NIMCET Number Series Previous Year Questions (PYQs) – Page 5 of 6
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Showing 56 questions
Examine the following sequence of numbers
1
11
21
1211
111221
312211
13112221
1113213211
31131211131221
What are the next two numbers in the given series?
1
2
3
4
Solution
This is the look-and-say sequence.
Describing the last term gives the next two terms shown in option (D).
The following series is obtained by considering representations of decimal 99 in the different number system. The next two numbers in the sequence are
99, 90, 83, 78, ____, ____
1
2
3
4
Solution
How many numbers between 1 and 1000 (both excluded) are both squares and cubes?
1
2
3
4
Solution
Numbers that are both squares and cubes are perfect 6th powers.
6th powers between 1 and 1000:
2⁶ = 64
3⁶ = 729
Only these two.
Correct answer: 2
The missing number in the following series 336, 210, 120, 60, ______, 6 is
1
2
3
4
Solution
What is the next number in each of the following 3 sequences?
8 17 33 67 133 ? (1)
7 23 67 203 607 ? (2)
6 27 105 423 1689 ? (3)
1
2
3
4
Solution
(1) 8 → 17 → 33 → 67 → 133 → ?
Pattern: ×2 +1, ×2 −1, ×2 +1, ×2 −1, …
Next: 133×2 + 1 = 267
(2) 7 → 23 → 67 → 203 → 607 → ?
Pattern: ×3 +2, ×3 −2, ×3 +2, ×3 −2, …
Next: 607×3 + 2 = 1823
(3) 6 → 27 → 105 → 423 → 1689 → ?
Pattern: ×4 +3, ×4 −3, ×4 +3, ×4 −3, …
Next: 1689×4 + 3 = 6759
✅ Answers: (1) 267, (2) 1823, (3) 6759
Pattern: ×2 +1, ×2 −1, ×2 +1, ×2 −1, …
Next: 133×2 + 1 = 267
(2) 7 → 23 → 67 → 203 → 607 → ?
Pattern: ×3 +2, ×3 −2, ×3 +2, ×3 −2, …
Next: 607×3 + 2 = 1823
(3) 6 → 27 → 105 → 423 → 1689 → ?
Pattern: ×4 +3, ×4 −3, ×4 +3, ×4 −3, …
Next: 1689×4 + 3 = 6759
✅ Answers: (1) 267, (2) 1823, (3) 6759
Which number replaces the question mark?
3, 6, 18, 72, ?, 432
1
2
3
4
Solution
Sequence: 3, 6, 18, 72, ?, 432
Pattern (symmetric multipliers): ×2, ×3, ×4, ×3, ×2
3 → 6 : ×2
6 → 18 : ×3
18 → 72: ×4
72 → ? : ×3 → 72 × 3 = 216
216 → 432: ×2 ✅
✅ Answer: 216
Pattern (symmetric multipliers): ×2, ×3, ×4, ×3, ×2
3 → 6 : ×2
6 → 18 : ×3
18 → 72: ×4
72 → ? : ×3 → 72 × 3 = 216
216 → 432: ×2 ✅
✅ Answer: 216
Which should be the next two numbers in the series 28 25 5 21 18 5 14 ?
1
2
3
4
Solution
Pattern: –3, –20, +16 then repeat with adjustments.
14 – 3 = 11, next repeats 5.
There are 8436 steel balls, each with a radius
of 1 centimeter, stacked in a pile, with 1 ball on top, 3 balls in the second
layer, 6 in the third layer, 10 in the fourth and so on. The number of
horizontal layers in the pile is
1
2
3
4
Solution
Find out the wrong number in the following series.
15, 16, 34, 105, 424, 2124, 12756
1
2
3
4
Solution
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