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01 Jul 2018, 02:05
Kudos
Bookmarks
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 \(\frac{x}{y}<1\)
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
Would add few more observations that would be useful in tackling such problems
questions testing these concepts will be added in the thread
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\(\frac{x-a}{y-a}<\frac{x}{y}\)
- 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\(\frac{x-a}{y-a}>\frac{x}{y}\)
- 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\(\frac{x*-a}{y*-a}=\frac{x}{y}\)
- 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
05 Jul 2018, 20:45
Kudos
Bookmarks
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 \(\frac{x}{y}<1\)
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\(\frac{x-a}{y-a}<\frac{x}{y}\)
- 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\(\frac{x-a}{y-a}>\frac{x}{y}\)
- 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\(\frac{x*-a}{y*-a}=\frac{x}{y}\)
- 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
05 Jul 2018, 20:58
Kudos
Bookmarks
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) \(xy > 0\)
(DS09315)
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)
