XAT 2015: Quantitative Reasoning - Numbers Puzzles

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Published : Tuesday, 19 August, 2014 02:55 PM 
 
 
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 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
 
Answer)
 
Option (3). 96 digits
 
Explanatory Answers)
 
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 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 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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