GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 19 Oct 2019, 06:50

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

If P and Q are positive integers, and n is the decimal

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Manager
Manager
avatar
Joined: 22 Dec 2011
Posts: 211
If P and Q are positive integers, and n is the decimal  [#permalink]

Show Tags

New post Updated on: 18 Nov 2012, 04:50
19
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

60% (01:40) correct 40% (01:57) wrong based on 453 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

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
Manager
avatar
Joined: 22 Dec 2011
Posts: 211
Re: If P and Q are positive integers,  [#permalink]

Show Tags

New post 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
VP
User avatar
Joined: 02 Jul 2012
Posts: 1105
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: If P and Q are positive integers,  [#permalink]

Show Tags

New post 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
Intern
avatar
Status: wants to beat the gmat
Joined: 18 Jul 2012
Posts: 18
Location: United States
Re: If P and Q are positive integers, and n is the decimal  [#permalink]

Show Tags

New post 18 Nov 2012, 13:49
1
It is given in the question stem that P and Q are positive integers.
Intern
Intern
avatar
Joined: 04 May 2013
Posts: 39
Re: If P and Q are positive integers, and n is the decimal  [#permalink]

Show Tags

New post 20 Jul 2013, 10:51
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
Intern
avatar
Joined: 02 Feb 2012
Posts: 23
GPA: 4
Re: If P and Q are positive integers,  [#permalink]

Show Tags

New post 20 Jul 2013, 23:08
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...
VP
VP
User avatar
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1007
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
GMAT ToolKit User
Re: If P and Q are positive integers, and n is the decimal  [#permalink]

Show Tags

New post 20 Jul 2013, 23:49
1
1
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
_________________
Manager
Manager
avatar
Joined: 14 Jun 2011
Posts: 65
Re: If P and Q are positive integers,  [#permalink]

Show Tags

New post 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
User avatar
B
Joined: 10 Oct 2012
Posts: 590
Re: If P and Q are positive integers,  [#permalink]

Show Tags

New post 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.
_________________
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58449
Re: If P and Q are positive integers,  [#permalink]

Show Tags

New post 21 Jul 2013, 01:42
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.
_________________
Manager
Manager
User avatar
S
Joined: 22 Jan 2014
Posts: 170
WE: Project Management (Computer Hardware)
Re: If P and Q are positive integers, and n is the decimal  [#permalink]

Show Tags

New post 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.
Manager
Manager
avatar
B
Joined: 24 May 2014
Posts: 86
Location: India
GMAT 1: 590 Q39 V32
GRE 1: Q159 V151

GRE 2: Q159 V153
GPA: 2.9
Re: If P and Q are positive integers, and n is the decimal  [#permalink]

Show Tags

New post 31 Dec 2018, 01:37
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?
Intern
Intern
avatar
B
Joined: 04 Aug 2018
Posts: 13
Re: If P and Q are positive integers, and n is the decimal  [#permalink]

Show Tags

New post 06 Sep 2019, 05:16
narendran1990 wrote:
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?


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
GMAT Club Bot
Re: If P and Q are positive integers, and n is the decimal   [#permalink] 06 Sep 2019, 05:16
Display posts from previous: Sort by

If P and Q are positive integers, and n is the decimal

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne