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

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SVP
Status: Preparing for the GMAT
Joined: 02 Nov 2016
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Location: Pakistan
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A terminating decimal is a number with a finite number of nonzero digi  [#permalink]

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16 Mar 2017, 10:23
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55% (hard)

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70% (01:15) correct 30% (01:21) wrong based on 23 sessions

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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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Joined: 13 Oct 2016
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Re: A terminating decimal is a number with a finite number of nonzero digi  [#permalink]

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16 Mar 2017, 12:39
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1
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.

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