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# XAT 2025: Quantitative Reasoning - Number Puzzles

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XAT 2025  takers on 5th January, 2025  are advised to read the following important questions on Quantitative Reasoning - Numbers Puzzles

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

Option (2). 204 squares

• 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 12 + 22 + 32 + 42 + ... + 82 = 204

Question 2)

How many digits will the number 3200 have if the value of log103 = 0.4771?

1. 95
2. 94
3. 96
4. 91

Option (3). 96 digits

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

Take for example, log103, the value of log103 = 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 log1030 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 anumber, 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 3200.

If we take log we get log103200 = 200(log103) = 200 (0.4771) = 95.42.

Here, the characteristic is 95. Therefore, the number will have 96 digits.

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