Logical Reasoning and Number Series for UGC NET Paper-1
Q.1: 1, 2, 6, 7, 21, 22, 66, ?
a) 67
b) 70
c) 132
d) 201
Ans: a)
Solution: Pattern is +1, × 3, +1,× 3…. 66 + 1 = 67
Q.2: 0, 6, 24, 60, 120, 210, ?
a) 240
b) 290
c) 336
d) 504
Ans: c)
Solution: Pattern is n³ – n: 1³-1, 2³-2, 3³-3, 4³-4, 5³-5, 6³-6. Next is 7³-7 = 343-7 = 336.
Q.3: 4, 9, 25, 49, 121, 169, ?
a) 196
b) 225
c) 256
d) 289
Ans: d)
Solution: These are squares of prime numbers: 2², 3², 5², 7², 11², 13². The next prime is 17, and 17² = 289.
Q.4: 2, 15, 41, 80, ?
a) 111
b) 120
c) 121
d) 132
Ans: d)
Solution: Differences are 13, 26, 39 (multiples of 13). Next difference is 52. So 80 + 52 = 132.
Q.5: 1, 2, 4, 7, 11, 16, ?
a) 20
b) 22
c) 23
d) 25
Ans: b)
Solution: Differences are +1, +2, +3, +4, +5. Next is +6. So 16 + 6 = 22.
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Q.6: 4, 7, 12, 19, 28, ?
a) 36
b) 39
c) 42
d) 49
Ans: b)
Solution: Pattern is n² + 3: 1²+3=4, 2²+3=7…. Next is 6²+3 = 39.
Q.7: 11, 13, 17, 19, 23, 25, ?
a) 26
b) 27
c) 29
d) 31
Ans: c)
Solution: Pattern is +2, +4, +2, +4…. 25 + 4 = 29. (Note: These are primes, but 25 is not. It’s a +2/+4 logic).
Q.8: 6, 12, 21, 33, ?
a) 38
b) 40
c) 45
d) 48
Ans: d)
Solution: Differences are +6, +9, +12. Next is +15. So 33+15 = 48.
Q.8: 2, 5, 10, 17, 26, 37, 50, ?
a) 63
b) 65
c) 67
d) 69
Ans: b)
Solution: Pattern is n² + 1: 1²+1, 2²+1…. Next is 8²+1 = 65.
Q.10: 3, 15, 35, 63, ?
a) 77
b) 84
c) 99
d) 105
Ans: c)
Solution: Pattern is (²2n)² – 1: 2²-1=3, 4²-1=15, 6^2-1=35, 8²-1=63. Next is 10²-1 = 99.
Q.11: 10, 18, 28, 40, 54, 70, ?
a) 85
b) 86
c) 87
d) 88
Ans: d)
Solution: Differences are 8, 10, 12, 14, 16. Next is 18. 70 + 18 = 88.
Q.12: 121, 112, ? , 94, 85, 76
a) 99
b) 103
c) 104
d) 108
Ans: b)
Solution: Constant difference of -9. 112 – 9 = 103.
Q.13: 2, 5, 11, 23, 47, ?
a) 77
b) 94
c) 95
d) 101
Ans: c)
Solution: Pattern is 2n + 1. 47 × 2 + 1 = 95.
Q.14: 1, 0.5, 0.25, 0.125, ?
a) 0.05
b) 0.0625
c) 0.0025
d) 0.625
Ans: b)
Solution: Each term is divided by 2. 0.125 ÷ 2 = 0.0625.
Q.15: 2, 15, 4, 12, 6, 7, ?, ?
a) 8, 8
b) 8, 0
c) 3, 8
d) 0, 8
Ans: b)
Solution: Alternate series:
Series 1: 2, 4, 6, 8 (increment of 2)
Series 2: 15, 12, 7… (differences -3, -5…). Next is -7 → 7-7 = 0.
Result: 8, 0.
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Q.16: 20, 19, 17, ?, 10, 5
a) 12
b) 13
c) 14
d) 15
Ans: c)
Solution: Differences are -1, -2, -3, -4, -5. 17 – 3 = 14.
Q.17: 3, 8, 13, 24, 41, ?
a) 70
b) 75
c) 80
d) 85
Ans: c)
Solution: This is a variant of the Fibonacci series: 3+8+2=13; 8+13+3=24; 13+24+4=41. Next is 24+41+5 = 70. Wait, let’s re-examine.
Alternative: 3+8=11(+2)=13; 8+13=21(+3)=24; 13+24=37(+4)=41. Next is 24+41=65(+5) = 70. Correct.
Q.18: 1, 3, 4, 8, 15, 27, ?
a) 45
b) 50
c) 55
d) 60
Ans: b)
Solution: Each term is the sum of the previous three terms: 1+3+4=8; 3+4+8=15; 4+8+15=27. Next is 8+15+27 = 50.
Q.19: 2, 4, 12, 48, 240, ?
a) 960
b) 1080
c) 1200
d) 1440
Ans: d)
Solution: Pattern is ×2, ×3, ×4, ×5. Next is ×6. 240 ×6 = 1440.
Q.20: 5, 2, 7, 9, 16, 25, ?
a) 41
b) 45
c) 48
d) 52
Ans: a)
Solution: Fibonacci type: 5+2=7, 2+7=9, 7+9=16, 9+16=25. Next is 16+25 = 41.
Q.21: 1, 2, 2, 4, 8, 32, ?
a) 64
b) 128
c) 256
d) 512
Ans: c)
Solution: Each term is the product of the previous two: 1×2=2, 2×2=4, 2×4=8, 4×8=32. Next is 8×32 = 256.
Q.22: 11, 10, 101, 100, 1001, 1000, ?
a) 10000
b) 10001
c) 11001
d) 1111
Ans: b)
Solution: Pattern is 10ⁿ+¹ followed by 10ⁿ.
10¹+¹=11, 10¹=10.
10²+¹=101, 10²=100.
10³+¹=1001, 10³=1000.
Next is 10⁴+¹ = 10001$.
Q.23: 7, 26, 63, 124, 215, ?
a) 315
b) 342
c) 343
d) 442
Ans: b)
Solution: Pattern is n³ – 1: 2³-¹=7, 3³-¹=26, 4³-¹=63, 5³-¹=124, 6³-¹=215. Next is 7³-¹ = 343-¹ = 342.
Q.24: 3, 12, 27, 48, 75, 108, ?
a) 147
b) 162
c) 183
d) 192
Ans: a)
Solution: Pattern is 3×n²: 3×1², 3×2², 3× 3²…. Next is 3 ×7² = 3 ×49 = 147
Q.25: 1, 2, 5, 26, ?
a) 676
b) 677
c) 725
d) 726
Ans: b)
Solution: Pattern is n² + 1: 1²+1=2; 2²+1=5; 5²+1=26; 26²+1 = 676+1 = 677.
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