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by sirisha.g » Sat Aug 28, 2010 4:21 am
this one is from veritas practice test.

is x^2+y^2>100?

1)2xy<100
2)(x+y)^2> 200

[spoiler]i feel the answer should be B because (x+y)^2 will be grater than 200 only for values from 15 onwards i.e 15^2, 16^2..
if we consider 15 then x, y=10,5 or5,10 or 3, 12 so on.. so for any value the x and y we will get a yes.. so statement 2 is sufficient.

the OA is C. [/spoiler]
Last edited by sirisha.g on Sat Aug 28, 2010 6:01 am, edited 1 time in total.
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by debmalya_dutta » Sat Aug 28, 2010 5:23 am
sirisha.g wrote:this one is from veritas practice test.

is x^2+y^2>100?

1)2xy<100
2)(x+y)^2> 200

[spoiler]i feel the answer should be B because (x+y)^2 will be grater than 200 only for values from 15 onwards i.e 15^2, 16^2..
if we consider 15 then x, y=10,1 or1,10 or 3, 12 so on.. so for any value the x and y we will get a yes.. so statement 2 is sufficient.

the OA is C. [/spoiler]
what if 2XY is negative ..... Will B be still sufficient ? I think you need to test with such cases... You will find that B is insufficient
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by Maciek » Sat Aug 28, 2010 5:30 am
Hi!

IMO C

1) 2xy < 100

let us plug in numbers:

x = 8, y = 5

2xy = 96

x^2+y^2 = 8^2 + 5^2 = 89 < 100

x = 4, y = 10

2xy = 80

x^2+y^2 = 16 + 100 > 100

statement 1 ALONE is INSUFFICIENT

2) (x + y)^2 > 200

(a + b)^2 = a^2 + b^2 + 2ab

(x + y)^2 = x^2 + y^2 + 2xy

x^2 + y^2 + 2xy > 200

x^2 + y^2 > 200 - 2xy

x^2 + y^2 > 100 + (100 - 2xy)

statement 2 ALONE is INSUFFICIENT

x^2 + y^2 > 100 + (100 - 2xy)

if 2xy <= 100 then x^2 + y^2 > 100

from statement 1 we know that

2xy < 100

so both statements 1 and 2 are TOGETHER SUFFICIENT

hope it helps!

Best,
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by sirisha.g » Sat Aug 28, 2010 5:37 am
Maciek wrote:Hi!

IMO C

1) 2xy < 100

let us plug in numbers:

x = 8, y = 5

2xy = 96

x^2+y^2 = 8^2 + 5^2 = 89 < 100

x = 4, y = 10

2xy = 80

x^2+y^2 = 16 + 100 > 100

statement 1 ALONE is INSUFFICIENT

2) (x + y)^2 > 200

(a + b)^2 = a^2 + b^2 + 2ab

(x + y)^2 = x^2 + y^2 + 2xy

x^2 + y^2 + 2xy > 200

x^2 + y^2 > 200 - 2xy

x^2 + y^2 > 100 + (100 - 2xy)

statement 2 ALONE is INSUFFICIENT

x^2 + y^2 > 100 + (100 - 2xy)

if 2xy <= 100 then x^2 + y^2 > 100

from statement 1 we know that

2xy < 100

so both statements 1 and 2 are TOGETHER SUFFICIENT

hope it helps!

Best,
Maciek
Maciek,
i agree with ur explanation. but, i tried plugging in and always got a YES. could anyone help in getting a NO with statement 2
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by pradeepkaushal9518 » Sat Aug 28, 2010 5:52 am
is x^2+y^2>100

1.2xy<100 if x=5 y=5 2xy<100 but 50<100 in case x=10 and y=1 101>100

so insuff

2.(x+y)^2>200

x=10 y=5 15^2=225 10^2+5^2>100 it will be always true hence suff.

hence B i think srisha u r correct
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by Maciek » Sat Aug 28, 2010 6:13 am
Hi all!

you're right and I was wrong.

statement 2 ALONE is SUFFICIENT

if you want to understand it better, you can draw XY graph.

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by sirisha.g » Sat Aug 28, 2010 6:08 pm
So can i consider the OA wrong?
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by anantbhatia » Sun Aug 29, 2010 2:30 am
experts please comment.. I am confused.
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by Maciek » Sun Aug 29, 2010 9:33 am
graph
Image
Hope it helps!
Best,
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