Number System Test

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Number System Test - 5

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Weekly Quiz Competition

Question 1
2 / -0.83

What is the number if 60% of it added to 60 gives the number itself ?

A
150

B
160

C
170

D
180

Solution

From ans …150
40% of numb = 60
60% of 150 = 90
90+60 = 150
Question 2
2 / -0.83

(6084)^1/2 = ?

A
78

B
±78

C
72

D
±72
Question 3
2 / -0.83

9/16 of a number is 51 greater than 50% of the number, then the number is

A
618

B
168

C
816

D
186

Solution

(9x/16)-(x/2) = 51
X = 51*16 = 816
Question 4
2 / -0.83

The sum of the number and its square is 1406. What is the number ?

A
47

B
42

C
32

D
37

Solution

See the last digit 06 …..go for 7
Last digit ..37+(37*37) = 7+49 = 16
So ans: 37
Question 5
2 / -0.83

The number is 0.01 is how many times as great as the number (0.0001)² ?

A
10⁵

B
10⁶

C
10⁴

D
10³

Solution

0.01 = 10^-2
(0.0001)² = 10^-8
10^-2 /10^-8 = 10⁶
Question 6
2 / -0.83

In a bag there are coins of 25 paise and 10 paise in the ratio of 5:16. If the bag contains Rs.16 then the number of 10 paise coin is

A
86

B
87

C
88

D
90

Solution

25*5+10*16 = 285
Rs 16 = 1600
No of 10p = 1600*16/285 = 89.82 = 90
Question 7
2 / -0.83

a+b = c and abc = 30, then what is the value of a³ + b³ –c³ ?

A
60

B
90

C
-90

D
-60

Solution

a³ + b³ –c³ = -3(abc) = -3(30) = -90
Question 8
2 / -0.83

a² + b² + c² = ab + bc + ca then the value of (a+b)/(b+c) is

A
1

B
2

C
3

D
4

Solution

Equation will be satisfied when a=b=c=1
(a+b)/c = (1+1)/(1+1) = 2/2 = 1
Question 9
2 / -0.83

(a-b) = 1, (b-c) = 2 and (c-a) = 3 then the value of (a³ +b³ +c³ -3abc)/(a+b+c) is

A
5

B
6

C
7

D
8

Solution

a³ + b³ + c³ - 3 a b c = ( a + b + c ) ( a² + b² + c² - bc - ab - ac ) .
(a³ +b³ +c³ -3abc)/(a+b+c)
= 1/2[(a-b) ² +(b-c)² +(c-a)² ]
= ½(1+4+9)
= 14/2 = 7
Question 10
2 / -0.83

If *=+, /=-, + = *, –= / then 43*561+500-100/10 = ?

A
3211

B
2388

C
2883

D
2838
Solution
Given the expression: 43*561+500-100/10
And the symbol replacements:
* becomes +
/ becomes -
+ becomes *
- becomes /
Substituting the symbols, the expression becomes:
43 + 561 * 500 / 100 - 10
Now, we solve step-by-step:
561 * 500 = 280500
280500 / 100 = 2805
Now the expression is:
43 + 2805 - 10
Continuing with addition and subtraction:
43 + 2805 = 2848
2848 - 10 = 2838
The correct answer is: (d) 2838
Question 11
2 / -0.83

Two third of a positive number and 25/216 of its reciprocal are equal.The number is

A
12/5

B
25/144

C
5/12

D
144/25

Solution

(2/3)x = (25/216)(1/x)
X² = (25 ×3)/(216 ×2) = 25/144
X = 5/12
Question 12
2 / -0.83

If 2(1/2) is added to a number and the sum multiplied by 4(1/2)and 3 is added to the product and then divide the sum by 1(1/5), the quotient becomes 25 .What is the number ?

A
5(1/2)

B
4(1/2)

C
2(1/2)

D
3(1/2)

Solution

{4(1/2)[X+2(1/2)]+3}/[1(1/5)] = 25
(9X/2)+(45/4)+3 = 25 ×(6/5)
9X/2 =63/4 X=7/2 or 3(1/2)
Question 13
2 / -0.83

In a division sum ,the divisor is 3 times the quotient and 6 times the remainder.If the remainder is 2 then the dividend is

A
36

B
40

C
45

D
50

Solution

Divident = Quotient ×Divisor +Remainder
Divisor = 6 ×2 = 12
Q = 12/3 = 4
Divident = 4 ×12+3 =48+2 = 50
Question 14
2 / -0.83

The sum of two number is 24.The greatest product of these two numbers can be

A
124

B
144

C
164

D
140

Solution

X + Y = 24
Greatest Product then x and y must be equal
Possibility of getting 24 12+12= 24
12 ×12 = 144
Question 15
2 / -0.83

Twenty times a positive integer is less than its square by 96.What is the integer ?

A
24

B
4

C
-24

D
-4

Solution

X² –20X = 96
X² -20X-96 = 0
(X-24)(X+4) = 0
X= 24, -4
positive integer = 24
Question 16
2 / -0.83

If (a-b) 3, (b-c) = 5 and (c-a) = 1 then the value of (a³ +b³ +c³ - 3abc)/(a+b+c)

A
17

B
17.5

C
18

D
18.5
Question 17
2 / -0.83

The product of the 2 consecutive odd number is 6723.What is the greater number ?

A
80

B
81

C
82

D
83

Solution

X ×(X+2) = 6723
X² + 2X = 6723
X² +2X-6723 = 0
(X –81)(X+83) = 0
Greatest number = 83
Question 18
2 / -0.83

The sum of three number is 264. If the first number be twice the second and third number be one third of the first then the second number is

A
82

B
72

C
76

D
87

Solution

2X+X+(2X/3) = 264
(6X+3X+2X)/3 = 264
11X/3 = 264
X= (264 ×3)/11 = 72
Question 19
2 / -0.83

If the number obtained on interchanging the digits of a 2 digit number is 18 more than the original number and the sum of the digit is 8.Then what is the original number?

A
35

B
53

C
32

D
34

Solution

Unit digit= x ; Ten ’s digit = (8-x)
[10(8-x)+x] –[10x+(8-x)] = 18
80-10x+x-10x-8+x = 18
-18x = 18-80+8
18x = 54
X = 54/18 = 3
8 –x = 8 –3 = 5
Hence the number is 35
Question 20
2 / -0.83

The sum of three consecutive multiple of 4 is 72 .What is the largest number ?

A
26

B
20

C
28

D
14

Solution

4x+(4x+4)+(4x+8) = 72
12x+12 = 72
X=(72-12)/12
X=5
Largest number = 4(5)+8 = 20+8 = 28

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Re-Attempt Weekly Quiz Competition

Number System Test - 5

Result

Number System Test - 5

Score

-

Rank

-

SHARING IS CARING

Question 1

150

160

170

180

Solution

Question 2

78

±78

72

±72

Question 3

618

168

816

186

Solution

Question 4

47

42

32

37

Solution

Question 5

105

106

104

103

Solution

Question 6

86

87

88

90

Solution

Question 7

60

90

-90

-60

Solution

Question 8

1

2

3

4

Solution

Question 9

5

6

7

8

Solution

Question 10

3211

2388

2883

2838

Solution

Question 11

12/5

25/144

5/12

144/25

Solution

Question 12

5(1/2)

4(1/2)

2(1/2)

3(1/2)

Solution

Question 13

10⁵

10⁶

10⁴

10³