Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 22 Dec 2011
Posts: 271

If P and Q are positive integers, and n is the decimal [#permalink]
Show Tags
Updated on: 18 Nov 2012, 04:50
Question Stats:
63% (01:17) correct 37% (01:34) wrong based on 401 sessions
HideShow timer Statistics
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
Official Answer and Stats are available only to registered users. Register/ Login.
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.



Senior Manager
Joined: 22 Dec 2011
Posts: 271

Re: If P and Q are positive integers, [#permalink]
Show Tags
17 Nov 2012, 09:51
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: 1194
Location: India
Concentration: Strategy
GPA: 3.8
WE: Engineering (Energy and Utilities)

Re: If P and Q are positive integers, [#permalink]
Show Tags
17 Nov 2012, 11:57
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.
_________________
Did you find this post helpful?... Please let me know through the Kudos button.
Thanks To The Almighty  My GMAT Debrief
GMAT Reading Comprehension: 7 Most Common Passage Types



Intern
Status: wants to beat the gmat
Joined: 18 Jul 2012
Posts: 19
Location: United States

Re: If P and Q are positive integers, and n is the decimal [#permalink]
Show Tags
18 Nov 2012, 13:49
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]
Show Tags
20 Jul 2013, 10:51
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: 28
GPA: 4

Re: If P and Q are positive integers, [#permalink]
Show Tags
20 Jul 2013, 23:08
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...



VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1271
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75

Re: If P and Q are positive integers, and n is the decimal [#permalink]
Show Tags
20 Jul 2013, 23:49
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
_________________
Prepositional Phrases ClarifiedElimination of BEING Absolute Phrases Clarified Rules For Posting www.UnivScholarships.com



Manager
Joined: 14 Jun 2011
Posts: 82

Re: If P and Q are positive integers, [#permalink]
Show Tags
20 Jul 2013, 23:57
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
_________________
Kudos always encourages me



Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 620

Re: If P and Q are positive integers, [#permalink]
Show Tags
20 Jul 2013, 23:59
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.
_________________
All that is equal and notDeep Dive Inequality
Hit and Trial for Integral Solutions



Math Expert
Joined: 02 Sep 2009
Posts: 46264

Re: If P and Q are positive integers, [#permalink]
Show Tags
21 Jul 2013, 01:42
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 nonnegative 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 2s and/or 5s 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: doesthedecimalequivalentofpqwherepandqare89566.htmlanydecimalthathasonlyafinitenumberofnonzerodigits101964.htmlifabcdandeareintegersandp2a3bandq2c3d5eispqaterminatingdecimal125789.html700question94641.htmlisrs2isaterminatingdecimal91360.htmlplexplain89566.htmlwhichofthefollowingfractions88937.htmlHope it helps.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 22 Jan 2014
Posts: 159
WE: Project Management (Computer Hardware)

Re: If P and Q are positive integers, and n is the decimal [#permalink]
Show Tags
11 Mar 2015, 13:53
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).
_________________
Illegitimi non carborundum.



NonHuman User
Joined: 09 Sep 2013
Posts: 7020

Re: If P and Q are positive integers, and n is the decimal [#permalink]
Show Tags
07 Jan 2018, 11:43
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: If P and Q are positive integers, and n is the decimal
[#permalink]
07 Jan 2018, 11:43






