Question 30
In a two-digit positive integer, the units digit is one less than the tens digit. The product of one less than the units digit and one more than the tens digit is 40. The number of such two-digit integers is
Correct Answer: 1
Solution
Let the tens digit be $$t$$, so the units digit is $$t - 1$$. The condition gives $$(t - 2)(t + 1) = 40$$, that is $$t^2 - t - 42 = 0$$, so $$(t - 7)(t + 6) = 0$$. Only $$t = 7$$ is a digit, so the only such number is 76 and there is exactly 1 such integer.
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