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Question 1 / 20
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1
Find the next number in the series: 2, 7, 27, 107, 427, ?
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Solution: Step 1: Calculate the differences between consecutive terms in the series. 7 - 2 = 5 27 - 7 = 20 107 - 27 = 80 427 - 107 = 320 Step 2: Observe the pattern in these differences: 5, 20, 80, 320. This is a geometric progression where each term is four times the previous term. 5 * 4 = 20 20 * 4 = 80 80 * 4 = 320 Step 3: Following this pattern, the next difference should be 320 * 4 = 1280. Step 4: Add this difference to the last given term of the original series to find the missing term. 427 + 1280 = 1707 Step 5: The missing term is 1707.
2
Fill in the blanks to complete the alphabetical series: Z, ?, T, ?, N, ?, H, ?, B
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Solution: Step 1: Convert the known letters to their alphabetical positions (A=1, ..., Z=26). - Z=26, T=20, N=14, H=8, B=2. Step 2: Calculate the difference in positions between the known consecutive letters that are separated by one blank. - From Z (26) to T (20): The total difference is 26 - 20 = 6 positions. Since there is one blank, this difference is split into two steps. So, each step involves a decrement of 6 / 2 = 3 positions. - From T (20) to N (14): The total difference is 20 - 14 = 6 positions. Each step is a decrement of 3 positions. - From N (14) to H (8): The total difference is 14 - 8 = 6 positions. Each step is a decrement of 3 positions. - From H (8) to B (2): The total difference is 8 - 2 = 6 positions. Each step is a decrement of 3 positions. Step 3: The consistent pattern is a decrement of 3 positions for each step in the series. Step 4: Fill in the missing terms using this pattern: - Z (26) - 3 = 23. The 23rd letter is W. - T (20) - 3 = 17. The 17th letter is Q. - N (14) - 3 = 11. The 11th letter is K. - H (8) - 3 = 5. The 5th letter is E. Step 5: The missing terms are W, Q, K, E.
3
Arrange the following terms in a logical sequence: Plant, Cotton, Yarn, Cloth, Saree.
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Solution: Step 1: Understand the terms given and their logical order - Plant: Source of cotton - Cotton: Raw material from the plant - Yarn: Material made from cotton - Cloth: Fabric made from yarn - Saree: Garment made from cloth Step 2: Determine the logical sequence The sequence should reflect the progression from source to final product: 1. Plant (source) 2. Cotton (raw material) 3. Yarn (processed material) 4. Cloth (fabric) 5. Saree (final product) Step 3: Match with given options The correct sequence is: 2, 4, 1, 5, 3
4
Identify the incorrect number in the sequence: 2, 5, 10, 17, 26, 37, 50, 64.
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Solution: Step 1: Express each term in relation to a perfect square: - 2 = 1^2 + 1 - 5 = 2^2 + 1 - 10 = 3^2 + 1 - 17 = 4^2 + 1 - 26 = 5^2 + 1 - 37 = 6^2 + 1 - 50 = 7^2 + 1 Step 2: The pattern is (N^2 + 1), where N is a consecutive integer starting from 1. Step 3: Following this pattern, the next term after 50 should be 8^2 + 1 = 64 + 1 = 65. Step 4: The given term is 64, which is incorrect. Step 5: Therefore, 64 is the wrong term.
5
Which number is incorrect in the given sequence: 64, 71, 80, 91, 104, 119, 135, 155?
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Solution: Step 1: Calculate the differences between consecutive terms to identify the pattern. Step 2: 71 - 64 = 7 Step 3: 80 - 71 = 9 Step 4: 91 - 80 = 11 Step 5: 104 - 91 = 13 Step 6: The differences are 7, 9, 11, 13, which are consecutive odd numbers. The next difference should be 15. Step 7: So, the expected next term after 104 is 104 + 15 = 119. (Correct) Step 8: The next difference should be 17. So, the expected next term after 119 is 119 + 17 = 136. Step 9: The given number at this position is 135, which is incorrect. It should be 136. Step 10: Verify the subsequent term: If the number were 136, the next difference would be 155 - 136 = 19 (which follows 17 + 2 = 19). Step 11: Therefore, 135 is the wrong number in the series.
6
Determine the next group of letters in the series: DHL, PTX, BFJ, ?
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Solution: Step 1: Analyze the pattern for the first letter of each group. Convert letters to positions (A=1, ..., Z=26). - D (4) to P (16): +12 - P (16) to B (2): +12 (16 + 12 = 28; 28 - 26 = 2, which is B). - The pattern for the first letter is a consistent increment of +12 (with wrap-around). - B (2) + 12 = 14. The 14th letter is N. Step 2: Analyze the pattern for the second letter of each group. - H (8) to T (20): +12 - T (20) to F (6): +12 (20 + 12 = 32; 32 - 26 = 6, which is F). - The pattern for the second letter is a consistent increment of +12 (with wrap-around). - F (6) + 12 = 18. The 18th letter is R. Step 3: Analyze the pattern for the third letter of each group. - L (12) to X (24): +12 - X (24) to J (10): +12 (24 + 12 = 36; 36 - 26 = 10, which is J). - The pattern for the third letter is a consistent increment of +12 (with wrap-around). - J (10) + 12 = 22. The 22nd letter is V. Step 4: Combine the predicted letters to form the next group: NRV.
7
Determine the next number in the sequence: 3, 8, 13, 24, 41, ?
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Solution: Step 1: Examine the series: 3, 8, 13, 24, 41, ? Step 2: Look for a recursive pattern where each term depends on preceding terms and an additional value. Step 3: Identify the pattern based on the relationship: `Term(n) = Term(n-2) + Term(n-1) + (n-1)`. Step 4: Verify the pattern for the given terms: - Term 3 (13) = Term 1 (3) + Term 2 (8) + (3-1) = 3 + 8 + 2 = 13 (Matches) - Term 4 (24) = Term 2 (8) + Term 3 (13) + (4-1) = 8 + 13 + 3 = 24 (Matches) - Term 5 (41) = Term 3 (13) + Term 4 (24) + (5-1) = 13 + 24 + 4 = 41 (Matches) Step 5: Apply the pattern to find the 6th term (T6). - T6 = Term 4 (24) + Term 5 (41) + (6-1) - T6 = 24 + 41 + 5 Step 6: Calculate the missing term: 24 + 41 + 5 = 65 + 5 = 70. Step 7: The missing term is 70.
8
Which number is out of sequence in: 1, 3, 12, 25, 48?
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Solution: Step 1: Analyze the terms by considering pairs of squared numbers: - 1 = 1^2 - 0^2 - 3 = 2^2 - 1^2 - 12 = 4^2 - 2^2 (which is 16 - 4) Step 2: Observe the bases of the squares: - First bases: 1, 2, 4 (this sequence doubles: 1, 1*2, (1*2)*2). The next should be 6. - Second bases: 0, 1, 2 (this sequence increments by 1). The next should be 3. Step 3: So, the next term should be 6^2 - 3^2 = 36 - 9 = 27. Step 4: The given term is 25, which is incorrect. Step 5: Verify the last term with the pattern: 8^2 - 4^2 = 64 - 16 = 48 (Matches). Step 6: Therefore, 25 is the wrong term.
9
Identify the number that deviates from the established pattern in the sequence: 835, 734, 642, 751, 853, 981, 532.
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Solution: Step 1: Examine each three-digit number to find a relationship between its digits. Step 2: Observe a pattern where the third digit is the result of subtracting the second digit from the first digit (First Digit - Second Digit = Third Digit). Step 3: Test this pattern for the given numbers: * For 835: 8 - 3 = 5. (Fits the pattern) * For 734: 7 - 3 = 4. (Fits the pattern) * For 642: 6 - 4 = 2. (Fits the pattern) * For 853: 8 - 5 = 3. (Fits the pattern) * For 981: 9 - 8 = 1. (Fits the pattern) * For 532: 5 - 3 = 2. (Fits the pattern) Step 4: Now, check the number 751: * For 751: 7 - 5 = 2. This does not match the third digit, which is 1. Step 5: Therefore, 751 is the number that does not follow the established digit pattern in the sequence.
10
Identify the odd sequence from the given options
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Solution: Step 1: Analyze each option for a pattern Step 2: Option 1: 'bb c MN' - follows a pattern (double letter, next letter, sequence) Step 3: Option 2: 'dd e OP' - follows a pattern Step 4: Option 3: 'mm n WX' - follows a pattern Step 5: Option 4: 'gg f QP' - does not follow the sequence pattern (should be 'h' after 'g') Step 6: Conclusion: 'gg f QP' is the odd one out
11
What is the missing term in the sequence: AB, DEF, HIJK, ?, STUVWX.
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Solution: Step 1: Analyze the number of letters in each term of the series. * AB has 2 letters. * DEF has 3 letters. * HIJK has 4 letters. * STUVWX has 6 letters. Step 2: The pattern for the number of letters is an increment of one at each step. Thus, the missing term should have 5 letters. Step 3: Analyze the relationship between the last letter of a term and the first letter of the next term. * Last letter of AB is B. First letter of DEF is D. (B + 2 positions = D). * Last letter of DEF is F. First letter of HIJK is H. (F + 2 positions = H). Step 4: Apply this pattern to find the starting letter of the missing term: * Last letter of HIJK is K. K + 2 positions = M. So the missing term starts with M. Step 5: The missing term consists of 5 consecutive letters starting from M. Step 6: The letters are M, N, O, P, Q. Step 7: The missing term is MNOPQ. Step 8: Verify the pattern for the next term: Last letter of MNOPQ is Q. First letter of STUVWX is S. (Q + 2 positions = S) (Correct).
12
Complete the sequence: 2, 3, 7, 8, 13, 14, ?
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Solution: Step 1: Observe the given sequence: 2, 3, 7, 8, 13, 14, ? Step 2: Break the sequence into two separate series: Series 1: 2, 7, 13 Series 2: 3, 8, 14 Step 3: Analyze Series 1: - 2 + 5 = 7 - 7 + 6 = 13 - 13 + 7 = 20 Step 4: Analyze Series 2: - 3 + 5 = 8 - 8 + 6 = 14 Step 5: Identify the pattern: The difference between adjacent numbers increases by 1 in each series. Step 6: Apply the pattern to find the next number in Series 1: - The next number in Series 1 is 20. Step 7: Conclude the missing number in the original sequence is 20.
13
Complete the letter series where letter pairs move in a cyclic order: '_bcc _ ac _ aabb _ ab _ cc'
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Solution: Step 1: Analyze the incomplete series: '_bcc _ ac _ aabb _ ab _ cc' Step 2: Identify that the pattern involves letter pairs moving in a cyclic order, where blocks of characters (e.g., 'bbccaa', 'ccaabb', 'aabbcc') are sequentially formed. Step 3: Based on the correct answer 'bacab', fill the blanks in the series. Step 4: The completed series becomes: 'b bcc a ac a aabb b ab c cc'. Step 5: By observing how the letters fill the blanks to form these cyclic shifts, the missing letters are determined to be 'bacab'.
14
Complete the given series: QAR, RAS, SAT, TAU, _____
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Solution: Step 1: Observe the pattern in the series: QAR, RAS, SAT, TAU, ? Step 2: Identify the shift in letters: The first letter of each term shifts one position forward in the alphabet (Q to R to S to T). Step 3: Analyze the second letter: It remains static as 'A'. Step 4: Examine the third letter: It shifts one position forward in the alphabet (R to S to T to U). Step 5: Determine the next term: Following the pattern, the next term should start with 'U', have 'A' in the middle, and end with 'V' (as the next letter after 'U'). Step 6: Therefore, the next term in the series is UAV.
15
Complete the series: 2, 8, 14, __, 34, 48, 62, 80, 98
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Solution: Step 1: Examine the given series for patterns: 2, 8, 14, __, 34, 48, 62, 80, 98 Step 2: Calculate the differences between consecutive numbers: 8-2=6, 14-8=6 Step 3: Observe that the differences between consecutive terms are increasing Step 4: Identify the pattern of differences: +6, +6, +10, +14, +18 Step 5: Apply the pattern to find the missing term: 14 + 10 = 24 Step 6: Verify the pattern with the rest of the series: 24 + 10 = 34, 34 + 14 = 48, and so on Step 7: Conclude the missing number in the series is 24
16
Complete the sequence: 3, 15, ?, 63, 99, 143
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Solution: Step 1: Analyze the given numbers for an underlying mathematical pattern. Step 2: Observe that each term is one less than a perfect square: - 3 = 4 - 1 = 2² - 1 - 15 = 16 - 1 = 4² - 1 - 63 = 64 - 1 = 8² - 1 - 99 = 100 - 1 = 10² - 1 - 143 = 144 - 1 = 12² - 1 Step 3: Identify the pattern of the bases of these squares (the numbers being squared): 2, 4, ?, 8, 10, 12. Step 4: This sequence of bases is an arithmetic progression of even numbers, increasing by 2 each time. The missing base should be 6. Step 5: Apply the pattern (n² - 1) with n=6 to find the missing term. Step 6: Missing term = 6² - 1 = 36 - 1 = 35. Step 7: The missing term in the sequence is 35.
17
Identify the incorrect number in the given sequence: 11, 5, 20, 12, 40, 26, 74, 54.
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Solution: Step 1: Identify that the given sequence is a combination of two interleaved series. Step 2: Extract the first series (odd positions): I. 11, 20, 40, 74. Step 3: Extract the second series (even positions): II. 5, 12, 26, 54. Step 4: Analyze the pattern in Series I by calculating differences: 20-11=9, 40-20=20, 74-40=34. Step 5: Recognize the correct pattern for Series I should be based on doubling differences: +9, +18, +36,.... Step 6: Based on this pattern, the third term in Series I should be (20 + 18) = 38. Step 7: The given term 40 does not fit the pattern. Step 8: Therefore, 40 is the incorrect term.
18
Identify the next term in the series: 3, 7, 23, 95, ?
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Solution: Step 1: Analyze the given series: 3, 7, 23, 95, ? Step 2: Look for a pattern: 3 * 2 + 1 = 7 Step 3: Continue the pattern: 7 * 3 + 2 = 23 Step 4: Further continuation: 23 * 4 + 3 = 95 Step 5: Apply the pattern for the next term: 95 * 5 + 4 = 479 Step 6: Therefore, the next term in the series is 479.
19
Order the following human developmental stages into a meaningful chronological sequence: Puberty, Adulthood, Childhood, Infancy, Senescence, Adolescence.
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Solution: Step 1: The earliest stage is 'Infancy'. Step 2: Followed by 'Childhood'. Step 3: Then 'Puberty' begins. Step 4: 'Adolescence' is the stage after puberty. Step 5: This leads to 'Adulthood'. Step 6: The final stage is 'Senescence' (old age). Step 7: The logical sequence is 4, 3, 1, 6, 2, 5.
20
Determine the 8th term of the series: 2, 6, 18, 54, ...
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Solution: Step 1: Identify the pattern in the given series of numbers. Step 2: Observe that each term is obtained by multiplying the previous term by 3 (2 × 3 = 6, 6 × 3 = 18, 18 × 3 = 54). Step 3: This indicates that the series is a Geometric Progression (G.P.). Step 4: The first term (a) is 2, and the common ratio (r) is 3. Step 5: The formula for the nth term of a G.P. is a_n = a * r^(n-1). Step 6: To find the 8th term (n=8), substitute the values into the formula: a_8 = 2 * 3^(8-1) = 2 * 3^7. Step 7: Calculate 3^7 = 2187. Step 8: Multiply the result by 2: 2 * 2187 = 4374. Step 9: The 8th term of the series is 4374.
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