Numbers

TYPES OF NUMBERS
  • Integers : All numbers whose fractional part is 0 (zero) like -3, -2, 1, 0, 10, 100 are integers.
  • Natural Numbers : Counting numbers like 1, 2, 3, 4, 5, 6 … Basically, all integers greater than 0 are natural numbers … More on Numbers
Question 1
Which is not the prime number?
Cross
43
Tick
57
Cross
73
Cross
101


Question 1-Explanation: 
A positive natural number is called prime number if nothing divides it except the number itself and 1. 57 is not a prime number as it is divisible by 3 and 19.
Question 2
How many terms are there in 3,9,27,81........531441?
Cross
25
Tick
12
Cross
13
Cross
14


Question 2-Explanation: 
3, 9, 27, 81..............531441 form a G.P. 
with a = 3 and r = 9/3 = 3
Let the number of terms be n
According to the formula, Nth term of the G.P is represented as Tn = a x rn-1
Then 3 x 3n-1 = 531441
∴ 3n = 312
∴ n = 12
Question 3

If the average of four consecutive odd numbers is 16, find the smallest of these numbers?

Cross

5

Cross

7

Tick

13

Cross

11



Question 3-Explanation: 
Let the numbers be x, x+2, x+4 and x+6
Then (x + x + 2 + x + 4 + x + 6)/4  = 16
∴ 4x + 12 = 64
∴ x = 13
Question 4
If the sum of two numbers is 13 and the sum of their square is 85. Find the numbers?
Tick
6 & 7
Cross
5 & 8
Cross
4 & 9
Cross
3 & 10


Question 4-Explanation: 
Let the numbers be x and 13-x Then x2 + (13 – x)2 = 85 ∴ x2 + 169 + x2 – 26x = 85 ∴ 2 x2 – 26x + 84 = 0 ∴ x2 – 13x + 42 = 0 ∴ (x-6)(x-7)=0 Hence numbers are 6 & 7
Question 5

The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?

Tick

4

Cross

5

Cross

6

Cross

None of these



Question 5-Explanation: 

Let the ten’s digit be x and the unit’s digit be y
Then (10x + y) – (10y + x) = 36
         9(x – y) = 36
           x – y = 4

Hence Option (A) is correct.

Question 6
A two-digit number is such that the product of the digits is 12. When 9 is subtracted from the number, the digits are reversed. The number is:
Cross
34
Cross
62
Tick
43
Cross
26


Question 6-Explanation: 
Let the tens digit of the number be a and ones digit be b.
Given:
ab = 12 ................(i) and,
(10a + b) - (10b + a) = 9
10a + b - 10b - a = 9
9a - 9b = 9
9(a-b) = 9
(a-b) = 1 .................(ii)
Factors of 12 = 1, 2, 3, 4, 6, 12. and from equation (ii), (a - b) = 1 So, a = 4 & b = 3. Required number = ab = 43.
Question 7
Find a positive number which when increased by 16 is equal to 80 times the reciprocal of the number
Cross
20
Cross
-4
Cross
-10
Tick
4


Question 7-Explanation: 
Let the number be x.
Then x + 16 = 80 * (1/x)
x2 + 16x – 80 = 0
x2 + 20x – 4x – 80 =0
(x + 20) (x -4)
Therefore x = 4
Question 8
What is the sum of two consecutive odd numbers, the difference of whose squares is 56?
Cross
30
Tick
28
Cross
34
Cross
32


Question 8-Explanation: 
Let the no. be x and (x +2).
Then (x + 2)2 – x2 = 56
4x + 4 = 56
x + 1 = 14
x = 13
Sum of numbers = x + (x +2) = 28
Question 9
The product of two numbers is 108 and the sum of their squares is 225. The difference of the number is:
Cross
5
Cross
4
Tick
3
Cross
None of these


Question 9-Explanation: 
Let the numbers be x and y.
Then xy = 108 and x2 + y2 = 225
(x –y)2 = x2 + y2 – 2xy
(x –y)2 = 225 – 216
(x –y)2 = 9
Therefore (x –y) = 3
Question 10
The average of 21 results is 20. Average of 1st 10 of them is 24 that of last 10 is 14. the result of 11'th is :
Cross
42
Cross
44
Cross
46
Tick
40


Question 10-Explanation: 
 11\'th result = sum of 21 results – sum of 20 results
             = 21 x 20 – (24 x 10 + 14 x 10)
             = 420 – (240 + 140)
             = 420- 380 = 40
There are 28 questions to complete.

  • Last Updated : 28 Jun, 2021

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