1
Identify the incorrect number in the sequence: 5, 16, 6, 16, 7, 16, 9.
0:00
Solution: Step 1: Analyze the given series: 5, 16, 6, 16, 7, 16, 9.
Step 2: Recognize this as an alternating series with two interwoven sub-series.
Step 3: Separate the terms into odd-positioned terms and even-positioned terms:
Odd-positioned terms: 5, 6, 7, 9
Even-positioned terms: 16, 16, 16
Step 4: Analyze the pattern for the odd-positioned terms (5, 6, 7, 9). This sub-series is an arithmetic progression where each term increases by 1: 5, 6, 7, (7+1)=8.
Step 5: Analyze the pattern for the even-positioned terms (16, 16, 16). This sub-series is constant, with each term being 16.
Step 6: According to the pattern for odd-positioned terms, the last term in the series (which is the 7th term) should be 8, not 9.
Step 7: Therefore, 9 is the wrong term; it should be 8.
3
Determine the missing term in the sequence: 3, 7, 6, 5, 9, 3, 12, 1, 15, (....)
0:00
Solution: Step 1: Observe the given series: 3, 7, 6, 5, 9, 3, 12, 1, 15, (....).
Step 2: Identify that there are two interleaved sub-series.
Step 3: Sub-series 1 (numbers at odd positions: 1st, 3rd, 5th, etc.): 3, 6, 9, 12, 15. This series follows a pattern of adding 3 to the previous term (3 + 3 = 6, 6 + 3 = 9, and so on).
Step 4: Sub-series 2 (numbers at even positions: 2nd, 4th, 6th, etc.): 7, 5, 3, 1. This series follows a pattern of subtracting 2 from the previous term (7 - 2 = 5, 5 - 2 = 3, and so on).
Step 5: The missing term is the next term in Sub-series 2.
Step 6: Calculate the next term for Sub-series 2: 1 - 2 = -1.
7
Find the missing term in the sequence: 2, 3, 3, 5, 10, 13, ?, 43, 172, 177
0:00
Solution: Step 1: Analyze the operations between consecutive terms to find a consistent pattern.
Step 2: Observe the sequence of operations:
- 2 + 1 = 3
- 3 × 1 = 3
- 3 + 2 = 5
- 5 × 2 = 10
- 10 + 3 = 13
Step 3: The pattern alternates between addition and multiplication, with the operand (the number being added or multiplied) increasing by 1 each time. The sequence of operations is: '+1, ×1, +2, ×2, +3, ×3, ...'
Step 4: The last operation identified was '+3' (10 + 3 = 13).
Step 5: Therefore, the next operation in the sequence should be '×3'.
Step 6: Calculate the missing term: 13 × 3 = 39.
Step 7: The missing term is 39.
Step 8: (Optional verification) To confirm, the next operations would be '+4' (39 + 4 = 43), then '×4' (43 × 4 = 172), then '+5' (172 + 5 = 177). The pattern holds true throughout the series.
8
Determine the missing term in the sequence: 5, 6, 9, 15, ?, 40
0:00
Solution: Step 1: Calculate the differences between consecutive terms in the series.
Step 2: Differences:
- 6 - 5 = 1
- 9 - 6 = 3
- 15 - 9 = 6
Step 3: Observe the pattern in these differences: 1, 3, 6.
Step 4: Analyze this sequence of differences. The increments between them are increasing:
- From 1 to 3: +2
- From 3 to 6: +3
Step 5: Following this pattern, the next increment should be +4. So, the next difference in the sequence of differences (1, 3, 6, ...) should be 6 + 4 = 10.
Step 6: Add this new difference to the last known term of the original series to find the missing term: 15 + 10 = 25.
Step 7: The missing term in the sequence is 25.
Step 8: (Optional verification) To confirm, the next difference in the sequence of differences would be 10 + 5 = 15. Adding this to 25 gives 25 + 15 = 40, which matches the next number in the given series.
9
Find the number that does not fit the pattern in the series: 3, 10, 27, 4, 16, 64, 5, 25, 125.
0:00
Solution: Step 1: Observe the series as groups of three terms:
- Group 1: 3, 10, 27
- Group 2: 4, 16, 64
- Group 3: 5, 25, 125
Step 2: Analyze the pattern within Groups 2 and 3:
- For Group 2: 4, 4^2 (16), 4^3 (64) - This follows N, N^2, N^3.
- For Group 3: 5, 5^2 (25), 5^3 (125) - This also follows N, N^2, N^3.
Step 3: Apply this pattern to Group 1:
- The first term is 3.
- The second term should be 3^2 = 9.
- The third term should be 3^3 = 27 (Matches the given term).
Step 4: The given second term in Group 1 is 10, which is incorrect.
Step 5: Therefore, 10 is the wrong term.
10
Arrange the given words in a logical sequence: 1) Furniture, 2) Plant, 3) Seed, 4) Tree
0:00
Solution: Step 1: Understand the task is to arrange the words in a meaningful sequence.
Step 2: Analyze the words: Seed, Plant, Tree, Furniture.
Step 3: The logical sequence is based on the growth or transformation process.
Step 4: Seed grows into a Plant, which grows into a Tree, and from a Tree, Furniture can be made.
Step 5: The correct sequence is: Seed (3), Plant (2), Tree (4), Furniture (1).
Step 6: Therefore, the correct order is 3, 2, 4, 1 or 3241.
11
Identify the incorrect number in the sequence: 25, 36, 49, 81, 121, 169, 225.
0:00
Solution: Step 1: Analyze the given series: 25, 36, 49, 81, 121, 169, 225.
Step 2: Recognize that all numbers in the series are perfect squares:
25 = 5^2
36 = 6^2
49 = 7^2
81 = 9^2
121 = 11^2
169 = 13^2
225 = 15^2
Step 3: Observe the base numbers of the squares: 5, 6, 7, 9, 11, 13, 15.
Step 4: Identify the pattern in these base numbers. The pattern should be consecutive odd numbers starting from 5: 5, 7, 9, 11, 13, 15.
Step 5: The base number 6 (from 36) breaks this pattern, as it is an even number between 5 and 7.
Step 6: Therefore, 36 is the wrong term; it should be the square of the next odd number after 5, which is 7^2 = 49 (or 36 should not be present in a series of squares of odd numbers).
12
Identify the number that does not fit the pattern in the sequence: 4, 6, 8, 9, 10, 11, 12.
0:00
Solution: Step 1: Analyze the given series: 4, 6, 8, 9, 10, 11, 12.
Step 2: Examine the properties of each number (prime or composite):
4 is a composite number (factors: 1, 2, 4).
6 is a composite number (factors: 1, 2, 3, 6).
8 is a composite number (factors: 1, 2, 4, 8).
9 is a composite number (factors: 1, 3, 9).
10 is a composite number (factors: 1, 2, 5, 10).
11 is a prime number (factors: 1, 11).
12 is a composite number (factors: 1, 2, 3, 4, 6, 12).
Step 3: Observe that all numbers in the series are composite numbers, with the sole exception of 11.
Step 4: Therefore, 11 is the wrong term as it is a prime number, while the established pattern consists of composite numbers.
14
Arrange the following words in a logical sequence reflecting a typical career progression: Study, Job, Examination, Earn, Apply.
0:00
Solution: Step 1: The process begins with 'Study'.
Step 2: After studying, one takes an 'Examination'.
Step 3: One then 'Apply' for positions.
Step 4: Successfully applying leads to a 'Job'.
Step 5: In a job, one 'Earn's money.
Step 6: The logical sequence is 1, 3, 5, 2, 4.
15
Identify the next number in the sequence: 8, 15, 12, 19, 16, 23?
0:00
Solution: Step 1: Observe the given sequence: 8, 15, 12, 19, 16, 23.
Step 2: Identify the pattern. The sequence alternates between adding 7 and subtracting 3.
Step 3: Apply the pattern: Start with 8, add 7 to get 15, subtract 3 from 15 to get 12, add 7 to get 19, subtract 3 from 19 to get 16, add 7 to get 23, subtract 3 from 23 to get 20.
Step 4: Therefore, the next number in the sequence is 20.
16
Identify the incorrect number in the sequence: 93, 309, 434, 498, 521, 533.
0:00
Solution: Step 1: Analyze the differences between consecutive terms.
Step 2:
* 309 - 93 = 216
* 434 - 309 = 125
* 498 - 434 = 64
* 521 - 498 = 23
* 533 - 521 = 12
Step 3: Recognize that the differences (216, 125, 64) are perfect cubes: 6^3, 5^3, 4^3.
Step 4: The correct pattern for differences should be adding decreasing cubes: +6^3, +5^3, +4^3, +3^3, +2^3.
Step 5: Apply this pattern to the series:
* 93 + 6^3 (216) = 309 (Correct)
* 309 + 5^3 (125) = 434 (Correct)
* 434 + 4^3 (64) = 498 (Correct)
* 498 + 3^3 (27) = 525 (Expected next term)
Step 6: The given term is 521, which does not match the expected 525.
Step 7: If the sequence continued with the corrected term: 525 + 2^3 (8) = 533 (Matches subsequent term).
Step 8: Therefore, 521 is the incorrect term.
19
Identify the incorrect number within the provided sequence: 835, 734, 642, 751, 853, 981, 532.
0:00
Solution: Step 1: Analyze the given sequence of numbers: 835, 734, 642, 751, 853, 981, 532.
Step 2: Look for a pattern within the digits of each number.
Step 3: Observe that for most numbers, the third digit is the result of subtracting the second digit from the first digit (First - Second = Third).
Step 4: Verify this pattern for each number:
* 835: 8 - 3 = 5 (Correct)
* 734: 7 - 3 = 4 (Correct)
* 642: 6 - 4 = 2 (Correct)
* 751: 7 - 5 = 2. The third digit is 1, not 2. This number deviates from the pattern.
* 853: 8 - 5 = 3 (Correct)
* 981: 9 - 8 = 1 (Correct)
* 532: 5 - 3 = 2 (Correct)
Step 5: Conclude that 751 is the wrong number in the sequence.