Number and Letter Series: How to Spot the Pattern — MCQs with Answers (Set 1)

The given set is (3, 4, 55). Cube the second number: 4 x 4 x 4 = 64. Now square the first number: 3 x 3 = 9. Subtract: 64 – 9 = 55. This matches. So the rule is: third number = (second cubed) minus (first squared). Test (4, 3, 13): 3 cubed is 27, and 4 squared is 16, so 27 – 16 = 11, not 13. This fails. Test (5, 6, 190): 6 cubed is 216, and 5 squared is 25, so 216 – 25 = 191, not 190. This fails. Test (1, 3, 27): 3 cubed is 27, and 1 squared is 1, so 27 – 1 = 26, not 27. This fails. Test (2, 5, 121): 5 cubed is 125, and 2 squared is 4, so 125 – 4 = 121. This matches, so it works. Only (2, 5, 121) follows the rule. So the answer is (2, 5, 121).

The given set is (3, 2, 16). Square the first number: 3 x 3 = 9. Now double that square: 9 x 2 = 18. Then subtract the second number: 18 – 2 = 16. This matches. So the rule is: third number = (2 x first squared) minus second number. Test (2, 1, 8): 2 squared is 4, doubled is 8, and 8 – 1 = 7, not 8. This fails. Test (5, 3, 45): 5 squared is 25, doubled is 50, and 50 – 3 = 47, not 45. This fails. Test (4, 5, 27): 4 squared is 16, doubled is 32, and 32 – 5 = 27. This matches, so it works. Test (6, 10, 64): 6 squared is 36, doubled is 72, and 72 – 10 = 62, not 64. This fails. Only (4, 5, 27) follows the rule. So the answer is (4, 5, 27).

The given set is (9, 12, 33). Find the LCM of 9 and 12: the lowest common multiple is 36. Now find the HCF of 9 and 12: the highest common factor is 3. Subtract: 36 – 3 = 33. This matches. So the rule is: third number = LCM of the first two numbers, minus their HCF. Test (10, 15, 27): LCM of 10 and 15 is 30, and their HCF is 5. So 30 – 5 = 25, not 27. This fails. Test (8, 20, 36): LCM of 8 and 20 is 40, and their HCF is 4. So 40 – 4 = 36. This matches, so it works. Test (6, 8, 21): LCM of 6 and 8 is 24, and their HCF is 2. So 24 – 2 = 22, not 21. This fails. Test (12, 16, 47): LCM of 12 and 16 is 48, and their HCF is 4. So 48 – 4 = 44, not 47. This fails. Only (8, 20, 36) follows the rule. So the answer is (8, 20, 36).

The given set is (3, 4, 37). Square both numbers: 3 squared is 9, and 4 squared is 16. Now multiply the two numbers together: 3 x 4 = 12. Add all three results: 9 + 16 + 12 = 37. This matches. So the rule is: third number = (first squared) + (second squared) + (first x second). Test (5, 2, 39): 25 + 4 + 10 = 39. This matches, so it works. Test (2, 6, 50): 4 + 36 + 12 = 52, not 50. This fails. Test (6, 1, 42): 36 + 1 + 6 = 43, not 42. This fails. Test (3, 5, 47): 9 + 25 + 15 = 49, not 47. This fails. Only (5, 2, 39) follows the rule. So the answer is (5, 2, 39).

The given set is (3, 6, 12, 21), again a set of four numbers. Divide each number by the first: 6 / 3 = 2, 12 / 3 = 4, and 21 / 3 = 7. So the four numbers are always in the fixed ratio 1 : 2 : 4 : 7. So the rule is: second = 2 x first, third = 4 x first, fourth = 7 x first. Test (4, 8, 16, 27): 2 x 4 = 8, correct. 4 x 4 = 16, correct. But 7 x 4 = 28, not 27. This fails. Test (6, 12, 23, 42): 2 x 6 = 12, correct. But 4 x 6 = 24, not 23. This fails. Test (2, 5, 8, 14): 2 x 2 = 4, not 5. This fails at the very first check. Test (5, 10, 20, 35): 2 x 5 = 10, correct. 4 x 5 = 20, correct. 7 x 5 = 35, correct too. It works. Only (5, 10, 20, 35) follows the fixed ratio. So the answer is (5, 10, 20, 35).

The given set is (3, 8, 16, 12), a set of four numbers this time. Add 5 to the first number to get the second: 3 + 5 = 8. This matches. Double the second number to get the third: 8 x 2 = 16. This matches. Subtract 4 from the third number to get the fourth: 16 – 4 = 12. This matches. So the rule is a three-step chain: add 5, then double, then subtract 4. Test (4, 9, 17, 13): 4 + 5 = 9, which is correct. But 9 x 2 = 18, not 17. This fails at step two. Test (7, 12, 24, 19): 7 + 5 = 12, correct. And 12 x 2 = 24, correct. But 24 – 4 = 20, not 19. This fails at step three. Test (6, 11, 22, 18): 6 + 5 = 11, correct. 11 x 2 = 22, correct. And 22 – 4 = 18, correct. It works. Test (5, 11, 20, 16): 5 + 5 = 10, not 11. This fails at step one. Only (6, 11, 22, 18) follows the full chain. So the answer is (6, 11, 22, 18).

The given set is (9, 5, 25). Find the gap between the two numbers: 9 – 5 = 4. Now square that gap and add the first number: (4 x 4) + 9 = 16 + 9 = 25. This matches. So the rule is: third number = (the gap between first and second, squared) plus the first number. Test (8, 3, 30): the gap is 8 – 3 = 5, and 5 squared is 25, so 25 + 8 = 33, not 30. This fails. Test (11, 7, 27): the gap is 11 – 7 = 4, and 4 squared is 16, so 16 + 11 = 27. This matches, so it works. Test (12, 4, 72): the gap is 12 – 4 = 8, and 8 squared is 64, so 64 + 12 = 76, not 72. This fails. Test (7, 9, 15): the gap is 7 – 9 = -2, and squared that is 4, so 4 + 7 = 11, not 15. This fails. Only (11, 7, 27) follows the rule. So the answer is (11, 7, 27).

The given set is (3, 5, 24). Multiply the two numbers: 3 x 5 = 15. Now square the first number and add it: 15 + (3 x 3) = 15 + 9 = 24. This matches. So the rule is: third number = (first x second) plus (first squared). Test (4, 6, 40): 4 x 6 = 24, and 4 squared is 16, so 24 + 16 = 40. This matches, so it works. Test (5, 3, 38): 5 x 3 = 15, and 5 squared is 25, so 15 + 25 = 40, not 38. This fails. Test (6, 2, 44): 6 x 2 = 12, and 6 squared is 36, so 12 + 36 = 48, not 44. This fails. Test (2, 7, 17): 2 x 7 = 14, and 2 squared is 4, so 14 + 4 = 18, not 17. This fails. Only (4, 6, 40) follows the rule. So the answer is (4, 6, 40).

The given set is (23, 15, 47). Reverse the digits of the first number: 23 becomes 32. Now add the second number: 32 + 15 = 47. This matches. So the rule is: reverse the first number’s digits, then add the second number, to get the third. Test (34, 12, 46): reverse of 34 is 43, and 43 + 12 = 55, not 46. This fails. Test (52, 18, 70): reverse of 52 is 25, and 25 + 18 = 43, not 70. This fails. Test (27, 30, 57): reverse of 27 is 72, and 72 + 30 = 102, not 57. This fails. Test (41, 20, 34): reverse of 41 is 14, and 14 + 20 = 34. This matches, so it works. Only (41, 20, 34) follows the rule. So the answer is (41, 20, 34).

The given set is (2, 6, 18). Square the middle number: 6 x 6 = 36. Now multiply the first and third numbers: 2 x 18 = 36. Both results are equal. So the rule is: the middle number squared equals the first number times the third number. This means the three numbers form a rising chain with a fixed multiplying factor. Test (4, 8, 15): 8 squared is 64, but 4 x 15 = 60. These do not match, so it fails. Test (5, 15, 40): 15 squared is 225, but 5 x 40 = 200. These do not match, so it fails. Test (3, 12, 48): 12 squared is 144, and 3 x 48 = 144. These match, so it works. Test (2, 10, 51): 10 squared is 100, but 2 x 51 = 102. These do not match, so it fails. Only (3, 12, 48) follows the rule. So the answer is (3, 12, 48).

The given set is (8, 13, 23). Double the first number and subtract 3: (2 x 8) – 3 = 13. This matches the second number. Now double that second number and subtract 3 again: (2 x 13) – 3 = 23. This matches the third number too. So the rule is: each later number equals double the one before it, minus 3. Test (9, 15, 25): (2 x 9) – 3 = 15, which is correct so far. But (2 x 15) – 3 = 27, not 25. This fails. Test (11, 19, 35): (2 x 11) – 3 = 19, which matches. And (2 x 19) – 3 = 35, which also matches, so it works. Test (5, 7, 9): (2 x 5) – 3 = 7, which is correct so far. But (2 x 7) – 3 = 11, not 9. This fails. Test (12, 21, 36): (2 x 12) – 3 = 21, which is correct so far. But (2 x 21) – 3 = 39, not 36. This fails. Only (11, 19, 35) follows the rule all the way through. So the answer is (11, 19, 35).

The given set is (4, 3, 22). Square the first number: 4 x 4 = 16. Now add double the second number: 16 + (2 x 3) = 16 + 6 = 22. This matches. So the rule is: third number = (first squared) plus twice the second number. Test (5, 6, 37): 5 squared is 25, and 25 + 12 = 37. This matches, so it works. Test (3, 7, 22): 3 squared is 9, and 9 + 14 = 23, not 22. This fails. Test (6, 4, 42): 6 squared is 36, and 36 + 8 = 44, not 42. This fails. Test (2, 10, 23): 2 squared is 4, and 4 + 20 = 24, not 23. This fails. Only (5, 6, 37) follows the rule. So the answer is (5, 6, 37).

The given set is (2, 5, 13). Cube the first number: 2 x 2 x 2 = 8. Now add the second number: 8 + 5 = 13. This matches. So the rule is: third number = (first cubed) plus second number. Test (4, 2, 68): 4 cubed is 64, and 64 + 2 = 66, not 68. This fails. Test (2, 9, 16): 2 cubed is 8, and 8 + 9 = 17, not 16. This fails. Test (5, 6, 130): 5 cubed is 125, and 125 + 6 = 131, not 130. This fails. Test (3, 4, 31): 3 cubed is 27, and 27 + 4 = 31. This matches, so it works. Only (3, 4, 31) follows the rule. So the answer is (3, 4, 31).

The given set is (3, 7, 46). Square the second number: 7 x 7 = 49. Now subtract the first number: 49 – 3 = 46. This matches. So the rule is: third number = (second squared) minus first number. Test (5, 8, 58): 8 squared is 64, and 64 – 5 = 59, not 58. This fails. Test (2, 9, 77): 9 squared is 81, and 81 – 2 = 79, not 77. This fails. Test (4, 6, 32): 6 squared is 36, and 36 – 4 = 32. This matches, so it works. Test (6, 5, 18): 5 squared is 25, and 25 – 6 = 19, not 18. This fails. Only (4, 6, 32) follows the rule. So the answer is (4, 6, 32).

The given set is (6, 8, 28). Square the first number: 6 x 6 = 36. Now subtract the second number: 36 – 8 = 28. This matches. So the rule is: third number = (first squared) minus second number. Test (5, 3, 23): 5 squared is 25, and 25 – 3 = 22, not 23. This fails. Test (7, 5, 44): 7 squared is 49, and 49 – 5 = 44. This matches, so it works. Test (8, 10, 53): 8 squared is 64, and 64 – 10 = 54, not 53. This fails. Test (9, 6, 74): 9 squared is 81, and 81 – 6 = 75, not 74. This fails. Only (7, 5, 44) follows the rule. So the answer is (7, 5, 44).

The given set is (4, 7, 14). Multiply the first two numbers: 4 x 7 = 28. Now halve that product: 28 / 2 = 14. This matches. So the rule is: third number = (first x second) divided by 2. Test (6, 5, 15): 6 x 5 = 30, and 30 / 2 = 15. This matches, so it works. Test (8, 3, 13): 8 x 3 = 24, and 24 / 2 = 12, not 13. This fails. Test (9, 4, 17): 9 x 4 = 36, and 36 / 2 = 18, not 17. This fails. Test (10, 3, 14): 10 x 3 = 30, and 30 / 2 = 15, not 14. This fails. Only (6, 5, 15) follows the rule. So the answer is (6, 5, 15).

The given set is (6, 7, 13). Add the first two numbers: 6 + 7 = 13. This matches. So the rule is: third number = first number plus second number. Test (10, 5, 16): 10 + 5 = 15, not 16. This fails. Test (12, 9, 20): 12 + 9 = 21, not 20. This fails. Test (14, 3, 18): 14 + 3 = 17, not 18. This fails. Test (9, 8, 17): 9 + 8 = 17. This matches, so it works. Only (9, 8, 17) follows the rule. So the answer is (9, 8, 17).

The given set is (5, 9, 13). Check the gap between the first two numbers: 9 – 5 = 4. Now check the gap between the last two numbers: 13 – 9 = 4. Both gaps are equal. So the rule is: the three numbers rise by the same fixed gap each time. Test (6, 10, 16): the gaps are 10 – 6 = 4, and 16 – 10 = 6. These gaps differ, so it fails. Test (11, 15, 20): the gaps are 15 – 11 = 4, and 20 – 15 = 5. These gaps differ, so it fails. Test (10, 14, 18): the gaps are 14 – 10 = 4, and 18 – 14 = 4. These gaps match, so it works. Test (2, 6, 9): the gaps are 6 – 2 = 4, and 9 – 6 = 3. These gaps differ, so it fails. Only (10, 14, 18) follows the rule. So the answer is (10, 14, 18).

The given set is (3, 6, 12). Multiply the first two numbers: 3 x 6 = 18. Now subtract 6: 18 – 6 = 12. This matches. So the rule is: third number = (first x second) – 6. Test (4, 5, 16): 4 x 5 = 20, and 20 – 6 = 14, not 16. This fails. Test (5, 4, 14): 5 x 4 = 20, and 20 – 6 = 14. This matches, so it works. Test (6, 3, 20): 6 x 3 = 18, and 18 – 6 = 12, not 20. This fails. Test (7, 2, 10): 7 x 2 = 14, and 14 – 6 = 8, not 10. This fails. Only (5, 4, 14) follows the rule. So the answer is (5, 4, 14).

The given set is (4, 5, 17). Try tripling the first number: 4 x 3 = 12. Now add the second number: 12 + 5 = 17. This matches. So the rule is: third number = (3 x first) + second. Test (6, 2, 20): 6 x 3 = 18, and 18 + 2 = 20. This matches, so it works. Test (5, 4, 18): 5 x 3 = 15, and 15 + 4 = 19, not 18. This fails. Test (7, 3, 25): 7 x 3 = 21, and 21 + 3 = 24, not 25. This fails. Test (8, 1, 26): 8 x 3 = 24, and 24 + 1 = 25, not 26. This fails. Only (6, 2, 20) follows the rule. So the answer is (6, 2, 20).

Check Row 1: 4 + 3 = 7, and 4 x 3 = 12. Add these two results: 7 + 12 = 19. This matches. Check Row 2: 6 + 5 = 11, and 6 x 5 = 30. Add these two results: 11 + 30 = 41. This also matches. The rule is: third number = (first plus second) plus (first times second). Apply it to Row 3: 8 + 7 = 15, and 8 x 7 = 56. So the answer is 15 + 56 = 71.

Check Row 1: 9 + 5 = 14, and 9 – 5 = 4. Multiply: 14 x 4 = 56. This matches. Check Row 2: 11 + 6 = 17, and 11 – 6 = 5. Multiply: 17 x 5 = 85. This also matches. The rule is: third number = (first plus second) multiplied by (first minus second). Apply it to Row 3: 13 + 7 = 20, and 13 – 7 = 6. So the answer is 20 x 6 = 120.

Check Row 1: 7 x 5 = 35. Now subtract 3 times the second number: 3 x 5 = 15. So 35 – 15 = 20. This matches. Check Row 2: 9 x 4 = 36, and 3 x 4 = 12. So 36 – 12 = 24. This also matches. The rule is: third number = (first x second) – (3 x second). Apply it to Row 3: 11 x 6 = 66, and 3 x 6 = 18. So the answer is 66 – 18 = 48.

Add up Row 1: 10 + 16 + 19 = 45. Add up Row 2: 12 + 20 + 13 = 45. Both rows total 45, so every row in this grid adds up to 45. Row 3 already has 18 and 11. Together these add up to 29. The missing first number is 45 – 29, which is 16.

Look at Row 1. Double the first number: 4 x 2 = 8. Triple the second number: 6 x 3 = 18. Add them: 8 + 18 = 26. This matches the third number given. The rule is: third number = (2 x first) + (3 x second). Apply it to Row 2: 5 x 2 = 10, and 7 x 3 = 21. So the answer is 10 + 21 = 31.