CAT Questions

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In the given puzzle, the logic followed is

First digits comes from the number of letters in the word

Second digit is its serial number

Third digit is the addition of first and second digits

=> SUNDAY = 6713

51 + 52 + 53 + ...........+ 100

 = (1 + 2 + 3 + .... + 100) - (1 + 2 + 3 + ...... + 50)

 = It is in the form of n(n+1)2 series summation

= n1 = 100 , n2 = 50

=100100+12 - 5050+12

 =  (5050 - 1275) = 3775

Here Grass is to Erosion and whereas Dam is to Water.

Since Grass prevents Erosion similarly Dam prevents Water flow.

Hence, Grass : Erosion :: Dam : Water.

This can be easily simplified by Approximation process

Given 39.96% of 649.85 ÷13.07 = 45.14 - ? can be written as 

40% of 650 ÷13 = 45 - ?

$$\begin{gathered} 40 x 65010013 = 45 - ? \\ ? = 45 - 20 \\ ? = 25. \end{gathered}$$

Here the given number series 625, 625, 600, ?, 475, 875 follows a pattern that

625

625 + (0 x 0) = 625

625 - (5 x 5) = 625 - 25 = 600

600 + (10 x 10) = 600 + 100 = 700

700 - (15 x 15) = 700 - 225 = 475

475 + (20 x 20) = 475 + 400 = 875

Hence, the missing number in the given number series is 700.