艾易艾斯（aeas)数学逻辑推理-3

If xy represents a two-digit number, where x and y are positive single digits, which of the following CANNOT be true?

如果XY代表一个两位数，且x 和 y 是一位数且都是正整数，以下哪个结论不可能是正确的？

a.x + y = 6x

b.x – y = 9

c.x = y

d.7x = y

Explanation：

Step 1

x + y = 6x

⇒ y = 6x – x

⇒ y = 5x

The digit y of the number xy is 5 times the digit x if xy = 15.

15 is a two digit number of positive digits and hence x + y = 6x is true.

Step 2

x – y = 9 is possible only if 9 – 0 = 9

So, y = 9 and x = 0 and the number would be 09, which is one digit number and hence, x – y = 9 cannot be true.

Step 3

It is given that x and y are positive.

Both digits of the number xy may be equal if the number xy = 22. 22 is a two digit number of positive digits and hence x = y is true.

Step 4

7x = y

The digit y of the number xy is 7 times the digit x, if xy = 17.

17 is a two digit number of positive digits and hence 7x = y is true.