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Is xy > x/y? (1) xy > 0 (2) y < 0

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Is xy > x/y? (1) xy > 0 (2) y < 0 [#permalink]

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New post 04 Sep 2008, 09:02
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Is xy > x/y?
(1) xy > 0
(2) y < 0

Ans is E - please provide explanation and possible quickest ways to approach these problems.

Note - i'm not sure if the question is already on forum as search results do not provide anything if i search for this "Is xy > x/y?"

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Re: inequality - DS [#permalink]

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New post 04 Sep 2008, 09:12
onesome68 wrote:
Is xy > x/y?
(1) xy > 0
(2) y < 0

Ans is E - please provide explanation and possible quickest ways to approach these problems.

Note - i'm not sure if the question is already on forum as search results do not provide anything if i search for this "Is xy > x/y?"



(1) xy > 0
both x and y must be +ve or -ve
x=2 y=3 xy>x/y true
x=2 y=1/3 xy>x/y false
insuffcient
(2) y<0
x=-2 y=-3 xy>x/y true
x=-2 y=-1/3 xy>x/y false
insufficient

combined.
y must be -ve. and x must be -ve.
x=-2 y=-3 xy>x/y true
x=-2 y=-1/3 xy>x/y false
two solutions - insuffcient.
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Re: inequality - DS [#permalink]

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New post 04 Sep 2008, 09:17
onesome68 wrote:
Is xy > x/y?
(1) xy > 0
(2) y < 0

Ans is E - please provide explanation and possible quickest ways to approach these problems.

Note - i'm not sure if the question is already on forum as search results do not provide anything if i search for this "Is xy > x/y?"


May I suggest that the answers are not posted along with the Q. These boards are very active and we receive response in no time. Just my 2 cents

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Re: inequality - DS [#permalink]

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New post 04 Sep 2008, 09:35
onesome68 wrote:
Is xy > x/y?
(1) xy > 0
(2) y < 0

Ans is E - please provide explanation and possible quickest ways to approach these problems.

Note - i'm not sure if the question is already on forum as search results do not provide anything if i search for this "Is xy > x/y?"


If xy > x/y:
- when x >0 >>> y > 1/y >>> y > 1 or -1 < y < 0
- when x < 0 >>> y < 1/y >>> y < -1 or 0 < y < 1

So clearly both (1) and (2) insuff

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Re: inequality - DS [#permalink]

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New post 04 Sep 2008, 09:41
Is there a way to solve this algebraically? by breaking down xy>x/y to equal to xy^2-x>0?

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Re: inequality - DS [#permalink]

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New post 04 Sep 2008, 10:00
Thank you x2suresh

- i will take care of the suggestion to not post OA.
Only reason i posted was to save time as my prime concern here was to figure out how to approach the problem in a way which will take minimum time.

As i see in your approach you are taking numbers as examples. But it is not always that simple.

My approach was like this.. which was taking too much time and sort of got unwieldy..

xy - x/y > 0
=> x(y^2) - x > 0
=> x(y -1)(y+1) > 0
=>
4 cases for y and 2 for x
y > 1 / x as +ve or -ve
0 < y < 1 / x as +ve or -ve
-1 < y < 0 / x as +ve or -ve
y < -1 / x as +ve or -ve
--------------------------
Results will be the same if i give it all that time.. but my approach will take too much time to figure out that its inconclusive with given info.

Basically , when will you choose to do it by example only??
--------------------------------------------

:?:
fiesta - i think you are trying to approach the problem in some reverse order.
Is this what you are trying to conclude?
-- when x > y => we expect something like |y| > 1 to be provided in premises. And its not provided so not sufficient.
-- when x < y => we expect something like |y| < 1 to be provided in premises. And its not provided so not sufficient.
Please clarify, thanks.

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Re: inequality - DS [#permalink]

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New post 04 Sep 2008, 10:53
onesome68 wrote:
Is xy > x/y?
(1) xy > 0
(2) y < 0

Ans is E - please provide explanation and possible quickest ways to approach these problems.

Note - i'm not sure if the question is already on forum as search results do not provide anything if i search for this "Is xy > x/y?"


The answer is E

Is xy > x/y ?
or xy - x/y > 0 ?

1) xy > 0

This means that EITHER x and y are positive together OR x and y are negative together. As a result, (x/y) is always positive. Check with the question stem above
(xy) - (x/y) > 0
(Positive) - (Positive) > 0
This could be true or false. INSUFF

2) y < 0
(xy) - (x/y) > 0
x(y - 1/y) > 0
We don't know the sign of x . INSUFF

1) & 2) y is negative then x must be negative too. However, everything is quite the same
(xy) - (x/y) > 0
(Positive) - (Positive) > 0
This could be true of false. INSUFF

E

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Re: inequality - DS [#permalink]

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New post 04 Sep 2008, 11:36
devilmirror wrote:
onesome68 wrote:
Is xy > x/y?
(1) xy > 0
(2) y < 0

Ans is E - please provide explanation and possible quickest ways to approach these problems.

Note - i'm not sure if the question is already on forum as search results do not provide anything if i search for this "Is xy > x/y?"


The answer is E

Is xy > x/y ?
or xy - x/y > 0 ?

1) xy > 0

This means that EITHER x and y are positive together OR x and y are negative together. As a result, (x/y) is always positive. Check with the question stem above
(xy) - (x/y) > 0
(Positive) - (Positive) > 0
This could be true or false. INSUFF

2) y < 0
(xy) - (x/y) > 0
x(y - 1/y) > 0
We don't know the sign of x . INSUFF

1) & 2) y is negative then x must be negative too. However, everything is quite the same
(xy) - (x/y) > 0
(Positive) - (Positive) > 0
This could be true of false. INSUFF

E




Thanks devilmirror - I like your approach. It is very clear. thanks.

One question (just for a benchmark maybe!) - how much time do you think you will take up in solving this question? would appreciate your input.

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Re: inequality - DS [#permalink]

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New post 04 Sep 2008, 11:47
onesome68 wrote:



Thanks devilmirror - I like your approach. It is very clear. thanks.

One question (just for a benchmark maybe!) - how much time do you think you will take up in solving this question? would appreciate your input.


I believe that I can solve this question in 2 - 2.5 min. If you practice enough GMAT Quantitative, you will get an idea how to solve some particular questions.

The technique I used is often useful with this type of question. You just carefully check the sign of each term and see the end result.

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Re: inequality - DS [#permalink]

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New post 04 Sep 2008, 12:40
1) xy > 0 .... for xy > x/y
x +ve, y +ve OR x -ve, y -ve
x ...... y ...... xy ...... x/y ....... xy>x/y
2 ...... 1 ....... 2 ....... 2 .......... NO
3 ...... 2 ....... 6 ....... 1.5 ........ YES
-3 ..... -2 ..... 6 ....... 1.5 ........ YES

Not always true
Insufficient

2) y < 0 .... for xy > x/y
x ...... y ...... xy ...... x/y ....... xy>x/y
2 ...... -1 ....... -2 ....... -2 .......... NO
-3 ..... -2 ..... 6 ....... 1.5 ........ YES

Not always true
Insufficient

3) together
xy > 0 and y < 0
x ...... y ...... xy ...... x/y ....... xy>x/y
-2 ......-1 ..... 2 ....... 2 .......... NO
-3 ..... -2 ..... 6 ....... 1.5 ........ YES

Not sufficient

------------------------------------

1. Insufficient
2. Insuffcient
3. together Insufficient

IMO 'E'

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Re: inequality - DS   [#permalink] 04 Sep 2008, 12:40
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