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20 Mar 2020, 04:12
Kudos
Bookmarks
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
63% (02:55) correct
37%
(02:44)
wrong
based on 192
sessions
History
Date
Time
Result
Not Attempted Yet
If x and y are integers and \(z = |x − 2| − |y + 2|\), does \(z = 0\)?
(1) \(\frac{9}{5} < x < \frac{7}{2}\) and \(-3 \leq y < -\frac{21}{11}\)
(2) \(2 \leq x < \frac{7}{3}\) and \(-\frac{22}{7} \leq y < -\frac{13}{7}\)
(1) \(\frac{9}{5} < x < \frac{7}{2}\) and \(-3 \leq y < -\frac{21}{11}\)
(2) \(2 \leq x < \frac{7}{3}\) and \(-\frac{22}{7} \leq y < -\frac{13}{7}\)
20 Mar 2020, 04:28
Kudos
Bookmarks
Bunuel
If x and y are integers and \(z = |x − 2| − |y + 2|\), does \(z = 0\)?
(1) \(\frac{9}{5} < x < \frac{7}{2}\) and \(-3 \leq y < -\frac{21}{11}\)
1.8 < x < 3.5 and -3<=y <= - 2
x = 2 or 3 and y= -3 or -2
NOT SUFFICIENT
(2) \(2 \leq x < \frac{7}{3}\) and \(-\frac{22}{7} \leq y < -\frac{13}{7}\)
2 <= x < 2 1/3 and - 3 1/7 <= y < - 1 6/7
x = 2 and y = -3 or -2
NOT SUFFICIENT
(1) + (2)
(1) \(\frac{9}{5} < x < \frac{7}{2}\) and \(-3 \leq y < -\frac{21}{11}\)
1.8 < x < 3.5 and -3<=y <= - 2
x = 2 or 3 and y= -3 or -2
(2) \(2 \leq x < \frac{7}{3}\) and \(-\frac{22}{7} \leq y < -\frac{13}{7}\)
2 <= x < 2 1/3 and - 3 1/7 <= y < - 1 6/7
x = 2 and y = -3 or -2
x = 2 and y = -3 or -2
NOT SUFFICIENT
IMO E
01 Apr 2020, 12:54
Kudos
Bookmarks
Please help me out here to know if my approach is correct?
In Question Stem,
For z to be = 0,
|x-2| - |y+2| = 0
|x-2| = |y+2|
Squaring both sides,
(x-2)^2 = (y+2)^2
(x-2)^2 - (y+2)^2 = 0
In the form of a^2 - b^2
Hence, (x+y)(x-y-4)=0
Either x = -y or x - y = 4
Statement 1,
Considering x = 2 and y = -3 Not Sufficient
Statement 2,
Considering x = 2 and y = -3 Not Sufficient
Therefore Option E!
In Question Stem,
For z to be = 0,
|x-2| - |y+2| = 0
|x-2| = |y+2|
Squaring both sides,
(x-2)^2 = (y+2)^2
(x-2)^2 - (y+2)^2 = 0
In the form of a^2 - b^2
Hence, (x+y)(x-y-4)=0
Either x = -y or x - y = 4
Statement 1,
Considering x = 2 and y = -3 Not Sufficient
Statement 2,
Considering x = 2 and y = -3 Not Sufficient
Therefore Option E!
