Find the values of the letters in each of the following and give reasons for the steps involved. 1.
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If \[21y5\] is a multiple of 9, where y is a digit, what is the value of y?
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If \[31z5\] 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?
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If \[24x\] is a multiple of 3, where \[x\] is a digit, what is the value of \[x\]? (Since \[24x\] is a multiple of 3, its sum of digits \[6+x\] is a multiple of 3; so \[6+x\] is one of these numbers: 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 or 15. Therefore, \[x=0\] or 3 or 6 or 9. Thus, \[x\] can have any of four different values.)
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