Number System/Averages

Question 1

Least prime no

Answer 1

2

Question 2

Prime nos between 1-100?

Answer 2

4422322321

Question 3

Sum of prime no less than 100

Answer 3

1060

Question 4

π is rational irrational?

Value?

Answer 4

Irrational

22/7

Question 5

Sum of first n natural nos?

Answer 5

n(n+1) /2

Question 6

Sum of first n odd nos?

Answer 6

n^2

Question 7

Sum of first n even nos?

Answer 7

n(n+1)

Question 8

Sum of squares of first n nos?

Answer 8

n(n+1) (2n+1) /6

Question 9

Sum of cubes of first n nos?

Answer 9

{n(n+1) /2}^2

Question 10

Divisibility rule of 7?

Answer 10

Remove last digit
Double it
Subtract from leftover no
Result divisible by 7

Question 11

Sequence of operation?

Answer 11

VODMAS

Question 12

(a+b) ^2 + (a-b) ^2

(a+b) ^2 - (a-b) ^2

Answer 12

2(a^2+b^2)

4 ab

Question 13

HCF and LCM given and one number given find other no?

Answer 13

HCF * LCM = one no. * other no.

Question 14

A number when divided by 120 gives 17 as remainder on dividing the same number by 15 what would be the remainder?

Answer 14

120/15 = 0 remainder
17/15 = 2 remainder

Ans: 2

Question 15

GCD of 1/2, 2/3, 3/4, 4/5

Answer 15

GCD : Greatest common divisor

LCM of 2,3,4,5 then reciprocal

Ans: 60

Question 16

The least number which when divided by 5,6,4 and 3 leaves a remainder 1 but when divided by 7 leaves no remainder.

Answer 16

LCM of 5,6,4,3 = 60
60+1
But not divisible by 7
Multiples check!

602 + 1 = 121
603 + 1 = 181
60*5 + 1 = 301

Ans: 301

Question 17

Five bells begin to toll together and toll respectively at intervals of 6, 5, 7, 10 and 12 seconds. How many times will they toll together in one hour excluding the one at the start ? A. 7 times B. 8 times C. 9 times D. 11 times

Answer 17

To toll together we need to take the LCM of each seconds of bell.

L.C.M. of 6, 5, 7, 10 and 12 = 420.

420/60 = 7 minutes

So, the bells will toll together after every 7 minutes.

Therefore, in 1-hour (or 60 minutes), the bells will toll together 8 times (7 x 8 = 56), excluding the one at the start.

Question 18

m/s to km/hr

Km/hr to m/s

Answer 18

18/5

5/18

Question 19

A is thrice as efficient as B then ratio of work done by A to B is?

Answer 19

3:1

Question 20

Average of 1st 23 multiples of 3?

Answer 20

23+1/2 = 12th place is in mid

So avg : 3*12 = 36

Question 21

Average of 1st n natural nos?

Answer 21

n+1/2

Question 22

Average of odd numbers between 2 numbers?

Answer 22

Avg = total number of odd numbers

Total no of odd numbers = n+1/2

Question 23

Avg of first n even nos?

Answer 23

n+1

Question 24

A               B
20            30
(Avg)       (Avg) 
         Total 
          Avg? 
3                  2   (ration of number)

Answer 24

203 + 302/3+2

Ans: 24

Question 25

Arithmetic Mean

• a, b
• a, b, c

Answer 25

a+b/2

a+b+c/3

Question 26

Geometric Mean

• a, b
• a, b, c

Answer 26

√ab
Or
(ab)^1/2

(abc) ^1/3

Question 27

Harmonic mean?

• a, b
• a, b, c

Answer 27

• 2 2ab
  ________ = _______

1/a + 1/b a+b

• 3 3abc
  ________ = ____________

1/a + 1/b + 1/c ab+bc+ac

Question 28

The average of 5 consecutive odd no is 25, find the largest no?

Answer 28

29

When the difference between two consecutive numbers is same then average is the middle value.
Difference between all the odd numbers are to show the average is 25 that is it is the middle value so the previous two and the after two values can be found out.

Question 29

Average age of ABCD 5 years ago was 45 years so their average age in the current year would be.

Answer 29

45+5 = 50

Question 30

A motorist travels to a place 150 km away at an average speed of 50 km per hour and returns at 30 km/h is average speed for the whole journey in kilometre per hour is?

Answer 30

Use harmonic mean to directly find the answer.

Or

150/50 = t1= 3
150/30 = t2 = 5

8 min total

Distance total = 300

Avg speed = 300/8 = 37.5 kn/hr