Test

It is a good time for new post because a young student from Pakistan sent a test asking me the solution.

You could still see the question and the solution. 

1. 

Mr. and Mrs. Singh went to the magic show with their 3 children. The children were charged half the entrance fee. If the total fee charged was Rs.42, what is the entrance fee for each adult?

Solution:

They paid Rs 42 for 2 full entrance fees (tickets) and 3 halfs of an entrance fee. That means 3 and a half tickets, so the price of a full ticket (adult entrance fee) is Rs 42/3,5, which means Rs 12.

2.

 If we use (x+) to indicate the following sum

1+2+3+....+x

then find the value of k in the following equation

(21+) - (20+) = (k+)

Solution:

1    If you use (x+) to indicate the sum of the natural numbers from 1 to x, then you can rewrite the equation. Instead of (21+) – (20+), you’ll have (1+2+…+20+21) – (1+2+…+20) = 1+2+…+20+21-1-2-…-20 = 21. Now you need to find the k which resolves the equation: (k+) = 21. Here, you can apply Gauss’s sum, which says that (1+2+…+k) = [k*(k+1)]/2. Now [k*(k+1)]/2 = 21, and you multiply by 2, so k*(k+1) = 42. Which are the consecutive natural numbers that multiplied equal 42? k=6 and k+1=7.

3. 

Find total length of lines shown in the picture (all dimensions are in meters).

Solution:
The figure is a rectangle, which has the property that the opposite sides are parallel and equal, two by two, so the other 2 sides of the rectangle have the lengths of 108 and 144 meters. The fifth line is one of the diagonals of the rectangle, whose length can be calculated with Pythagorean theorem. This theorem says that the square of the hypotenuse equals to the sum of the squares of the two others sides, so 108^2 + 144^2 = x^2. You calculate the sum and you obtain 32400, so x^2 = 32400. x is the square root of 32400, which means 180. Now you can calculate the sum of all the lines in the figure, which is 108+144+108+144+180 = 684 m.
4. 

       Wich diagram shows relationship between animals, horses and lions?

Solution:

The figures have one big square, which represent the animals, and two more smaller squares, which represent the lions and the horses.

      Figure a) is wrong, because animals include lions, but lions don’t include horses.    

    Figure b) is wrong, because animals include both of lions and horses, not just only one of them.

    Figure c) is wrong, because lions and horses are different species, so there is no contact between them. 

     With all of this being said, figure d) is correct, because animals include both lions and horses, and there is no contact between the species.