**Bonus**: Download XAT Tips PDF to crack XAT Exam 2022

**Question 1)**

How many squares can be formed using the checkered 1 * 1 squares in a normal chessboard?

(1) 64 squares

(2) 204 squares

(3) 1296 squares

(4) 65 squares

**Answer)**

Option (2). 204 squares

**Explanatory Answers)**

- There are 64 (1 * 1) squares in a chess board
- There are 49 (2 * 2) squares in a chess board
- There are 36 (3 * 3) squares in a chess board
- There are 25 (4 * 4) squares in a chess board
- There are 16 (5 * 5) squares in a chess board
- There are 9 (6 * 6) squares in a chess board
- There are 4 (7 * 7) squares in a chess board
- There is 1 (8 * 8) square in a chess board

The number of squares that can be formed using the 1 * 1 checkered squares of a chess board is therefore, given by the relation 1

^{2}+ 2^{2}+ 3^{2}+ 4^{2 }+ ... + 8^{2}= 204**Question 2)**

How many digits will the number 3200 have if the value of log

_{10}3 = 0.4771?(1) 95

(2) 94

(3) 96

(4) 91

**Answer)**

Option

**(3)**. 96 digits**Explanatory Answers)**

The logarithm of any number has two components. The characteristic and the mantissa.

Take for example, log

_{10}3, the value of log_{10}3 = 0.4771.Here, the 0 in the integral part is known as the characteristic and the value .4771 is known as the mantissa.

The value of log

_{10}30 is 1.4771.Notice that the value of mantissa remained the same while that of the characteristic changed from 0 to 1.

Given the log of a number, we will be able to find out the number of digits that the original number had by knowing the value of the characteristic.

- If the characteristic is '0', then the number is a single digit number
- If the characteristic is '1', then the number is a two-digit number
- If the characteristic is '5', then the number is a six-digit number

In the given problem, we need to find the number of digits of 3

^{200}.If we take log we get log

_{10}3^{200}= 200(log_{10}3) = 200 (0.4771) = 95.42.Here, the characteristic is 95. Therefore, the number will have 96 digits.

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