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A terminating decimal is a number with a finite number of nonzero digi

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A terminating decimal is a number with a finite number of nonzero digi [#permalink]

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New post 16 Mar 2017, 10:23
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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

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Re: A terminating decimal is a number with a finite number of nonzero digi [#permalink]

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New post 16 Mar 2017, 12:39
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SajjadAhmad wrote:
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


Hi

(1) x=odd integer

\(p=5*(x-2) + 5*x + 5*(x+2) = 5*3*x\), that is, p has at least one factor of 3. (ex. 5*7 + 5*9 + 5*11 = 5*27)

But we don't have any information about q.

(2) \(2q^2 - 36q + 144 = 0\)

\(q^2 - 18q + 72 = 0\)

\((q - 6)*(q - 12) = 0\)

\(q = 2*3\) or \(q = 2^2*3.\)

In order to be a terminating decimal denominator should be in the form \(2^a*5^b\).

We don't know whether 3 will divide \(p\) evenly or not. Insufficient.

(1)&(2) Now we definitely know that our nominator has at least one factor of 3 which after cancellation leaves denominators: \(2^1\) or \(2^2\). Sufficient.

Answer C.
Re: A terminating decimal is a number with a finite number of nonzero digi   [#permalink] 16 Mar 2017, 12:39
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A terminating decimal is a number with a finite number of nonzero digi

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