Arithmetical Reasoning Questions

Here given formula is 

a2 + b2 + c2 -ab- bc - ca = 0

and it is possible if and only if a = b = c.

From the trial and error method, 

1) Let a = b = c = 1

Now substitute these values of a, b, c in the above formula.

We get 1 + 1 + 1 - 1 - 1 - 1 = 3 - 3 = 0

2) Now, let a = b = c = 4

Now substitute these values of a, b, c in the above formula.

We get 16 + 16 + 16 - 16 - 16 - 16 = 48 - 48 = 0.

Hence, it is possible that 

a2 + b2 + c2 -ab- bc - ca = 0 iff a = b = c.

Technically or logically it is possible only once. As if you subtract 5 from 25 at first te result will be 20. Now, you can't subtract 5 from 25 since the left number is 20.

But if you go mathematically, it can be done infinite times and only 5 times without going into the negatives.

To find the sum of first 10 prime numbers

First 10 prime numbers = 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

Hence, The sum of the first 10 prime numbers is

(2+3+5+7+11+13+17+19+23+29) = 129 (ODD Number).

6 choose 3 means number of possible unordered combinations when 3 items are selected from 6 available items i.e, nothing but 6C3.

Now 6C3 = 6 x 5 x 4/3 x 2 x 1 = 120/6 = 20.

The given statement about similar triangles is TRUE.

Similar Triangles Theorem :: Similar triangles are two triangles with corresponding angles of equal measure, and the ratios of their corresponding sides' lengths are equal.

The process of collecting, organizing and analyzing data is called Statistics.