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Manager  Joined: 22 Dec 2011
Posts: 226
If P and Q are positive integers, and n is the decimal  [#permalink]

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12 00:00

Difficulty:   55% (hard)

Question Stats: 60% (01:40) correct 40% (02:02) wrong based on 508 sessions

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If P and Q are positive integers, and n is the decimal equivalent of P/Q, which of the following must make n a finite number?

I. P = 49, Q = 256
II. Q = 32
III. P = 75, Q = 384

A. None
B. I only
C. II only
D. III only
E. I, II, III

Originally posted by Jp27 on 17 Nov 2012, 09:48.
Last edited by Bunuel on 18 Nov 2012, 04:50, edited 1 time in total.
Renamed the topic and edited the question.
Manager  Joined: 22 Dec 2011
Posts: 226
Re: If P and Q are positive integers,  [#permalink]

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My doubt is if it were given P and Q to be positive numbers and I)& III) are only correct right?
As the P can be 1/3.

Cheers
VP  Joined: 02 Jul 2012
Posts: 1161
Location: India
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GMAT 1: 740 Q49 V42 GPA: 3.8
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Re: If P and Q are positive integers,  [#permalink]

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Jp27 wrote:
My doubt is if it were given P and Q to be positive numbers and I)& III) are only correct right?
As the P can be 1/3.

Cheers
]
I should think so... Infact.. If it had been given as postive numbers, P could be any irrational number such as $$\sqrt{2},\sqrt{3}, \sqrt{5}$$

So, the answer would be only 1 & 3.

Kudos Please... If my post helped.
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Joined: 18 Jul 2012
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Re: If P and Q are positive integers, and n is the decimal  [#permalink]

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1
It is given in the question stem that P and Q are positive integers.
Intern  Joined: 04 May 2013
Posts: 44
Re: If P and Q are positive integers, and n is the decimal  [#permalink]

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1
A. P/Q = (49/256)= (7)(7)/(16)(16)
P/Q = (7/16)*(7/16) = .4125 * .4125 = finite
B. 32 = 2^5. Any number (odd/even) divided by 2^n will always be finite.
C. 75/384 = (3*5^2)/(2^7*3) ---> 3 gets cancelled and we have 5^2 / 2^7 - always finite because of 2^7.

Correct answer: E (I, II, and III)
Intern  Joined: 02 Feb 2012
Posts: 25
GPA: 4
Re: If P and Q are positive integers,  [#permalink]

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1
MacFauz wrote:
Jp27 wrote:
My doubt is if it were given P and Q to be positive numbers and I)& III) are only correct right?
As the P can be 1/3.

Cheers
]
I should think so... Infact.. If it had been given as postive numbers, P could be any irrational number such as $$\sqrt{2},\sqrt{3}, \sqrt{5}$$

So, the answer would be only 1 & 3.

Kudos Please... If my post helped.

As long as the denominator can be expressed as powers of prime factors, the fraction will always be finite...
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Re: If P and Q are positive integers, and n is the decimal  [#permalink]

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The best trick to find out whether a fraction will yield a definite decimal number is to check whether the denominator can be expressed in terms of the power of 2 and/or 5. If yes, then the fraction will yield a definite decimal.
In the above question 256, 32 and 384 can be expressed in powers of 2 as well.
Hence I, II and III are correct.
Regards
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Manager  Joined: 14 Jun 2011
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Re: If P and Q are positive integers,  [#permalink]

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avinashrao9 wrote:
MacFauz wrote:
Jp27 wrote:
My doubt is if it were given P and Q to be positive numbers and I)& III) are only correct right?
As the P can be 1/3.

Cheers
]
I should think so... Infact.. If it had been given as postive numbers, P could be any irrational number such as $$\sqrt{2},\sqrt{3}, \sqrt{5}$$

So, the answer would be only 1 & 3.

Kudos Please... If my post helped.

As long as the denominator can be expressed as powers of prime factors, the fraction will always be finite...

I dont think so... In 121/81 , 81 can be expressed as powers of prime factor(3), but the fraction will not be finite
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Re: If P and Q are positive integers,  [#permalink]

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avinashrao9 wrote:
MacFauz wrote:
Jp27 wrote:
My doubt is if it were given P and Q to be positive numbers and I)& III) are only correct right?
As the P can be 1/3.

Cheers
]
I should think so... Infact.. If it had been given as postive numbers, P could be any irrational number such as $$\sqrt{2},\sqrt{3}, \sqrt{5}$$

So, the answer would be only 1 & 3.

Kudos Please... If my post helped.

As long as the denominator can be expressed as powers of prime factors, the fraction will always be finite...

That is not entirely correct. What you state is valid only for 2,5 or both.Also, the given fraction should be a reduced fraction.
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Joined: 02 Sep 2009
Posts: 53709
Re: If P and Q are positive integers,  [#permalink]

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1
1
avinashrao9 wrote:
MacFauz wrote:
Jp27 wrote:
My doubt is if it were given P and Q to be positive numbers and I)& III) are only correct right?
As the P can be 1/3.

Cheers
]
I should think so... Infact.. If it had been given as postive numbers, P could be any irrational number such as $$\sqrt{2},\sqrt{3}, \sqrt{5}$$

So, the answer would be only 1 & 3.

Kudos Please... If my post helped.

As long as the denominator can be expressed as powers of prime factors, the fraction will always be finite...

That's not true. Any positive integer can be expressed as powers of primes.

Theory:
Reduced fraction $$\frac{a}{b}$$ (meaning that fraction is already reduced to its lowest term) can be expressed as terminating decimal if and only $$b$$ (denominator) is of the form $$2^n5^m$$, where $$m$$ and $$n$$ are non-negative integers. For example: $$\frac{7}{250}$$ is a terminating decimal $$0.028$$, as $$250$$ (denominator) equals to $$2*5^2$$. Fraction $$\frac{3}{30}$$ is also a terminating decimal, as $$\frac{3}{30}=\frac{1}{10}$$ and denominator $$10=2*5$$.

Note that if denominator already has only 2-s and/or 5-s then it doesn't matter whether the fraction is reduced or not.

For example $$\frac{x}{2^n5^m}$$, (where x, n and m are integers) will always be the terminating decimal.

We need reducing in case when we have the prime in denominator other then 2 or 5 to see whether it could be reduced. For example fraction $$\frac{6}{15}$$ has 3 as prime in denominator and we need to know if it can be reduced.

Questions testing this concept:
does-the-decimal-equivalent-of-p-q-where-p-and-q-are-89566.html
any-decimal-that-has-only-a-finite-number-of-nonzero-digits-101964.html
if-a-b-c-d-and-e-are-integers-and-p-2-a3-b-and-q-2-c3-d5-e-is-p-q-a-terminating-decimal-125789.html
700-question-94641.html
is-r-s2-is-a-terminating-decimal-91360.html
pl-explain-89566.html
which-of-the-following-fractions-88937.html

Hope it helps.
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Re: If P and Q are positive integers, and n is the decimal  [#permalink]

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Jp27 wrote:
If P and Q are positive integers, and n is the decimal equivalent of P/Q, which of the following must make n a finite number?

I. P = 49, Q = 256
II. Q = 32
III. P = 75, Q = 384

A. None
B. I only
C. II only
D. III only
E. I, II, III

the thing to know here is that in any base x a fraction 1/n (in the smallest form) results in a finite decimal form if n can be represented in power of x or of x's factor(s).
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Re: If P and Q are positive integers, and n is the decimal  [#permalink]

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I can understand that option 1 & 2 's denominator can be expressed in terms of 2^m, but in option 3, 384 cannot be fully expressed in powers of 2. So, how can it be terminating decimal? Re: If P and Q are positive integers, and n is the decimal   [#permalink] 31 Dec 2018, 01:37
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# If P and Q are positive integers, and n is the decimal

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