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# If x and y are positive numbers, is x<y?

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e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2456
If x and y are positive numbers, is x<y?  [#permalink]

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30 Jun 2018, 10:47
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Question Stats:

76% (01:57) correct 24% (01:52) wrong based on 70 sessions

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Question-3

If x and y are positive numbers, is $$x<y$$?
1. $$\frac{(x+1)}{(y+1)}>\frac{x}{y}$$
2. $$\frac{(x-1)}{(y-1)} < \frac{(x+1)}{(y+1)}$$

Options

A. Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.
C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statement (1) and (2) TOGETHER are NOT sufficient.

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Intern
Joined: 14 Mar 2018
Posts: 4
Re: If x and y are positive numbers, is x<y?  [#permalink]

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30 Jun 2018, 19:37
imo d
case 1 : (x+1)*y>x*(y+1) xy+y > xy+x -> y>x , sufficient

case 2
(x-1)(y+1)< (x+1)(y-1) -> 2x<2y -> sufficient , hence D
Math Expert
Joined: 02 Aug 2009
Posts: 7202
If x and y are positive numbers, is x<y?  [#permalink]

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30 Jun 2018, 22:25
EgmatQuantExpert wrote:

Question-3

If x and y are positive numbers, is $$x<y$$?
1. $$\frac{(x+1)}{(y+1)}>\frac{x}{y}$$
2. $$\frac{(x-1)}{(y-1)} < \frac{(x+1)}{(y+1)}$$

TIPS for these question :-
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$$\frac{x-a}{y-a}>\frac{x}{y}$$

let's see the choices

1. $$\frac{(x+1)}{(y+1)}>\frac{x}{y}$$
TIP 1a, x<y..
this so happens...because since x<y, any number will constitue as 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
suff

2. $$\frac{(x-1)}{(y-1)} < \frac{(x+1)}{(y+1)}$$
combination of tip 1a and 1b
x<y
suff

D
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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

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If x and y are positive numbers, is x<y? &nbs [#permalink] 30 Jun 2018, 22:25
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