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# If |x/y| < 1, then which of the following must be true?

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Math Expert
Joined: 02 Sep 2009
Posts: 59622
If |x/y| < 1, then which of the following must be true?  [#permalink]

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25 Nov 2019, 03:04
00:00

Difficulty:

65% (hard)

Question Stats:

38% (02:16) correct 62% (01:48) wrong based on 52 sessions

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If $$|\frac{x}{y}| < 1$$, then which of the following must be true?

I. $$\frac{|x+1|}{|y+1|}< 1$$

II. $$\frac{|x^2+1|}{|y^2+1|} < 1$$

III. $$\frac{|x-1|}{|y-1|} < 1$$

A. I only
B. II only
C. III only
D. I and II only
E. II and III only

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Joined: 18 Aug 2017
Posts: 5466
Location: India
Concentration: Sustainability, Marketing
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WE: Marketing (Energy and Utilities)
Re: If |x/y| < 1, then which of the following must be true?  [#permalink]

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25 Nov 2019, 04:13
check with 2/3 , -2/3 and 2/-3
only $$\frac{|x^2+1|}{|y^2+1|} < 1$$
will be valid
IMO B

Bunuel wrote:
If $$|\frac{x}{y}| < 1$$, then which of the following must be true?

I. $$\frac{|x+1|}{|y+1|}< 1$$

II. $$\frac{|x^2+1|}{|y^2+1|} < 1$$

III. $$\frac{|x-1|}{|y-1|} < 1$$

A. I only
B. II only
C. III only
D. I and II only
E. II and III only

Are You Up For the Challenge: 700 Level Questions
Manager
Joined: 10 Dec 2017
Posts: 151
Location: India
Re: If |x/y| < 1, then which of the following must be true?  [#permalink]

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26 Nov 2019, 00:11
Bunuel wrote:
If $$|\frac{x}{y}| < 1$$, then which of the following must be true?

I. $$\frac{|x+1|}{|y+1|}< 1$$

II. $$\frac{|x^2+1|}{|y^2+1|} < 1$$

III. $$\frac{|x-1|}{|y-1|} < 1$$

A. I only
B. II only
C. III only
D. I and II only
E. II and III only

Are You Up For the Challenge: 700 Level Questions

lxl<lyl
lxl^2<lyl^2
x^2<y^2
x^2+1<y^2+1
$$lx^2+1l<ly^2+1l$$
$$[lx^2+1l/ly^2+1l ]<1$$
Since we do not know about x and y (x>y, x<y) we can't say about rest of the options.
if x=-2, y=-5
lxl<lyl
lx+1l/ly+1l=1/4<1 (True)
But x=3, y=-5
1<1(absurd)
B:)
Re: If |x/y| < 1, then which of the following must be true?   [#permalink] 26 Nov 2019, 00:11
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