- Question-1
- Explanation

(248 * 5^{3}) = ?

a) 21000

b) 31000

c) 41000

d) 51000

**Answer:** b) 31000

248 * (10/ 2)^{3} = (248 * 10 ^{3})/ 2^{3}

= 248000 / 8

= 31000

- Question-2
- Explanation

A number whose fifth part increased by 4 is equal to its fourth part diminished by 10, is

a) 240

b) 260

c) 280

d) 270

**Answer:** c) 280

Let the number be A

A / 5 + 4 = A/4 – 10

+ 4 + 10 = A/4 – A/5

14 = (5A – 4A) / 20

A = 280

- Question-3
- Explanation

At a farewell party of 60 students, each students shakes hands with every other student. How many total handshakes will there be?

a) 3540

b) 1770

c) 3600

d) 3000

Answer: b) 1770

First Student shakes hand with 59 others, Second student shakes hand with 58 others, and third with 57 others and so on till all have finished.

Thus the number of handshakes = 59 + 58+ 57 + 56……+ 3+ 2+ 1

Sum of n natural numbers = n(n+1)/2. In our case n = 59 and hence the sum becomes (59 * 60)/2 = 59 * 30 = 1770

- Question-4
- Explanation

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

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

X^{2 }+ X = 240

X^{2} + X – 240 = 0

By factoring the above equation we get

X2 – 15X + 16X – 240 = 0 ( The middle term is obtained by the multiplications of last term i.e. 15 * 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 or X = – 16

X = 15 ( Since number of days cannot be negative).

So Priya required 15 days to send all messages.

- Question-5
- Explanation

An IT Company conducted interview for 15 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

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 tenth 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

= 1^{3} + 2^{3} +…….. 10^{3}.

By using the formula,

=1^{3} + 2^{3} + 3^{3} +…….. +n^{3} = (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.