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

In the arithmetic sequence the first term is $8$, the common difference is $4$, and the sum of the first $n$ terms is $2808$. Find the value of $n$.
  1. $31$
  2. $36$
  3. $78$
  4. $41$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The sum of an arithmetic series is given by S = n/2 * (2a + (n-1)d). Plugging in a=8, d=4, and S=2808 gives 2808 = n/2 * (16 + (n-1)4), which simplifies to 2808 = n(8 + 2n - 2) = 2n^2 + 6n. Solving the quadratic 2n^2 + 6n - 2808 = 0 or n^2 + 3n - 1404 = 0 yields n=36.

Multiple choice

Given an arithmetic progression with its first three terms as $2t, 5t-1$ and $6t+2$, for some real number $t$. Find the value of the fourth term of the sequence.
  1. $4$
  2. $8$
  3. $10$
  4. $16$
  5. $19$
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

In an AP, the difference between consecutive terms is constant: (5t-1) - 2t = (6t+2) - (5t-1). So, 3t - 1 = t + 3, which means 2t = 4, so t = 2. The terms are 2(2)=4, 5(2)-1=9, 6(2)+2=14. The common difference is 5. The fourth term is 14 + 5 = 19.

Multiple choice

Find the wrong term in sequence : 5, 27, 61, 122, 213, 340, 509

  1. 27

  2. 61

  3. 122

  4. 509

  5. 213
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The sequence follows the pattern n^3 - 1, starting from n=2. For n=2, 2^3-1=7; n=3, 3^3-1=26; n=4, 4^3-1=63; n=5, 5^3-1=124; n=6, 6^3-1=215; n=7, 7^3-1=342; n=8, 8^3-1=511. The given sequence 5, 27, 61, 122, 213, 340, 509 does not match this pattern, suggesting a different logic; however, checking differences: 22, 34, 61, 91, 127, 169. The second differences are 12, 27, 30, 36, 42. The term 27 is clearly the outlier in the progression.

Multiple choice

Find the wrong term in sequence : 1, 5, 5, 9, 7, 11, 11, 15, 12, 17

  1. 11

  2. 12

  3. 17

  4. 15

  5. 9
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The sequence is formed by repeating the difference pattern of +4, +0, +4, -2. Following this pattern, after 15, we should subtract 2 to get 13, and then add 4 to get 17. Therefore, 12 is the wrong term and should be replaced by 13.

Multiple choice

Find the wrong term in sequence : 17, 18, 22, 31, 46, 72

  1. 17

  2. 18

  3. 31

  4. 46
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Differences: 18-17=1, 22-18=4, 31-22=9, 46-31=15, 72-46=26. The sequence of differences is 1^2, 2^2, 3^2, 4^2 (which should be 16), 5^2 (which should be 25). 31+16 = 47. 47+25 = 72. So 46 is the wrong term.