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If x^2 +y^2 is less than 9, is x^2 less than x ? (1) y^2 is 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.



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If x^2 +y^2 is less than 9, is x^2 less than x ? (1) y^2 is 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).
Attachments

Fig1_Y power 2 above 8.gif
Fig1_Y power 2 above 8.gif [ 4.32 KiB | Viewed 1923 times ]

Fig2_X divided by 3.gif
Fig2_X divided by 3.gif [ 4.32 KiB | Viewed 1944 times ]

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If x^2 +y^2 is less than 9, is x^2 less than x ? (1) y^2 is 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..

Fig
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>>> 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>>> 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).
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Fig
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If x^2 +y^2 is less than 9, is x^2 less than x ? (1) y^2 is 18 Apr 2007, 13:08
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fresinha12
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..

Fig
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>>> 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>>> 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).
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Yes... Probably, it's not 3 times as I understood it but rather 3 upper than y.

So, we have a line y = x-3 and then make sens to have only a few part of it, at bottom of the circle, that is only between 0 < x < 1 limit and y < -2*sqrt(2).

C it is :)
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FN
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If x^2 +y^2 is less than 9, is x^2 less than x ? (1) y^2 is 18 Apr 2007, 13:12
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nice graphs by the way :)

Fig
fresinha12
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..

Fig
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>>> 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>>> 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).

Yes... Probably, it's not 3 times as I understood it but rather 3 upper than y.

So, we have a line y = x-3 and then make sens to have only a few part of it, at bottom of the circle, that is only between 0 < x < 1 limit and y < -2*sqrt(2).

C it is :)
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:lol: :lol:
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If x^2 +y^2 is less than 9, is x^2 less than x ? (1) y^2 is 19 Apr 2007, 13:03
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good one. i was drawn to B but agree with C.



fresinha12
nice graphs by the way :)

Fig
fresinha12
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..

[quote="Fig"]I would like to say (E) :)

I prefer to solve it with the XY Plan.

x^2 x^2 - x x*(x-1) 0 x^2 + y^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 8
2*qrt(2) or y >> 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).

Yes... Probably, it's not 3 times as I understood it but rather 3 upper than y.

So, we have a line y = x-3 and then make sens to have only a few part of it, at bottom of the circle, that is only between 0 < x < 1 limit and y < -2*sqrt(2).

C it is :)
:lol: :lol:[/quote]



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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