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

It is currently 18 Apr 2019, 09:47

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

A natural number is divided into two positive unequal parts

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

Hide Tags

 
Manager
Manager
avatar
Status: Working hard to score better on GMAT
Joined: 02 Oct 2012
Posts: 82
Location: Nepal
Concentration: Finance, Entrepreneurship
GPA: 3.83
WE: Accounting (Consulting)
A natural number is divided into two positive unequal parts  [#permalink]

Show Tags

New post Updated on: 08 Jun 2013, 04:01
4
15
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

66% (02:58) correct 34% (02:48) wrong based on 213 sessions

HideShow timer Statistics

A natural number is divided into two positive unequal parts such that the ratio of the original number to the larger (divided) part is equal to the ratio of the larger part to the smaller part. What is the value of this ratio?

A. (5^1/2 − 1)
B. (5^1/2 + 1) / 2
C. (5^1/2 + 1) / 4
D. (5^1/2 + 1) / (5^1/2 − 1)
E. (5^1/2 + 3) / (5^1/2 − 1)

_________________
Do not forget to hit the Kudos button on your left if you find my post helpful.

Originally posted by atalpanditgmat on 08 Jun 2013, 02:40.
Last edited by Bunuel on 08 Jun 2013, 04:01, edited 2 times in total.
Edited the question.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 54369
Re: A natural number is divided into two positive unequal parts  [#permalink]

Show Tags

New post 08 Jun 2013, 04:00
8
2
atalpanditgmat wrote:
A natural number is divided into two positive unequal parts such that the ratio of the original number to the larger (divided) part is equal to the ratio of the larger part to the smaller part. What is the value of this ratio?

A. (5^1/2 − 1)
B. (5^1/2 + 1) / 2
C. (5^1/2 + 1) / 4
D. (5^1/2 + 1) / (5^1/2 − 1)
E. (5^1/2 + 3) / (5^1/2 − 1)


Say a natural number (integer) is n, then given that n=a+b, where a>b.

The ratio of the original number to the larger (divided) part is equal to the ratio of the larger part to the smaller part --> \(\frac{n}{a}=\frac{a}{b}\).

Question: \(\frac{a}{b}=?\)

Now, since \(n=a+b\), then \(\frac{a+b}{a}=\frac{a}{b}\) --> \(1+\frac{b}{a}=\frac{a}{b}\) --> \(1+\frac{1}{x}=x\), where \(\frac{a}{b}=x\).

Solving: \(x=\frac{a}{b}=\frac{1\pm\sqrt{5}}{2}\) --> \(\frac{a}{b}=\frac{1+\sqrt{5}}{2}\) (since a/b must be positive).

Answer: B.

Hope it's clear.

P.S. Please format the questions properly.
_________________
General Discussion
Manager
Manager
avatar
Status: Trying.... & desperate for success.
Joined: 17 May 2012
Posts: 60
Location: India
Concentration: Leadership, Entrepreneurship
Schools: NUS '15
GPA: 2.92
WE: Analyst (Computer Software)
Re: A natural number is divided into two positive unequal parts  [#permalink]

Show Tags

New post 08 Jun 2013, 08:51
1
Bunuel wrote:
atalpanditgmat wrote:
A natural number is divided into two positive unequal parts such that the ratio of the original number to the larger (divided) part is equal to the ratio of the larger part to the smaller part. What is the value of this ratio?

A. (5^1/2 − 1)
B. (5^1/2 + 1) / 2
C. (5^1/2 + 1) / 4
D. (5^1/2 + 1) / (5^1/2 − 1)
E. (5^1/2 + 3) / (5^1/2 − 1)


Say a natural number (integer) is n, then given that n=a+b, where a>b.

The ratio of the original number to the larger (divided) part is equal to the ratio of the larger part to the smaller part --> \(\frac{n}{a}=\frac{a}{b}\).

Question: \(\frac{a}{b}=?\)

Now, since \(n=a+b\), then \(\frac{a+b}{a}=\frac{a}{b}\) --> \(1+\frac{b}{a}=\frac{a}{b}\) --> \(1+\frac{1}{x}=x\), where \(\frac{a}{b}=x\).

Solving: \(x=\frac{a}{b}=\frac{1\pm\sqrt{5}}{2}\) --> \(\frac{a}{b}=\frac{1+\sqrt{5}}{2}\) (since a/b must be positive).

Answer: B.

Hope it's clear.

P.S. Please format the questions properly.


Hi,
Can you please explain how the numerical values were assigned?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 54369
Re: A natural number is divided into two positive unequal parts  [#permalink]

Show Tags

New post 09 Jun 2013, 03:06
1
navigator123 wrote:
Bunuel wrote:
atalpanditgmat wrote:
A natural number is divided into two positive unequal parts such that the ratio of the original number to the larger (divided) part is equal to the ratio of the larger part to the smaller part. What is the value of this ratio?

A. (5^1/2 − 1)
B. (5^1/2 + 1) / 2
C. (5^1/2 + 1) / 4
D. (5^1/2 + 1) / (5^1/2 − 1)
E. (5^1/2 + 3) / (5^1/2 − 1)


Say a natural number (integer) is n, then given that n=a+b, where a>b.

The ratio of the original number to the larger (divided) part is equal to the ratio of the larger part to the smaller part --> \(\frac{n}{a}=\frac{a}{b}\).

Question: \(\frac{a}{b}=?\)

Now, since \(n=a+b\), then \(\frac{a+b}{a}=\frac{a}{b}\) --> \(1+\frac{b}{a}=\frac{a}{b}\) --> \(1+\frac{1}{x}=x\), where \(\frac{a}{b}=x\).

Solving: \(x=\frac{a}{b}=\frac{1\pm\sqrt{5}}{2}\) --> \(\frac{a}{b}=\frac{1+\sqrt{5}}{2}\) (since a/b must be positive).

Answer: B.

Hope it's clear.

P.S. Please format the questions properly.


Hi,
Can you please explain how the numerical values were assigned?


\(1+\frac{1}{x}=x\) --> \(\frac{x+1}{x}=x\) --> \(x^2-x-1=0\) --> \(x=\frac{1\pm\sqrt{5}}{2}\).

Solving and Factoring Quadratics:
http://www.purplemath.com/modules/solvquad.htm
http://www.purplemath.com/modules/factquad.htm

Hope it helps.
_________________
Intern
Intern
avatar
Joined: 09 Dec 2010
Posts: 3
Re: A natural number is divided into two positive unequal parts  [#permalink]

Show Tags

New post 11 Jul 2014, 10:52
cant we do this by assuming numbers???????

say n=20 , a=18 , b =2

kindly explain.



thanks
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 54369
Re: A natural number is divided into two positive unequal parts  [#permalink]

Show Tags

New post 11 Jul 2014, 11:11
riskygurpreet wrote:
cant we do this by assuming numbers???????

say n=20 , a=18 , b =2

kindly explain.



thanks


No. The question is about finding numerical value of the golden ratio: two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. As you can see from the solution above this ratio is irrational number and thus cannot be written as the ratio of two integers.
_________________
Manager
Manager
avatar
Joined: 03 May 2013
Posts: 67
Re: A natural number is divided into two positive unequal parts  [#permalink]

Show Tags

New post 26 Apr 2015, 21:16
yes, poor wording, it seems n=ab rather then n = a+b
Director
Director
User avatar
D
Affiliations: IIT Dhanbad
Joined: 13 Mar 2017
Posts: 718
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: A natural number is divided into two positive unequal parts  [#permalink]

Show Tags

New post 24 Jul 2017, 11:49
atalpanditgmat wrote:
A natural number is divided into two positive unequal parts such that the ratio of the original number to the larger (divided) part is equal to the ratio of the larger part to the smaller part. What is the value of this ratio?

A. (5^1/2 − 1)
B. (5^1/2 + 1) / 2
C. (5^1/2 + 1) / 4
D. (5^1/2 + 1) / (5^1/2 − 1)
E. (5^1/2 + 3) / (5^1/2 − 1)


Let N be the natural number...
Let N be divided into 2 parts p (larger part) and m (smaller part)

So, N = m+p........(i)

Also Given N/p = p/m
-> Nm = p^2 ......(ii)

Multiplying m on both sides of (i), we get
Nm = m^2 + pm
Putting value from (ii), we get

P^2 = m^2 + pm
Dividing both sides by m^2 , we get
(p/m)^2 = 1+ p/m

Let p/m = x
SO, x^2 = 1+x
X^2 - x - 1 = 0
\(x = (1+\sqrt{5})/2, (1-\sqrt{5})/2\)
Ratio must be +ve
So, x =\((1+\sqrt{5})/2\)


Answer B
_________________
CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu


Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)



What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".
GMAT Club Bot
Re: A natural number is divided into two positive unequal parts   [#permalink] 24 Jul 2017, 11:49
Display posts from previous: Sort by

A natural number is divided into two positive unequal parts

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.