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# If P and Q are Positive Integers, is P/Q terminating?

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If P and Q are Positive Integers, is P/Q terminating?  [#permalink]

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Updated on: 06 Nov 2016, 09:22
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If P and Q are Positive Integers, is P/Q terminating?

(1) Every Prime Factor of Q is Greater than 2
(2) Every Prime Factor of Q is less than 13

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Originally posted by stonecold on 06 Nov 2016, 09:20.
Last edited by Bunuel on 06 Nov 2016, 09:22, edited 1 time in total.
Edited the question.
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Re: If P and Q are Positive Integers, is P/Q terminating?  [#permalink]

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07 Nov 2016, 19:34
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stonecold wrote:
If P and Q are Positive Integers, is P/Q terminating?

(1) Every Prime Factor of Q is Greater than 2
(2) Every Prime Factor of Q is less than 13

RULE any fraction having denominator with ONLY factors of 2 or 5 or both will be terminating decimal....

Now let's see the statements
1) if the denominator has only 5s, it is terminating otherwise not
Insuff

2) if the denominator has 2 or 5, then terminating, and if 3,7,11 then no
Insuff

Combined
Still if only 5, yes and if 3,7,11 No
Insuff

E
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Re: If P and Q are Positive Integers, is P/Q terminating?  [#permalink]

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09 Nov 2016, 11:09
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stonecold wrote:
If P and Q are Positive Integers, is P/Q terminating?

(1) Every Prime Factor of Q is Greater than 2
(2) Every Prime Factor of Q is less than 13

This problem is testing us on our knowledge of terminating decimals.

When solving this problem, we should remember that there is a special property of fractions that allows their decimal equivalents to terminate. This property states that:

In its most-reduced form, any fraction with a denominator whose prime factorization contains only 2s, 5s, or both produces decimals that terminate. A denominator with any other prime factors produces decimals that do not terminate.

Therefore, to determine whether P/Q can be expressed as a terminating decimal, we need to determine whether the prime factorization of Q contains only 2s and/or 5s.

Statement One Alone:

Every Prime Factor of Q is Greater than 2

The information in statement one is not enough to determine whether P/Q is terminating. For instance, if Q = 3, P/Q will NOT terminate; however, if Q = 5, P/Q WILL terminate. We can eliminate answer choices A and D.

Statement Two Alone:

Every Prime Factor of Q is less than 13

The information in statement two is not enough to determine whether P/Q is terminating. For instance, if Q = 3, P/Q will NOT terminate; however, if Q = 5, P/Q WILL terminate. We can eliminate answer choice B.

Statements One and Two Together:

Using statements one and two together, we still see that Q can still be 3 or 5. Thus, we cannot determine whether P/Q is terminating.

Answer: E
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Re: If P and Q are Positive Integers, is P/Q terminating?  [#permalink]

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04 Oct 2018, 08:19
stonecold wrote:
If P and Q are Positive Integers, is P/Q terminating?

(1) Every Prime Factor of Q is Greater than 2
(2) Every Prime Factor of Q is less than 13

P/Q terminating decimal means Q has to be 2,5,10 any combinations of 2,5

1) Prime factors of Q are greater than 2 this could be 3,5,7,11 etc.. maybe yes and maybe no

If Q = 5 then P/5 = terminating
if Q = 3 then P/3 = non-terminating.

Not sufficient.

2) Prime factors of Q are less than 13, this could be 11,7,5,3,2

if q = 2 then yes if q = 3 then no.

Not sufficient.

Even when combined Q could be 3,5,7,11 5 is terminating but any other value of Q is non-terminating.

so answer choice E
Re: If P and Q are Positive Integers, is P/Q terminating?   [#permalink] 04 Oct 2018, 08:19
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# If P and Q are Positive Integers, is P/Q terminating?

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