The addition of A and 5 is giving 2 i. This is possible only when digit A is 7. In that case, the addition of A 7 and 5 will give 12 and thus, 1 will be the carry for the next step. In the next step,. The addition of A and 8 is giving 3 i. This is possible only when digit A is 5. In that case, the addition of A and 8 will give 13 and thus, 1 will be the carry for the next step.
The multiplication of A with A itself gives a number whose ones digit is A again. However, here the tens digit is given as 9. Considering the first step in which the addition of B and 7 is giving A i.
However, A is a single digit number. Hence, it is not possible. The multiplication of B and 5 is giving a number whose ones digit is B again. Therefore, this value of A is not possible.
The addition of 1 and B is giving 0 i. This is possible only when digit B is 9. In that case, the addition of 1 and B will give 10 and thus, 1 will be the carry for the next step.
The addition of B and 1 is giving 8 i. This is possible only when digit B is 7. In that case, the addition of B and 1 will give 8. The addition of A and B is giving 9 i. The sum can be 9 only as the sum of two single digit numbers cannot be Therefore, there will not be any carry in this step. Clearly, A is 8. We know that the addition of A and B is giving 9.
As A is 8, therefore, B is 1. If 21 y 5 is a multiple of 9, where y is a digit, what is the value of y? However, since y is a single digit number, this sum can be 9 only. Therefore, y should be 1 only. If 31 z 5 is a multiple of 9, where z is a digit, what is the value of z? However, since z is a single digit number, this sum can be either 9 or Therefore, z should be either 0 or 9. If 24 x is a multiple of 3, where x is a digit, what is the value of x? Thus, x can have any of four different values.
Since x is a single digit number, the sum of the digits can be 6 or 9 or 12 or 15 and thus, the value of x comes to 0 or 3 or 6 or 9 respectively. If 31 z 5 is a multiple of 3, where z is a digit, what might be the values of z?
Numbers can be written in general form. The general form of numbers are helpful in solving puzzles or number games. The games involve reversing two digit and three digit numbers , forming two digit numbers with given three digit numbers. To make the content more attractive and interesting some games and puzzles related to numbers are given. These games will be fun to play and will also clear the concepts of students. In certain number games, letters are replaced with numbers to form a code and vice-versa.
These are interesting trick number games based on the concept of general form of numbers. Divisibility tests explained in this chapter are as follows: Divisibility by If the one's digit of a number is 0, then the number is a multiple of 10; and if the one's digit is not 0, then the number is not a multiple of Divisibility by 5: If the one's digit of a number is 0 or 5, then it is divisible by 5. Divisibility by 9: A number is divisible by 9 if the sum of its digits is divisible by 9.
Otherwise, it is not divisible by 9. Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3. Otherwise, it is not divisible by 3. In this chapter, emphasis will be laid on why certain tests are done to check the divisibility. The entire chapter is summarized at the end with a focus on important points. Page No Question 1: Find the values of the letters in the following and give reasons for the steps involved.
Answer: The addition of A and 5 is giving 2 i. Clearly, B is 6. Hence, A and B are 7 and 6 respectively. Question 2: Find the values of the letters in the following and give reasons for the steps involved. Answer: The addition of A and 8 is giving 3 i. Clearly, B and C are 4 and 1 respectively. Hence, A, B, and C are 5, 4, and 1 respectively. Question 3: Find the value of the letter in the following and give reasons for the steps involved. Answer: The multiplication of A with A itself gives a number whose ones digit is A again.
Therefore, A should be 6. The multiplication is as follows. Hence, the value of A is 6. Question 4: Find the values of the letters in the following and give reasons for the steps involved.
Answer: The addition of A and 3 is giving 6. There can be two cases. Hence, the values of A and B are 2 and 5 respectively. Question 5: Find the values of the letters in the following and give reasons for the steps involved. Answer: The multiplication of 3 and B gives a number whose ones digit is B again. Hence, B must be 0 or 5. Let B is 5.
Hence, B must be 0 only. However, A cannot be 0 as AB is a two-digit number. Therefore, A must be 5 only. Hence, the values of A, B, and C are 5, 0, and 1 respectively. Question 6: Find the values of the letters in the following and give reasons for the steps involved. Answer: The multiplication of B and 5 is giving a number whose ones digit is B again. Hence, A can be 5 only. Hence, there are 3 possible values of A, B, and C. Question 7: Find the values of the letters in the following and give reasons for the steps involved.
Therefore, this value of B is not possible. Hence, the values of A and B are 7 and 4 respectively. Question 8: Find the values of the letters in the following and give reasons for the steps involved. Answer: The addition of 1 and B is giving 0 i. Hence, the values of A and B are 7 and 9 respectively. Question 9: Find the values of the letters in the following and give reasons for the steps involved. Answer: The addition of B and 1 is giving 8 i.
Hence, the values of A and B are 4 and 7 respectively. Question Find the values of the letters in the following and give reasons for the steps involved.
Answer: The addition of A and B is giving 9 i. Therefore, the addition is as follows. Hence, the values of A and B are 8 and 1 respectively. Question 1: If 21 y 5 is a multiple of 9, where y is a digit, what is the value of y? Answer: If a number is a multiple of 9, then the sum of its digits will be divisible by 9. Question 2: If 31 z 5 is a multiple of 9, where z is a digit, what is the value of z?
You will find that there are two answers for the last problem. Why is this so? Question 3: If 24 x is a multiple of 3, where x is a digit, what is the value of x?
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