Below are three number series questions that will help you to prepare for Wipro and other company papers that would have number series questions in their pattern. Hope these questions help your preparation.

Question 1

Priya wanted to mail 120 messages to her friend Banu. She mailed 1 message on the first day, 2 messages on the second day, 3 messages on the third day and so on. How many days she required to send all messages to Banu?

a)16 days b) 17 days c) 15 days d) 14 days.

Answer : c) 15 days.

Solution:

Total number of messages = 120
On the 1^st day, Priya mailed 1 message to Banu.
On the 2^nd day, she mailed 2 messages to Banu and so on.....
Let X denote the number of messages send on the X^th day.
Therefore, 1^st day messages + 2^nd day messages + ....... + X^th day messages = 120.
1 + 2 + 3 + ...... + X = 120
X ( X + 1) / 2 = 120
X² + X = 240
X² + X - 240 = 0

By factoring the above eqn. we get
X ² - 15 X + 16 X - 240 = 0 ( the middle term is obtained by the multiplicants of last term i.e 15 x 16 =240 and the subtracted value is 1 which is the middle term)
X(X - 15) + 16 ( X - 15) = 0 or (X + 16)(X-15)
X = 15 0r X = -16
X = 15 ( since number of days cannot be negative).
So Priya required 15 days to send all messages.

Question 2

An IT company conducted interview for B.E Students. On the first day, they selected one student. On the second day, they selected 8 students and on the third day, they selected 27 students and so on. How many students will be selected if they conduct interview for 10 days?

a) 6050 b) 2530 c) 3025 d) 6025

Answer : c) 3025

Solution:

On the first day, they selected 1 student.
On the second day, they selected 8 students.
On the third day, they selected 27 students and so on.
Since they conduct interview for 10 days, the number of students selected on the 10^th day is 103 = 1000 students.
Total number of students selected = No. of students selected on 1^st day + No. of students selected on 2^nd day + ..... + No. of students selected on 10^th day.
Therefore, Total number of students selected = 1 + 8 + 27 + ..... + 1000.

= 1³ + 2³ + 3³ + .... + 10³.
By using the formula,
1³ + 2³ + 3³ + .... + n³ = (n (n+1) / 2)², we get
Number of students selected = (10 (10+1) / 2)².
= (10 *11*10*11) / 4
= 3025.
Hence, the company has selected 3025 students in 10 days.

Question 3

Jeeva has a story book of 2047 pages. He read 1 page on the first day, 2 pages on the second day, 4 pages on the third day, 8 pages on the fourth day and so on. How many days it took for Jeeva to complete the book?

a)10 days b) 12 days c) 11days d) 13 days

Answer : c) 11 days

Solution:

Total number of Pages = 2047
On the 1^st day, Jeeva read 1 page.
On the 2^nd day, he read 2 pages
On the 3^rd day, he read 4 pages and so on.....
Let X denote the number of pages read on the X^th day.
Therefore, 1 + 2 + 4 + .... + X = 2047

Then by using the formula, the sum of X numbers in G.P = a ( r^X -1)/(r-1) where a – First term & r – Common ratio, we get
1 (2^x - 1) / (2 - 1) = 2047
2^X-1 = 2047
2^X = 2048
2^X = 2¹¹
X = 11.
So, Jeeva took 11 days to complete the book.