summer101 wrote:
What is the units digit of the number z?
(1) 17 < z < 20
(2) 18 < z < 21
OFFICIAL SOLUTION
Correct Answer: E
The units digit is the digit in the "ones" column; that is, it's the number directly to the left of the decimal point.
Statement 1 indicates tells us that the units digit is 8 or 9 because z could be the integers 18 or 19 and any associated mixed number- we don't know if z is an integer or not. Because we could arrive at multiple answers, this statement is insufficient.
Statement 2 indicates that z could be the integers 19 or 20 (or any associated mixed number), giving us the units digits 9 and 0, respectively. This statement is also insufficient. When taken together, the statements indicate that z must be between 18 and 20, but they do not specify that z must be an integer. For example, z could very well be 19, but it could be 18.5. Because we can still have two different units digits (8 and 9), the statements, even together, are insufficient, and the correct answer is E.
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