It is currently 23 Aug 2019, 05:06

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

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

Effect of Arithmetic operations on fraction

Author Message
Supreme Moderator
Joined: 01 Nov 2017
Posts: 370
Followers: 5

Kudos [?]: 123 [3] , given: 4

Effect of Arithmetic operations on fraction [#permalink]  18 Oct 2018, 03:55
3
KUDOS
Expert's post
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

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

_________________

Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

Intern
Joined: 05 Nov 2018
Posts: 5
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: Effect of Arithmetic operations on fraction [#permalink]  16 Nov 2018, 13:44
interesting
Re: Effect of Arithmetic operations on fraction   [#permalink] 16 Nov 2018, 13:44
Display posts from previous: Sort by