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18 Apr 2007, 08:17
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If x^2 +y^2 is less than 9, is x^2 less than x ?
(1) y^2 is greater than 8.
(2) x is 3 greater than y.
(1) y^2 is greater than 8.
(2) x is 3 greater than y.
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18 Apr 2007, 12:42
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I would like to say (E) 
I prefer to solve it with the XY Plan.
x^2 < x ?
<=> x^2 - x < 0 ?
<=> x*(x-1) < 0 ?
<=> 0 < x < 1 ?
x^2 +y^2 < 9
<=> x^2 + y^2 < 3^2 >>> In the XY plan, this represents a surface delimited by the circle with 0(0,0) as center and 3 as radius.
So, 0 < x < 1 creates a part of this circle's surface.
From 1
y^2 > 8
<=> y > 2*qrt(2) or y < -2*qrt(2)
Creating 2 horizontal lines (Fig 1), one at -2*qrt(2) and one at 2*qrt(2), we observe especially for negative values of x that we have a surface out of 0 < x < 1.
Also, we have a part of the surface created by these 2 lines that are in the 0 < x < 1.
INSUFF.
From 2
x=3*y
<=> y = 1/3*x >>> it's a line passing by 0(0,0) (Fig 2).
All negative values of x will create negative values of y. In this case, we are not in the section 0 < x < 1.
Also, we have a part of the line that passes throught 0 < x < 1.
INSUFF.
Both (1) & (2)
Here, looking the 2 conditions and so 2 graphs, there is no common area within the circle.... So, it's pretty weird and we cannot conclude...
I tend to say (E).
I prefer to solve it with the XY Plan.
x^2 < x ?
<=> x^2 - x < 0 ?
<=> x*(x-1) < 0 ?
<=> 0 < x < 1 ?
x^2 +y^2 < 9
<=> x^2 + y^2 < 3^2 >>> In the XY plan, this represents a surface delimited by the circle with 0(0,0) as center and 3 as radius.
So, 0 < x < 1 creates a part of this circle's surface.
From 1
y^2 > 8
<=> y > 2*qrt(2) or y < -2*qrt(2)
Creating 2 horizontal lines (Fig 1), one at -2*qrt(2) and one at 2*qrt(2), we observe especially for negative values of x that we have a surface out of 0 < x < 1.
Also, we have a part of the surface created by these 2 lines that are in the 0 < x < 1.
INSUFF.
From 2
x=3*y
<=> y = 1/3*x >>> it's a line passing by 0(0,0) (Fig 2).
All negative values of x will create negative values of y. In this case, we are not in the section 0 < x < 1.
Also, we have a part of the line that passes throught 0 < x < 1.
INSUFF.
Both (1) & (2)
Here, looking the 2 conditions and so 2 graphs, there is no common area within the circle.... So, it's pretty weird and we cannot conclude...
I tend to say (E).
Attachments
Fig1_Y power 2 above 8.gif [ 4.32 KiB | Viewed 1874 times ]
Fig2_X divided by 3.gif [ 4.32 KiB | Viewed 1893 times ]
18 Apr 2007, 13:01
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statement 1 simply means that y^2 is greater than 8.. or X is less than 1..we dont know if X is positive or negative..therefore insuff..
statement 2..x is 3 greater than y..to me means x=y+3?
not knowing the sign of y or x ..we cant really say anything ..
together..we know that y has to be negative..then we know that x is 3+y; which means x is positive..and is less than 1..this is sufficient..
C it is..
statement 2..x is 3 greater than y..to me means x=y+3?
not knowing the sign of y or x ..we cant really say anything ..
together..we know that y has to be negative..then we know that x is 3+y; which means x is positive..and is less than 1..this is sufficient..
C it is..
Fig
