3, +4, +5. The next difference is +6, so 15 + 6 = 21.

The differences between terms are decreasing powers of 2 multiplied by -1: 200-4=196 (2^2), 196-16=180 (2^4), 180-64=116 (2^6). The next difference should be 2^8=256. 116 - 256 = -140.

The series consists of the cubes of consecutive integers starting from 2: 2^3=8, 3^3=27, 4^3=64, 5^3=125, 6^3=216. The next number is 7^3 = 343.

The sequence alternates between adding 7 and adding 10: 3+7=10, 10+10=20, 20+7=27, 27+10=37. The next step is to add 7, so 37+7=44.

This is a number series: 0.099, 0.99, 9.9, 99, 990, ____. Each number is 10 times the previous number (0.099 × 10 = 0.99, 0.99 × 10 = 9.9, etc.). Following this pattern, 990 × 10 = 9900, which is the correct answer (Option D).

The pattern is x(n) = 2 * x(n-1) + 2. (22+2=6; 62+2=14; 142+2=30; 302+2=62). The next number is 62 * 2 + 2 = 126.

This is a geometric progression where each term is multiplied by 1/2. 2 * 1/2 = 1; 1 * 1/2 = 1/2; 1/2 * 1/2 = 1/4. The next term is 1/4 * 1/2 = 1/8.

This is an alternating series. The first pattern adds 3 (7, 10; 8, 11; 9, 12) and the second pattern subtracts 2 (10, 8; 11, 9). After 12, the next step follows the 'subtract 2' rule from the previous peak, but more simply, the sequence is (7, 8, 9...) and (10, 11, 12...). The next number in the second sub-sequence is 10? No, the next number is 10 because it follows 9 (9+1). Wait, the sequence is 7(+3), 10(-2), 8(+3), 11(-2), 9(+3), 12(-2) = 10.

The series follows an alternating subtraction pattern: -2, -4, -2, -4. Starting from 36: 36-2=34, 34-4=30, 30-2=28, 28-4=24. The next step is to subtract 2, resulting in 22.

The pattern alternates between subtracting 1 and adding 2: 22-1=21, 21+2=23, 23-1=22, 22+2=24, 24-1=23. To find the next number, add 2 to 23, which gives 25. Option A (22) would continue the subtract-1 pattern, but we're at the add-2 step.

This series repeats each number twice before subtracting 13: 53, 53, then 53-13=40, 40, then 40-13=27, 27. The next number after 27 is 27-13=14. Option A (12) would require subtracting 15, which doesn't match the established pattern.

The odd positions (1st, 3rd, 5th, 7th) are all 21. The even positions show 9, 11, 13, which increase by 2 each time. The next number is at position 8 (even), so it follows 13+2=15. Option A (14) would break the +2 pattern, and option C (21) is at the wrong position.

This is a simple arithmetic sequence where each term decreases by 6: 58-6=52, 52-6=46, 46-6=40, 40-6=34. The next term is 34-6=28. Option B (26) would require subtracting 8, which doesn't match the pattern.

The pattern alternates between adding 1 and adding 3: 3+1=4, 4+3=7, 7+1=8, 8+3=11, 11+1=12. The next operation is +3, giving 12+3=15. Option B (10) would require subtracting 2, and option C (14) would need +2, neither of which fit the established pattern.

The number 8 repeats at every odd position (1st, 3rd, 5th). The even positions show 22, 28, which increase by 6. The next number is at position 6 (even), so it should be 28+6=34. Option B (29) would add only 1, and option C (32) would add 4, neither matching the +6 pattern.

The pattern alternates between subtracting 2 and subtracting 5: 31-2=29, 29-5=24, 24-2=22, 22-5=17. The next operation should be -2, giving 17-2=15. Option A (12) would require subtracting 5, which is the wrong alternating step.

We know Kingston > Galleria and Four Corners < Galleria. By transitivity, if Kingston has more stores than Galleria, and Galleria has more stores than Four Corners, then Kingston must have more stores than Four Corners. Statement 3 is necessarily true.