NEW HERE? LEARN MORE
closeclose
Last visit was: 23 Apr 2024, 11:09 It is currently 23 Apr 2024, 11:09
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

A natural number is divided into two positive unequal parts

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
atalpanditgmat
Manager
Manager
Joined: 02 Oct 2012
Status:Working hard to score better on GMAT
Posts: 70
Own Kudos [?]: 579 [26]
Given Kudos: 23
Location: Nepal
Concentration: Finance, Entrepreneurship
GPA: 3.83
WE:Accounting (Consulting)
Send PM
A natural number is divided into two positive unequal parts [#permalink] New post   Updated on: 08 Jun 2013, 04:01
5
Kudos
21
Bookmarks
00:00
A
B
C
D
E

Difficulty:

85% (hard)

Question Stats:

57% (02:57) correct 43% (02:42) wrong based on 174 sessions
Hide Show 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)
ShowHide Answer
Official Answer
B

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 Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92876
Own Kudos [?]: 618557 [10]
Given Kudos: 81561
Send PM
CAT Tests Forum Quiz Mode
Re: A natural number is divided into two positive unequal parts [#permalink] New post   08 Jun 2013, 04:00
8
Kudos
2
Bookmarks
Expert Reply
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
User avatar
navigator123
Intern
Intern
Joined: 17 May 2012
Status:Trying.... & desperate for success.
Posts: 47
Own Kudos [?]: 425 [1]
Given Kudos: 61
Location: India
Concentration: Leadership, Entrepreneurship
Schools: NUS '15
GPA: 2.92
WE:Analyst (Computer Software)
Send PM
Re: A natural number is divided into two positive unequal parts [#permalink] New post   08 Jun 2013, 08:51
1
Kudos
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?
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92876
Own Kudos [?]: 618557 [1]
Given Kudos: 81561
Send PM
CAT Tests Forum Quiz Mode
Re: A natural number is divided into two positive unequal parts [#permalink] New post   09 Jun 2013, 03:06
1
Kudos
Expert Reply
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:
https://www.purplemath.com/modules/solvquad.htm
https://www.purplemath.com/modules/factquad.htm

Hope it helps.
avatar
riskygurpreet
Intern
Intern
Joined: 09 Dec 2010
Posts: 3
Own Kudos [?]: [0]
Given Kudos: 7
Send PM
Re: A natural number is divided into two positive unequal parts [#permalink] New post   11 Jul 2014, 10:52
cant we do this by assuming numbers???????

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

kindly explain.



thanks
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92876
Own Kudos [?]: 618557 [0]
Given Kudos: 81561
Send PM
CAT Tests Forum Quiz Mode
Re: A natural number is divided into two positive unequal parts [#permalink] New post   11 Jul 2014, 11:11
Expert Reply
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.
User avatar
B
vipulgoel
Manager
Manager
Joined: 03 May 2013
Posts: 95
Own Kudos [?]: 50 [0]
Given Kudos: 114
Location: India
Schools: Anderson '24 LBS '24 Madison Marshall '24 Mays McCombs '24 McDonough '24 Mendoza Merage
Send PM
Re: A natural number is divided into two positive unequal parts [#permalink] New post   26 Apr 2015, 21:16
yes, poor wording, it seems n=ab rather then n = a+b
User avatar
D
shashankism
Director
Director
Joined: 13 Mar 2017
Affiliations: IIT Dhanbad
Posts: 628
Own Kudos [?]: 589 [0]
Given Kudos: 88
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE:Engineering (Energy and Utilities)
Send PM
Re: A natural number is divided into two positive unequal parts [#permalink] 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
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32627
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: A natural number is divided into two positive unequal parts [#permalink] New post   07 May 2020, 01:19
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 Club Bot
gmatclubot
Re: A natural number is divided into two positive unequal parts [#permalink]
07 May 2020, 01:19
Moderators:
Bunuel
Math Expert
92875 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions