M31-35

Question

In which quadrant of the coordinate plane does the point  (x,y)  lie?

(1)  xy = 7 
 
(2)  5x + 7y < -\frac{1}{2}

Bunuel · Accepted Answer

Official Solution:

In which quadrant of the coordinate plane does the point  (x,y)  lie?  
 
(1)  xy = 7 . This implies that  x  and  y  are either both negative or both positive, thus  (x,y)  lies either in III quadrant or in I quadrant. Not sufficient.
 
(2)  5x + 7y < -\frac{1}{2} . Both  x  and  y  can be negative or one of them can be negative and another positive. Not sufficient.
 
 Notice that from this statement it's NOT possible both  x  and  y  to be positive:  5x + 7y = positive + positive = positive , not negative number  -\frac{1}{2} . 
 
(1)+(2) Since (2) rules out possibility of both  x  and  y  being positive, then from (1) we are left with negative  x  and  y :  (x,y)  lies either in III quadrant. Sufficient.

Answer: C

Aurion · Answer

I think this is a  high-quality  question and I agree with explanation. The link to the discussion in the website is broken.

Thanks
Aurion

Bunuel · Answer

Thank you for reporting. We are looking into it.

sadikabid27 · Answer

Bunuel  I'm not sure that how "x and y are either both negative or both positive, lies either in III quadrant or in I quadrant., " and Both xx and yy can be negative or one of them can be negative and another positive." Please provide detailed solution.

Bunuel · Answer

1. Check this: https://gmatclub.com/forum/math-coordin ... 87652.html The first quadrant consists of all points with positive x and y coordinates. The product of x and y coordinates = positive. The third quadrant consists of all points with negative x and y coordinates. The product of x and y coordinates = positive. 2. 5x + 7y < -\frac{1}{2} . Here if both x and y are positive, 5x + 7y, would have been positive, NOT negative, so both x and y cannot be negative. Which means that either both of them are negative or one of them is negative and another positive.

AdityaHongunti · Answer

02 min 11 sec
Your time result is better
than the general system result
of 11 min 14 sec

Could you please explain the later statement. " You time result is better
than the general system result
of 11 min 14 sec" what does it mean? general systemresult?  chetan2u  @sayantc2k  Bunuel

Bunuel · Answer

Could you please post the screenshot? Thank you.

AdityaHongunti · Answer

i found this analysis in "question stats" next to "show explanation"Could you please also explain " the average time incorrect and average tme correct " because on forum the average time is different. Also the above mentioned doubt regarding the general system result .  Bunuel

patto · Answer

I think this is a  high-quality  question and I agree with explanation.

raaz8522 · Answer

I have the same question- what does it mean by 'Your time result is better
than the general system result'. what is a general system result? does it mean a median time a student should take for a given question based on its difficulty?  Bunuel

MrFawkes · Answer

Statement 2: Taking x= 0, we get y<-1/14 and then y=0, we get x<-1/10. Since both are negative, it will lie in the third quadrant.

So, I marked the answer as (B).

Bunuel, can you please help. Am I thinking correctly?

M31-35

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