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# if p and q are positive integers , will the fraction P/Q terminating?

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if p and q are positive integers , will the fraction P/Q terminating?  [#permalink]

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29 Aug 2018, 02:34
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Difficulty:

45% (medium)

Question Stats:

54% (01:24) correct 46% (00:57) wrong based on 50 sessions

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if p and q are positive integers , will the fraction P/Q terminating?
1) 7 is the factor of Q
2) 14 is not factor of P

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if p and q are positive integers , will the fraction P/Q terminating?  [#permalink]

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Updated on: 29 Aug 2018, 03:13
GMATbuster92 wrote:
if p and q are positive integers , will the fraction P/Q terminating?
1) 7 is the factor of Q
2) 14 is not factor of P

Concept: A fraction will be a terminating decimal ONLY when it its least form (HCF of Numerator and denominator is 1) the denominator has no prime factor other than 2 and 5

Question : is P/Q a terminating decimal?

Statement 1: 7 is the factor of Q

but we don't know how will P/Q will look in its least form (when all common factors between P and Q are cancelled out) hence

NOT SUFFICIENT

Statement 2: 14 is not factor of P

but we don't know how will P/Q will look in its least form (when all common factors between P and Q are cancelled out), specially the denominator of P/Q, hence

NOT SUFFICIENT

Combining the two statements

Case 1: P=7, Q=7, P/Q = 1 a terminating decimal
Case 2: P=1, Q=7, P/Q = 1/7 a Non-terminating decimal

NOT SUFFICIENT

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Originally posted by GMATinsight on 29 Aug 2018, 03:10.
Last edited by GMATinsight on 29 Aug 2018, 03:13, edited 1 time in total.
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Re: if p and q are positive integers , will the fraction P/Q terminating?  [#permalink]

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29 Aug 2018, 03:12
GMATbuster92 wrote:
if p and q are positive integers , will the fraction P/Q terminating?
1) 7 is the factor of Q
2) 14 is not factor of P

Given, p>0, q>0 and they are integers.

Question stem:- will the fraction P/Q terminating?

St1:- 7 is the factor of Q
Or, Q=7*k , where k is non-negative integer
1) when k=1, Q=1 then P/Q is a terminating decimal
2) When k is other than a multiple of 2 or 5, P/Q is not a terminating decimal.
Insufficient.

St2:- 14 is not factor of P
The denominator of a fraction decides whether its a terminating decimal or not.
Since nature of denominator is not given, we can't say about the nature of the fraction.
Insufficient.

Combined, same scenarios as stated in st1.

Insufficient.

Ans. (E)
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Re: if p and q are positive integers , will the fraction P/Q terminating?   [#permalink] 29 Aug 2018, 03:12
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