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A terminating decimal is a number with a finite number of

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A terminating decimal is a number with a finite number of

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Source: Princeton Review

A terminating decimal is a number with a finite number of nonzero digits. For example, 35, 14.07, and 5.341 are three terminating decimals. For positive integers, p and q, when p/q is expressed as a decimal, is p/q a terminating decimal?

1) p is the sum of three consecutive odd multiples of 5.
2) 2q^2 + 144 = 36q

The OA is C

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BTGmoderatorLU wrote:
Source: Princeton Review

A terminating decimal is a number with a finite number of nonzero digits. For example, 35, 14.07, and 5.341 are three terminating decimals. For positive integers, p and q, when p/q is expressed as a decimal, is p/q a terminating decimal?

1) p is the sum of three consecutive odd multiples of 5.
2) 2q^2 + 144 = 36q
A fraction will yield a terminating decimal if -- when the fraction is fully reduced -- the prime-factorization of its denominator includes only 2's and or 5's.

Statement 1:
Let x = an odd multiple of 5.
Since the next largest odd multiples of 5 will be x+10 and x+20, we get:
p = x + (x+10) + (x+20) = 3x + 30 = 3(x+10).
No information about the denominator.
INSUFFICIENT.

Statement 2:
2q² - 36x + 144 = 0
q² - 18x + 72 = 0
(q-6)(q-12) = 0
q = 6 or q = 12.

Case 1: p=2 and q=6
In this case, p/q = 2/6 = 1/3 = 0.333...
Since the decimal is non-terminating, the answer to the question stem is NO.
Case 2: p=9 and q=6
In this case, p/q = 9/6 = 3/2 = 1.5.
Since the decimal is terminating, the answer to the question stem is YES.

Since the answer is NO in Case 1 but YES in Case 2, INSUFFICIENT.

Statements combined:
Case 1: p/q = [3(x+10)]/6 = (x+10)/2.
Case 2: p/q = [3(x+10)]/12 = (x+10)/4 = (x+10)/(2*2).
When the fraction in each case is fully reduced, the prime-factorization of the denominator includes only 2's, implying that the decimal will be terminating.
Thus, the answer to the question stem is YES.
SUFFICIENT.

The correct answer is C.

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