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

It is currently 19 Aug 2018, 03:11

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

Effects of arithmetic operations on Fractions

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6554
Effects of arithmetic operations on Fractions  [#permalink]

Show Tags

New post 01 Jul 2018, 02:05
3
5
We have many question testing our concepts on effects of arithmetic operations on a fraction.

It may be straightforward as

\(\frac{x+1}{y+1}>\frac{x}{y}\)
OR
it may be hidden ..

which is the greatest - \(\frac{7}{9}, \frac{31}{33},\frac{21}{24}\)?

so lets check the different scenarios....

x and y are integers and both are increased/decreased with same number
I. both are
>0 or both are <0
1) x and y are positive numbers and x<y or fraction \(\frac{x}{y}<1\)
    a) If you ADD same positive number to x and y, the fraction\(\frac{x+a}{y+a}>\frac{x}{y}\)
    b) If you subtract same positive number from x and y, the fraction\(\frac{x-a}{y-a}<\frac{x}{y}\)
2) x and y are positive numbers and x>y or fraction \(\frac{x}{y}>1\)
    a) If you ADD same positive number to x and y, the fraction\(\frac{x+a}{y+a}<\frac{x}{y}\)
    b) If you subtract same positive number from x and y, the fraction\(\frac{x-a}{y-a}>\frac{x}{y}\)
3) x and y are positive numbers and x<y or fraction \(\frac{x}{y}<1\)
    a) If you MULTIPLY or DIVIDE x and y with same positive number, the fraction\(\frac{x*a}{y*a}=\frac{x}{y}\)
    b) If you MULTIPLY or DIVIDE x and y with same negative number , the fraction\(\frac{x*-a}{y*-a}=\frac{x}{y}\)
2) x and y are positive numbers and x>y or fraction \(\frac{x}{y}>1\)
    a) If you ADD same negative number to x and y, the effect will be as subtracting a positive number and the fraction\(\frac{x+a}{y+a}>\frac{x}{y}\), where a is -x and x is a positive number
    b) If you SUBTRACT same negative number to x and y, the effect will be as adding a positive number and the fraction\(\frac{x-a}{y-a}<\frac{x}{y}\), where a is -x and x is a positive number

what can you answer now?
which is greater- \(\frac{31}{33}-or-\frac{31+10}{33+10}\)

why does this happens...because since x<y, any number will be a larger % of smaller number, so numerator has a BIGGER % change
example 1 is 50% of 2 but 1 is only 33.33% of 3

II. If x and y are integers and they undergo arithmetic operations with different number..
1. x and y are positive and x<y

    a) If numerator is increased but denominator is decreased with positive numbers,the fraction\(\frac{x+1}{y-2}>\frac{x}{y}\).. after the arithmetic operations too, the fraction should be positive... say x/y = 1/3 add 1 to numerator and subtract 4 from denominator so \(\frac{1+1}{3-4}=-2\)
    b) If numerator is decreased and denominator is increased with positive numbers,the fraction\(\frac{x-2}{y+1}<\frac{x}{y}\)
    c) similar observation can be deduced of subtracting a number


Would add few more observations that would be useful in tackling such problems

questions testing these concepts will be added in the thread
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6554
Re: Effects of arithmetic operations on Fractions  [#permalink]

Show Tags

New post 05 Jul 2018, 20:45
x and y are integers and both are increased/decreased with same number
I. both are
<0
1) x and y are negative numbers and x>y then fraction \(\frac{x}{y}<1\)
    a) If you ADD same positive number to x and y, the fraction\(\frac{x+a}{y+a}>\frac{x}{y}\)
    b) If you subtract same positive number from x and y, the fraction\(\frac{x-a}{y-a}<\frac{x}{y}\)
2) x and y are negative numbers and x<y then fraction \(\frac{x}{y}>1\)
    a) If you ADD same positive number to x and y, the fraction\(\frac{x+a}{y+a}<\frac{x}{y}\)
    b) If you subtract same positive number from x and y, the fraction\(\frac{x-a}{y-a}>\frac{x}{y}\)
3) x and y are negative numbers and x>y then fraction \(\frac{x}{y}<1\)
    a) If you MULTIPLY or DIVIDE x and y with same positive number, the fraction\(\frac{x*a}{y*a}=\frac{x}{y}\)
    b) If you MULTIPLY or DIVIDE x and y with same negative number , the fraction\(\frac{x*-a}{y*-a}=\frac{x}{y}\)
2) x and y are negative numbers and x<y then fraction \(\frac{x}{y}>1\)
    a) If you ADD same negative number to x and y, the effect will be as subtracting a positive number and the fraction\(\frac{x+a}{y+a}>\frac{x}{y}\), where a = -x and x is a positive number
    b) If you SUBTRACT same negative number to x and y, the effect will be as adding a positive number and the fraction\(\frac{x-a}{y-a}<\frac{x}{y}\), where a = -x and x is a positive number

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6554
Re: Effects of arithmetic operations on Fractions  [#permalink]

Show Tags

New post 05 Jul 2018, 20:58
1) https://gmatclub.com/forum/if-a-0-and-b-0-is-a-2p-b-2p-a-b-267075.html

If \(a<0\) and \(b<0\) , is \(\frac{(a-2p)}{(b-2p)}\) \(>\) \(\frac{a}{b}\) ?

(1) \(p>0\)

(2) \(a<b\)

2) https://gmatclub.com/forum/if-m-0-and-n-0-is-m-x-n-x-m-n-93967.html

If m > 0 and n > 0, is (m+x)/(n+x) > m/n?

(1) m < n.

(2) x > 0.

3) https://gmatclub.com/forum/is-x-1-y-1-x-y-1-0-x-y-2-xy-268847.html
Is \(\frac{x + 1}{y + 1} > \frac{x}{y}\)?


(1) \(0 < x < y\)

(2) \(xy > 0\)


NEW question from GMAT® Official Guide 2019


(DS09315)
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Re: Effects of arithmetic operations on Fractions &nbs [#permalink] 05 Jul 2018, 20:58
Display posts from previous: Sort by

Effects of arithmetic operations on Fractions

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

Events & Promotions

PREV
NEXT


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®.