shekar123 wrote:
A terminating decimal is defined as a decimal that has a finite number of nonzero digits. Examples of terminating decimals are 0.24, 52, and 6.0314. x and y are positive integers. If x/y is expressed as a decimal, is it a terminating decimal?
(1) 40 < x < 45
(2) y = 8
Question Stem Analysis:We need to determine whether x/y is a terminating decimal, where x and y are positive integers. Recall that the decimal equivalent of a fraction is a terminating decimal only if the denominator of the most reduced form of the fraction contains only prime factors of 2 and 5.
Statement One Alone:\(\Rightarrow\) 40 < x < 45
Without any information about y, we cannot determine whether x/y terminates. If x = 41 and y = 3, then x/y does not terminate. On the other hand, if x = 41 and y = 10, then x/y = 4.1 is a terminating decimal. Since there are more than one possible answers, statement one alone is not sufficient.
Eliminate answer choices A and D.
Statement Two Alone:\(\Rightarrow\) y = 8
If y = 8, then regardless of the value of x, the denominator of the most reduced form of x/y = x/8 cannot contain any prime factors other than 2. This means that x/y is a terminating decimal. Statement two alone is sufficient.
Answer: B