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

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

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

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


self made - a tricky one
[Reveal] Spoiler: OA

_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 6146 [1], given: 121

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Re: If x and y are integers, is |xy|/y>0? [#permalink]

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New post 17 Nov 2017, 10:20
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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.

Hence A answer.

Kudos [?]: 188 [1], given: 290

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Re: If x and y are integers, is |xy|/y>0? [#permalink]

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chetan2u wrote:
If x and y are integers, is \(\frac{|xy|}{y}\geq{0}\) ?

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


self made



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
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 6146 [1], given: 121

DS Forum Moderator
avatar
S
Joined: 21 Aug 2013
Posts: 577

Kudos [?]: 188 [0], given: 290

Location: India
Premium Member CAT Tests
Re: If x and y are integers, is |xy|/y>0? [#permalink]

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New post 18 Nov 2017, 21:26
chetan2u wrote:
chetan2u wrote:
If x and y are integers, is \(\frac{|xy|}{y}\geq{0}\) ?

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


self made



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!

Kudos [?]: 188 [0], given: 290

Re: If x and y are integers, is |xy|/y>0?   [#permalink] 18 Nov 2017, 21:26
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