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Number properties

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Source: — Problem Solving |
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by GmatKiss » Sun Oct 16, 2011 10:35 am
IMO: E
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by moonraker » Sun Oct 16, 2011 10:51 am
The answer should be C
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by GmatKiss » Sun Oct 16, 2011 12:03 pm
moonraker wrote:The answer should be C
Could you pls explain the same.

TIA,
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by samyukta » Sun Oct 16, 2011 1:08 pm
GmatKiss wrote:
moonraker wrote:The answer should be C
Could you pls explain the same.

TIA,
GK
From the stem we can knowthe signs of a & b.It will be in either Quad I (+,+ )or III(-,-).

st 1 : we are NOT certain of the sign of x & y... Insufficient

st 2 : we can find the sign of x only. We will have NO info about sign of y.. Insufficient

Combining; since we know the sign of x from st 2 & we know that x & y should have same sign ( from st 1) we can zero down the quadrant.

Yes (-x,y) belong to the same quadrant.Pick C.
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by moonraker » Mon Oct 17, 2011 9:01 am
GmatKiss wrote:
moonraker wrote:The answer should be C
Could you pls explain the same.

TIA,
GK
The only possible quadrants for (a,b) would be 1st and 3rd as the sign of the both a and b would be same. hence (-a,b) and (-b,a) would be in the same quadrant which would again either be 2nd or 3rd.

For example, 1,2 or -1,-2 .
now for (-a,b) the co-ordinates would be (-1,2) and for (-b,a) it would be (-2,1) which both lie in quadrant number 2.

For (-1,-2) :
Taking (-a,b) the co-ordinates would be (1,-2) and for (-b,a) it would be (2,-1) which lie in quadrant number 4.

Note: Try taking the co-ordinates from quadrant 2 and 4 for (a,b)------- you will not find the conditions of the co-ordinates lying in the same quadrant to be true.

So we now know that (a,b) will lie in quadrant number 1 or 3....................

Now for (-x,y) lying in the same quadrant as (-a,b) or (-b,a)....... which are Q1 and Q3.

Statement 1: xy > 0........ this is only possible when (x,y) lie in Q1 or Q3.

here we do not know which quadrant exactly and also we don't know where do (a,b) and (-a,b) or (-b,a) lie.

Statement 2: ax > 0...........
this tells us that both a and x will lie in the same quadrant i.e: Q1 or Q3 but always same quadrant.

Statement 1 and 2 individually do not provide any clear solution.

But combining both of them we see that (a,b) and (x,y) will always lie in the same quadrant........
hence (-a,b) and (-x,y) will also lie in the same quadrant along with (-b,a)(Q1 or Q3)..........

here the specific quadrant itself does not matter........but being in the same quadrant is all what matters

=> hence option C....
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