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Updated on: 09 Nov 2025, 05:15
Originally posted by ramjas1234 on 09 Nov 2025, 03:08.
Last edited by Bunuel on 09 Nov 2025, 05:15, edited 2 times in total.
Last edited by Bunuel on 09 Nov 2025, 05:15, edited 2 times in total.
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If |x − 2| = 9 and |y + 9| = 8, then find the minimum possible value of xy, where x and y are real numbers.
A. −207
B. −187
C. −154
D. −11
E. 119
A. −207
B. −187
C. −154
D. −11
E. 119
09 Nov 2025, 03:12
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My doubt is that in such questions, taking 2 cases each for x>=0, x<0 and y>=0 and y<0 , so if we get the answer/value of one with opposite sign to what we solved then do we reject that value? eg- here in this question, when taking y >=0
|y + 9| = 8
⇒ y + 9 = 8
⇒ y = −1
so, here we are getting value of y as negative but we solved for y>=0 so ans should have been positive, now since it's negative should we reject this option choice basis this? and go with evaluating the rest?
could you pls clarify this? as in some places we do reject the value basis this logic but in the explanation provided it's not rejected. Bunuel
|y + 9| = 8
⇒ y + 9 = 8
⇒ y = −1
so, here we are getting value of y as negative but we solved for y>=0 so ans should have been positive, now since it's negative should we reject this option choice basis this? and go with evaluating the rest?
could you pls clarify this? as in some places we do reject the value basis this logic but in the explanation provided it's not rejected. Bunuel
09 Nov 2025, 03:19
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Not quite.
|y + 9| = 8
Here your cases are y > -9 and y < -9
(You get the points by equating the term inside the mod to 0, ie y+9=0 gives y to be -9)
For y > -9: y+9 = 8 => y = -1 (here -1 is greater than -9)
For y < -9: -(y+9) = 8 => y = -17 (here -17 is smaller than -9)
So both values are fine.
To show an anomaly:
|y + 9| = -8
Here your cases are y > -9 and y < -9
For y > -9: y+9 = -8 => y = -17 (here -1 is Not greater than -9)
For y < -9: -(y+9) = -8 => y = -1 (here -1 is Not smaller than -9)
So both values are rejected.
Alternatively, in the second case, absolute value of anything cannot be negative, so there clearly is no solution
Hope this helps
|y + 9| = 8
Here your cases are y > -9 and y < -9
(You get the points by equating the term inside the mod to 0, ie y+9=0 gives y to be -9)
For y > -9: y+9 = 8 => y = -1 (here -1 is greater than -9)
For y < -9: -(y+9) = 8 => y = -17 (here -17 is smaller than -9)
So both values are fine.
To show an anomaly:
|y + 9| = -8
Here your cases are y > -9 and y < -9
For y > -9: y+9 = -8 => y = -17 (here -1 is Not greater than -9)
For y < -9: -(y+9) = -8 => y = -1 (here -1 is Not smaller than -9)
So both values are rejected.
Alternatively, in the second case, absolute value of anything cannot be negative, so there clearly is no solution
Hope this helps
