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

It is currently 20 Oct 2018, 01:37

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

Fractions : Faster calculation

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

Hide Tags

Intern
Intern
avatar
Joined: 30 Jul 2010
Posts: 11
Fractions : Faster calculation  [#permalink]

Show Tags

New post 01 Nov 2014, 07:23
3
9
1.Fractions - Comparing two fractions

Simple way to compare two fractions

\(\frac{45}{77}\) and \(\frac{63}{52}\)

Cross multiple ==> \(45*52 < 63*77\). Hence \(\frac{45}{77} < \frac{63}{52}\)

2. Fractions - finding highest/least value among multiple fractions with consistent pattern.


LEGEND
N= Numerator
D=Denominator
a= increase in numerator
b= increase in denominator

1. If N and D increased by constants value as the sequence of fractions progresses and if increase in numerator greater than or equal to increase in denominator then the last fraction is greatest among all given fractions.

EX: Which of the following fractions is greatest?
\(\frac{19}{24}\), \(\frac{28}{27}\), \(\frac{10}{21}\),\(\frac{1}{18}\)

Solution:
Re-writing the list to apply the above formula. \(\frac{1}{18}\), \(\frac{10}{21}\), \(\frac{19}{24}\),\(\frac{28}{27}\)
After clear observation we can find that the in above fractions both N and D are increased by constant values. i.e, N is incremented by 9 and D is incremented by 3. Clearly \(9>3\)

Hence 28/27 is the greatest value among the given fractions. It's pretty straight forward and can deduce the solution in seconds with clear observation.

Genralizing the formula:

\(\frac{x}{y}\), \(\frac{x+a}{y+b}\), \(\frac{x+2a}{y+2b}\),\(\frac{x+3a}{y+3b}\)...\(\frac{x+na}{y+nb}\)
Then \(\frac{x+na}{y+nb}\) is greatest among all given fractions.

1. Both numerator and denominator increase in constant values.(Numerator by a, denominator by b)
2. (\(a>=b\))


what if \(a<b\)

Rule 2:

If a<b,
Then compare \(\frac{a}{b}\) to first fraction of the list i.e\(\frac{x}{y}\)

1. If \(\frac{a}{b} > \frac{x}{y}\)

Then the last fraction is greatest . i.e \(\frac{x+na}{y+nb}\)

2. If \(\frac{a}{b} < \frac{x}{y}\)
Then the last fraction is least among all . i.e \(\frac{x+na}{y+nb}\)

3. If \(\frac{a}{b} = \frac{x}{y}\)
Then all fractions are equal.

EX: Rule 2. Type#1. Which of the following fractions is greatest?
\(\frac{4}{39}\), \(\frac{2}{25}\), \(\frac{3}{32}\),\(\frac{1}{18}\)

Solution:
Re-writing the list to apply the above formula. \(\frac{1}{18}\), \(\frac{2}{25}\), \(\frac{3}{32}\),\(\frac{4}{39}\)
After clear observation we can find that the in above fractions both N and D are increased by constant values. i.e, N is incremented by 1 and D is incremented by 7.

1. N increased by 1 and D increase by 7 (\(1<7\)) i.e \(a<b\)
2. compare \(a<b\) with first fraction \(1/18\) . This will give us \(1/7 >1/18\)

Hence the last fraction is greatest.

EX: Rule 2. Type#2. Which of the following fractions is least?
\(\frac{105}{401}\), \(\frac{100}{301}\), \(\frac{95}{201}\),\(\frac{90}{101}\)

Re-writing the list to apply the above formula. \(\frac{90}{101}\), \(\frac{95}{201}\), \(\frac{100}{301}\),\(\frac{105}{401}\)

a=5 and b=100
compare \(\frac{a}{b}\) i.e, \(\frac{1}{20}\) with first fraction i.e, \(\frac{90}{101}\). Clearly \(\frac{1}{20}<\frac{90}{101}\)
Hence the last fraction in the sequence is the least value. i.e, \(\frac{105}{401}\) is least among all.
Manager
Manager
User avatar
Joined: 23 Oct 2014
Posts: 91
Concentration: Marketing
Re: Fractions : Faster calculation  [#permalink]

Show Tags

New post 05 Nov 2014, 15:40
Thank you. This was enlightening.
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8462
Premium Member
Re: Fractions : Faster calculation  [#permalink]

Show Tags

New post 01 Oct 2018, 02:29
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

GMAT Club Bot
Re: Fractions : Faster calculation &nbs [#permalink] 01 Oct 2018, 02:29
Display posts from previous: Sort by

Fractions : Faster calculation

  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®.