Numbers - Quiz

5,12,20,29,39,__
Here, the difference between 5 and 12 is 7.
And the difference between 12 and 20 20 is 8.
And the difference between 20 and 29 is 9.
And the difference between 29 and 39 is 10. 
Since the difference is incredible by 1. 
And the next number could be 50.
Because the difference between 39 and 50 is 11 which is the next number of previous difference.
Option d is correct.

Let's say the number we are trying to find is x. We know that the number is multiplied by one-third of itself to get 192, so we can write the equation:

x * (1/3) * x = 192
Simplifying the left side of the equation, we get:

(1/3) * x^2 = 192
Multiplying both sides of the equation by 3, we get:

x^2 = 576
Taking the square root of both sides of the equation, we get:

x = 24
Therefore, the number we are looking for is 24.

 When multiplying numbers, the unit digit of the final product is determined by the product of the unit digits of the individual numbers. 

For example, if we multiply 148 by 163 by 236, the unit digit of the final product will be the product of the unit digits of each of these numbers, which is 8 * 3 * 6 = 24. 

Since 4 is the unit digit of 24, the unit digit of the final product will be 4.

Letting the positive number be x and then expressing the first condition in terms of x, we get:

2/3 x = 16/216 * 1/x

We can then multiply both sides by 216 and simplify to get:

x^2 = 16/144

Taking the square root of both sides gives:

x = sqrt(16/144)

Simplifying this expression gives:

x = sqrt(1/9)

Finally, since the number must be positive, we take the positive square root, which gives us:

x = 1/3 or 4/12

Therefore, the positive number that satisfies the given conditions is 1/3. 

To find the number of numbers between 100 and 600 that are divisible by 2, 3, and 7 simultaneously, we can first find the least common multiple (LCM) of 2, 3, and 7. The LCM of 2, 3, and 7 is 42, which means that any number that is divisible by 2, 3, and 7 must also be divisible by 42.
We can then count the number of multiples of 42 between 100 and 600. The first multiple of 42 greater than or equal to 100 is 105, and the last multiple of 42 less than or equal to 600 is 588. The number of multiples of 42 between these two numbers is:
(588 - 105) / 42 + 1 = 12
Therefore, there are 12 numbers between 100 and 600 that are divisible by 2, 3, and 7 simultaneously.

To find the quarter of the number, we need to first find the total number. We can set up an equation to represent the given information:
6/7 * x = 96


To solve for x, we can multiply both sides of the equation by 7/6:
x = (7/6) * 96
= 112


Now that we know the total number is 112, we can find one quarter of it by dividing it by 4:
1/4 * 112 = 28

Therefore, one quarter of the number is 28

Given:

x + (15 - x) = 15
x^2 + (15 - x)^2 = 113
Find:

x and (15 - x)
Substitute the first equation into the expression for (15 - x) to get:

x^2 + (15 - x)^2 = 113
x^2 + 225 + x^2 - 30x + x^2 = 113
3x^2 - 30x + 112 = 0
Factor the quadratic equation:

(x - 7)(x - 8) = 0
Solve for x:

x = 7 or x = 8
Therefore, the two numbers are x = 7 and (15 - x) = 8.

To find the values of x and y, we can use the information provided to create a system of equations and solve for x and y.

The first equation is given: x + y = 42
The second equation is given: xy = 437

To find the difference between x and y, we can use the equation x - y = sqrt[(x + y)^2 - 4xy], which is also given.

Substituting the values from the first two equations into the third equation, we get: x - y = sqrt[(42)^2 - 4 x 437] = sqrt[1764 - 1748] = sqrt[16] = 4.

From this equation, we can see that the difference between x and y is 4.
To find the values of x and y, we can set up the following system of equations:

x + y = 42
x - y = 4

Solving this system of equations using substitution, we get:

x = 23 and y = 19

Therefore, the values of x and y are 23 and 19, respectively.

0.008 = 8/100 = 1/1250.

Required difference = [3 ½ % of Rs.8400] – [3 1/3 % of Rs.8400]
= [(7/20-(10/3)]% of Rs.8400 =1/6 % of Rs.8400
= Rs. [(1/6)8(1/100)*8400] = Rs. 14