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Question 1 / 20
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1
Identify the incorrect number in the sequence: 5, 16, 6, 16, 7, 16, 9.
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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.
2
Fill the blanks in the following letter series to complete the pattern: '_ _aba _ _ ba _ ab'
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Solution: Step 1: Observe the given incomplete series: '_ _aba _ _ ba _ ab' Step 2: Identify the basic repeating pattern as 'ab'. Step 3: Fill the blanks by repeatedly inserting 'ab' into the series. Original: _ _aba _ _ ba _ ab Applying pattern: a b / ab / a b / a b / a b / ab Step 4: The letters that fill the blanks are 'a', 'b', 'b', 'a', 'b'. Step 5: The complete sequence of missing letters is 'abbab'.
3
Determine the missing term in the sequence: 3, 7, 6, 5, 9, 3, 12, 1, 15, (....)
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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.
4
Complete the letter sequence by identifying the repeating pattern: 'ab _ _ baa _ _ ab _'
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Solution: Step 1: Observe the given incomplete series: 'ab _ _ baa _ _ ab _' Step 2: Identify the basic repeating pattern as 'aba'. Step 3: Fill the blanks by repeatedly inserting 'aba' into the series. Original: ab _ _ baa _ _ ab _ Applying pattern: ab a / a ba / a ba / ab a Step 4: The letters that fill the blanks are 'a', 'a', 'b', 'a', 'a'. Step 5: The complete sequence of missing letters is 'aabaa'.
5
Find the number that does not follow the pattern in the series: 6, 15, 35, 77, 165, 221.
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Solution: Step 1: Break down each term into its prime factors: - 6 = 2 × 3 - 15 = 3 × 5 - 35 = 5 × 7 - 77 = 7 × 11 Step 2: The pattern observed is the product of two consecutive prime numbers. Step 3: Following this pattern, the next term after 77 should be the product of the next two consecutive prime numbers, which are 11 and 13. Step 4: Calculate the expected term: 11 × 13 = 143. Step 5: The given term is 165, which is incorrect. Step 6: Thus, 165 is the wrong term in the series.
6
In a given sequence of numbers, how many instances of the digit '7' are both preceded and followed by perfect square numbers? Sequence: 8 6 3 7 9 7 4 3 6 9 7 2 1 7 4 9 5 2 5 4 7 9 5 2 9 7 1 4 7 1
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Solution: Step 1: Identify perfect square numbers in the sequence: 9, 4, 1 Step 2: Examine each '7' in the sequence to check if it is both preceded and followed by a perfect square Step 3: Sequence analysis: - 7 9: 9 is a perfect square (valid) - 9 7 4: 9 and 4 are perfect squares (valid) - 9 7 2: 9 is a perfect square but 2 is not (invalid) - 1 7 4: 1 and 4 are perfect squares (valid) - 9 7 1: 9 and 1 are perfect squares (valid) - 4 7 1: 4 and 1 are perfect squares (valid) Step 4: Count valid instances: 5
7
Find the missing term in the sequence: 2, 3, 3, 5, 10, 13, ?, 43, 172, 177
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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
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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.
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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
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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.
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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.
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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.
13
Find the incorrect term in the sequence: 3, 7, 15, 27, 63, 127, 255.
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Solution: Step 1: Observe the pattern: each number is obtained by multiplying the previous number by 2 and then adding 1. (Previous term * 2 + 1) Step 2: Check the terms using this rule: Step 3: 3 * 2 + 1 = 7. (Correct) Step 4: 7 * 2 + 1 = 15. (Correct) Step 5: Following the pattern, the next term should be 15 * 2 + 1 = 30 + 1 = 31. Step 6: The given number at this position is 27, which is incorrect. It should be 31. Step 7: Verify with the corrected value: 31 * 2 + 1 = 62 + 1 = 63. This matches the next given term. Step 8: The subsequent terms also follow the rule: 63 * 2 + 1 = 127 and 127 * 2 + 1 = 255. (Correct) Step 9: Therefore, 27 is the wrong number in the series.
14
Arrange the following words in a logical sequence reflecting a typical career progression: Study, Job, Examination, Earn, Apply.
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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?
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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.
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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.
17
Determine the next term in the sequence: 1, 1, 4, 8, 9, 27, 16, ?
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Solution: Step 1: Analyze the sequence to identify the underlying pattern. Step 2: Notice that the terms alternate between squares and cubes of consecutive natural numbers. Step 3: Break down the sequence based on this observation: - 1st term: 1 = 1² - 2nd term: 1 = 1³ - 3rd term: 4 = 2² - 4th term: 8 = 2³ - 5th term: 9 = 3² - 6th term: 27 = 3³ - 7th term: 16 = 4² Step 4: Following this pattern, the 8th term should be the cube of the next natural number, which is 4. Step 5: Calculate 4³ = 64. Step 6: The missing term in the sequence is 64.
18
Identify the incorrect number in the sequence: 121, 143, 165, 186, 209.
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Solution: Step 1: Examine the differences between consecutive terms: - 143 - 121 = 22 - 165 - 143 = 22 Step 2: The pattern appears to be adding 22 to the preceding term. Step 3: Check the next term based on this pattern: 165 + 22 = 187. Step 4: The given term is 186, which does not fit the established pattern. Step 5: Therefore, 186 is the wrong term in the series.
19
Identify the incorrect number within the provided sequence: 835, 734, 642, 751, 853, 981, 532.
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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.
20
Identify the missing number in the sequence: 3, 10, 101, ?
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Solution: Step 1: Observe the relationship between consecutive terms in the series. Step 2: Notice that the second term (10) is obtained by squaring the first term (3) and adding 1 (3² + 1 = 9 + 1 = 10). Step 3: Similarly, the third term (101) is obtained by squaring the second term (10) and adding 1 (10² + 1 = 100 + 1 = 101). Step 4: The pattern is: Each term is obtained by adding 1 to the square of the preceding term. Step 5: Apply this pattern to find the missing term after 101. Step 6: Calculate the square of 101: 101² = 10201. Step 7: Add 1 to the result: 10201 + 1 = 10202. Step 8: The missing term in the series is 10202.
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