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1. Write a 2-digit number ab and the number obtained by reversing its digits i.e., ba. Find

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their sum. Let the sum be a 3-digit number dad i.e., ab + ba = dad

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(10a + b) + (10b + a) = dad

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11(a + b) = dad

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The sum a + b can not exceed 18 (Why?).

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Is dad a multiple of 11?

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Is dad less than 198?

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Write all the 3-digit numbers which are multiples of 11 upto 198.

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Find the values of a and d.

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3. If 21y5 is a multiple of 9, where y is a digit, what is the value of y?

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4. If 31z5 is a multiple of 9, where z is a digit, what is the value of z? You will find that

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there are two answers for the last problem. Why is this so?

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5. If 24x is a multiple of 3, where x is a digit, what is the value of x? (Since 24x is a

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multiple of 3, its sum of digits 6 + x is a multiple of 3; so 6 + x is one of these numbers:

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0, 3, 6, 9, 12, 15, 18, ... . But since x is a digit, it can only be that 6 + x = 6 or 9 or 12

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or15. Therefore, x = 0 or 3 or 6 or 9. Thus, x can have any of four different values.)

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6. If 31z5 is a multiple of 3, where z is a digit, what might be the values of z?

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(2) all the multiples of 11 are 121, 132, 143, 154, 165, 176. 187, 198.

 

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