Numerical Answer Type(NAT)

Numerical questions require you to enter a number for the answer. The question might also require you to enter units or to specify the correct number of significant figures. The kind of answer that is expected should be clear from the question.

Example. 1

Alakhnanda walks 37 kms in an approximate South-West direction from her home to reach her school. She walks around 13 kms in an approximate South-East direction from her home to reach the post office. The market is 35 kms exactly East of her school. If she walks straight North from the market she reaches her home. If she walks east from the market, she reaches the post office. How much distance would she travel if she had to go from her school to the post office? 

Answer-

Here, H = Home, S = School, M = Market, P = Post Office
We are suppose to find distance from School to Post Office i.e. SP.

There are two Right Angle Triangles SMH and PMH, so using Pythagoras Theorem we can find the unknown distances.

Note- ∠SHP is not 90° so beware of using Pythagoras here to find SP directly.

P.S. - always draw EWNS directions before solving these questions.

Example. 2

A solid cube, 8 inches x 8 inches x 8 inches is painted red on all the faces. The cube is then sliced into smaller equal sized cubes of 1 inch x 1 inch x 1 inch. How many of these small cubes will have exactly twored faces?

 

Solution:

Total Red Planes = 6

Total Blue Planes = 4 x 2 = 8

Total Yellow Planes = 4

Total Brown Planes = (2x4)x2 = 16

Total Black Planes = 4x2 = 8

So finally Total Planes (faces) = 6 + 8 + 4 + 16 + 8 = 42

P.S. - Don't use too much shortcuts but count actual faces after separating different types of faces. 

(I recommend to carry a tracing paper along with you in the examination center, shading of the faces will be an easy task as the exam will be on a computer system)

  

Example 3

Count the number of cubes 

Once again, without making it complex just start counting - (this time layer wise)-

1st Layer + Last Layer (5th Layer) = 8+8 = 16 Cubes
2nd Layer + Second Last Layer (4th Layer) = 17 + 17 = 34 Cubes (3x3 cubes are surrounded by 2 cubes at each corner)
Middle Layer (3rd Layer) = 9 Cubes

Total Cubes = 16 + 34 + 9 = 59

(If your observation is good and you love solving Rubic Cubes then you can visualize that there is a 3x3x3 Cube and 4 Cubes on each corner. Hence total cubes = 3x3x3 + 4x8 = 27+32 = 59)