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

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e-GMAT Representative
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Joined: 04 Jan 2015
Posts: 1900
If x and y are positive numbers, is x<y?  [#permalink]

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New post 30 Jun 2018, 11:47
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  35% (medium)

Question Stats:

74% (01:49) correct 26% (01:13) wrong based on 43 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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Joined: 14 Mar 2018
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Re: If x and y are positive numbers, is x<y?  [#permalink]

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New post 30 Jun 2018, 20:37
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
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If x and y are positive numbers, is x<y?  [#permalink]

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New post 30 Jun 2018, 23:25
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, 23:25
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