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# Is xy > 24?

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Joined: 18 Sep 2014
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Is xy > 24?  [#permalink]

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06 Apr 2016, 05:20
5
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Difficulty:

75% (hard)

Question Stats:

58% (02:32) correct 42% (02:25) wrong based on 124 sessions

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Is $$xy > 24$$?

1. $$y - 2 < x$$
2. $$2y > x + 8$$
Math Expert
Joined: 02 Aug 2009
Posts: 7979
Re: Is xy > 24?  [#permalink]

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06 Apr 2016, 05:34
3
Nevernevergiveup wrote:
Is $$xy > 24$$?

1. $$y - 2 < x$$
2. $$2y > x + 8$$

Hi,

Is $$xy > 24$$..

At the very first glance, we can rule out that any statement can be sufficient alone..
each statement has an equality sign and we do not know if the two are fraction, integer, positive or negative..

If time is running out, therefore C is the BEST bet..

lets see the statements--
1. $$y - 2 < x$$
if x=5, y=2.. ans NO
x= 8, y =5.. ans YES
Insuff

2. $$2y > x + 8$$
x= -6, y=2 .... NO
x=6, y=8.. YES
Insuff

Combined..
since x>y-2 and 2y > x+8
I can substitute x as y-2, since that is more than the least value of x..
2y>y-2+8
2y-y>6..
y>6..
if y>6 and x>y-2 x>6-2 or x>4..
therefore xy> 6*4...OR xy>24
Suff

C
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Re: Is xy > 24?  [#permalink]

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06 Apr 2016, 05:50
Hi Chetan,
I cant understand this ' since that is more than the least value of x'.
Cant y-2 be big that it cant be substituted here ?

Thanks for your help.
-Arun
Math Expert
Joined: 02 Aug 2009
Posts: 7979
Re: Is xy > 24?  [#permalink]

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06 Apr 2016, 06:08
raarun wrote:
Hi Chetan,
I cant understand this ' since that is more than the least value of x'.
Cant y-2 be big that it cant be substituted here ?

Thanks for your help.
-Arun

Hi arun,

since x>y-2and 2y > x+8
I can substitute x as y-2, since that is more than the least value of x..
Other way of SAMETHING can be
Now 2y>x+8...(i)
But x>y-2...(ii)

add the bigger parts that is 2y and x ...
And the smaller parts x+8 and y-2..

2y+x>x+8+y-2..
2y+x-x-y>8-2..
y>6
Hope it helps
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Is xy > 24?  [#permalink]

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06 Apr 2016, 08:12
1
Thanks a lot chetan.I understood.

This can also be solved by the following methods
Combining statement 1 and 2 by adding them together.
$$y−2<x$$
$$x+8<2y$$
solved the inequality wrongly
$$6 < x+y$$ and ended with ans E
The addition should also result in 6 < y

This can also be solved by subtracting 1 from 2.
$$y−2<x$$---1
$$2y>x+8$$ ----2

i got $$y >6$$

Both the cases will lead to answer C

-Arun
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Joined: 24 May 2013
Posts: 76
Re: Is xy > 24?  [#permalink]

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06 Apr 2016, 12:50
1
Is xy>24?

1. y−2<x
2. 2y>x+8

Individually both the inequalities are in sufficient.

Combining the two and plotting we can see that the shaded region of interest has xy>24.

hance C
Attachments

Inequality.png [ 10.44 KiB | Viewed 1720 times ]

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Re: Is xy > 24?  [#permalink]

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10 Apr 2018, 00:52
Nevernevergiveup wrote:
Is $$xy > 24$$?

1. $$y - 2 < x$$
2. $$2y > x + 8$$

It is clear that first and second statements are not sufficient separately.
However, if we take them together, we have
y-2<x<2y-8.
Thus,
2y-8>y-2 resulting in y>6 and x>4.
This is sufficient to answer the question.
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Re: Is xy > 24?   [#permalink] 10 Apr 2018, 00:52
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# Is xy > 24?

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