Quantitative Aptitude

Number Series

2,662 Questions
All First differences and arithmetic progressions 812 Successive multiplication or division 429 Step-wise calculations 349 Squares and cubes based 338 Separate alternate positions 241 Inter-term operations 144 Mixed-operation rules 138 Unconventional pattern solving 74 Fractional and decimal operations 60 Prime number based 54 Digit operations 23

Number Series Questions

Multiple choice

If the terms of a sequence is defined by Sn = 5 81 − n , n ≥ 1 . For a positive integer m, let Um = Sm + Sm-1 + Sm-2 + ....... + S1, i.e. Um denotes the sum of first m terms of the sequence. Find the value of U51 - U50.

  1. (531 + 530)

  2. (531 + 1)

  3. (530 – 1)

  4. 530

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Interpreting the sequence as S_n = 5^(81-n), the difference U_51 - U_50 contains only the 51st term, S_51. Therefore, S_51 = 5^(81-51) = 5^30.

Multiple choice

Directions: In the following number series, one of the numbers is wrong. Find it out. 8, 12, 28, 60, 180, 630

  1. 8

  2. 12

  3. 28

  4. 60

  5. 630
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The pattern is: 8*1+4=12, 12*2+4=28, 28*3+4=88. The sequence provided is 8, 12, 28, 60, 180, 630. The term 60 should be 88, and 88*4+4=356. Alternatively, checking the differences: 4, 16, 32, 120, 450. The pattern is likely multiplication based. 28 is the incorrect term as it breaks the progression.

Multiple choice

Directions: The following number series has a wrong number in it. Find it out and mark your answer accordingly: 29, 28, 32, 25, 39, 14

  1. 25

  2. 29

  3. 28

  4. 14

  5. 39
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The pattern is: 29 - 1 = 28, 28 + 4 = 32, 32 - 7 = 25, 25 + 10 = 35, 35 - 13 = 22. The sequence is -1, +4, -7, +10, -13. The numbers should be 29, 28, 32, 25, 35, 22. The number 39 and 14 are incorrect based on this pattern, but 25 is the first deviation point.

Multiple choice

Directions: Answer the question independently. What is the sum of first 30 terms of the series 1, 3, 6, 10, 15, 21, 28….

  1. 5960

  2. 4960

  3. 4495

  4. 4060
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The series is 1, 3, 6, 10... which are triangular numbers. The n-th term is n(n+1)/2. Sum of first 30 terms = sum_{n=1 to 30} [n(n+1)/2] = 0.5 * [sum(n^2) + sum(n)]. Sum(n^2) = 30(31)(61)/6 = 9455. Sum(n) = 30(31)/2 = 465. Total sum = 0.5 * (9455 + 465) = 0.5 * 9920 = 4960.