GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Oct 2018, 10:12

# Saturday Quant Quiz:

Starts promptly at 10 AM PST - Join in to Have Fun & Win Prizes

### 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

# If x and y are integers, is |xy|/y>0?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Aug 2009
Posts: 6967
If x and y are integers, is |xy|/y>0?  [#permalink]

### Show Tags

17 Nov 2017, 09:29
2
3
00:00

Difficulty:

95% (hard)

Question Stats:

14% (02:30) correct 86% (02:04) wrong based on 77 sessions

### HideShow timer Statistics

If x and y are integers, is $$\frac{|xy|}{y}\geq{0}$$ ?

(1) $$y^3<|y|$$
(2) $$|xy|>|y|$$

self made - a tricky one

_________________

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

GMAT online Tutor

DS Forum Moderator
Joined: 22 Aug 2013
Posts: 1348
Location: India
Re: If x and y are integers, is |xy|/y>0?  [#permalink]

### Show Tags

17 Nov 2017, 11:20
1
We know that |xy| will always be >=0, so the expression |xy|/y will be >=0 if y > 0 and it will be < 0 if y < 0 (we cannot take y=0 as that would make the question undefined).

(1) y^3 < |y|
This expression will be true for ALL negative values of y. Thats because |y| will be positive but y^3 will be negative.
Now this will also be true for 0<y<1. If y lies between 0 and 1, y^3 will be less than y or |y|. BUT the catch here is that we are given y is an integer. So it cannot lie between 0 and 1.
So from this statement we can safely say that y can only be negative. So |xy|/y will be negative. We got NO as our answer. Sufficient.

(2) |xy| > |y|
LHS can also be written as |x|*|y|. So |x|*|y| > |y| or |x| > |y|/|y| or |x| > 1. So either x > 1 or x < -1.
But this doesnt tell us anything about whether y is positive or negative. Insufficient.

Math Expert
Joined: 02 Aug 2009
Posts: 6967
Re: If x and y are integers, is |xy|/y>0?  [#permalink]

### Show Tags

18 Nov 2017, 20:22
1
1
chetan2u wrote:
If x and y are integers, is $$\frac{|xy|}{y}\geq{0}$$ ?

(1) $$y^3<|y|$$
(2) $$|xy|>|y|$$

Hi amanvermagmat,

your thinking has been correct but you have neglected the role of second variable x..

lets solve it..
$$\frac{|xy|}{y}\geq{0}$$
the numerator will be 0 if x is 0 OR it will be POSITIVE as the value is in MOD

(1) $$y^3<|y|$$
since y is an integer, y will be a negative integer..
BUT we have x too..
if x is 0, $$\frac{|xy|}{y}={0}$$, and ans is YES
If x is an integer, $$\frac{|xy|}{y}<{0}$$... ans is NO
insuff

(2) $$|xy|>|y|$$
square both sides...
$$(xy)^2>y^2......y^2(x^2-1)>0$$
although it does not give anything to solve but tells us that both x and y are non zero
insuff

combined-
y is negative and x is non zero
so $$\frac{|xy|}{y}\geq{0}$$ is always NO.

C
_________________

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

GMAT online Tutor

DS Forum Moderator
Joined: 22 Aug 2013
Posts: 1348
Location: India
Re: If x and y are integers, is |xy|/y>0?  [#permalink]

### Show Tags

18 Nov 2017, 22:26
chetan2u wrote:
chetan2u wrote:
If x and y are integers, is $$\frac{|xy|}{y}\geq{0}$$ ?

(1) $$y^3<|y|$$
(2) $$|xy|>|y|$$

Hi amanvermagmat,

your thinking has been correct but you have neglected the role of second variable x..

lets solve it..
$$\frac{|xy|}{y}\geq{0}$$
the numerator will be 0 if x is 0 OR it will be POSITIVE as the value is in MOD

(1) $$y^3<|y|$$
since y is an integer, y will be a negative integer..
BUT we have x too..
if x is 0, $$\frac{|xy|}{y}={0}$$, and ans is YES
If x is an integer, $$\frac{|xy|}{y}<{0}$$... ans is NO
insuff

(2) $$|xy|>|y|$$
square both sides...
$$(xy)^2>y^2......y^2(x^2-1)>0$$
although it does not give anything to solve but tells us that both x and y are non zero
insuff

combined-
y is negative and x is non zero
so $$\frac{|xy|}{y}\geq{0}$$ is always NO.

C

oh ok! Thanks so much. Kudos!
Re: If x and y are integers, is |xy|/y>0? &nbs [#permalink] 18 Nov 2017, 22:26
Display posts from previous: Sort by