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20 Mar 2020, 01:41
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
80% (01:23) correct
20%
(01:35)
wrong
based on 86
sessions
History
Date
Time
Result
Not Attempted Yet
Is p < 5?
(1) In the coordinate plane, (3,p) lies inside the circle whose equation is \(x^2 + y^2 = 16\)
(2) In the coordinate plane, the point (p,3) lies on the line \(5x - 3y = 8\)
20 Mar 2020, 02:03
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(1) In the coordinate plane, \((3,p)\) lies inside the circle whose equation is \(x^2 + y^2 = 16\)
--> Let the Center be C = \((0, 0)\) & A = \((3, p)\); radius = \(4\)
Note that, distance of point A from center C is less than radius
--> \(\sqrt{(3 - 0)^2 + (p - 0)^2} < 4\)
--> \(9 + p^2 < 16\)
--> \(p^2 < 7\)
--> \(-\sqrt{7} < p < \sqrt{7}\)
\(p\) is definitely less than \(5\) --> Sufficient
(2) In the coordinate plane, the point \((p,3)\) lies on the line \(5x − 3y = 8\)
--> \((p, 3)\) satisfies the equation
--> \(5*p - 3*3 = 8\)
--> \(5p = 17\)
--> \(p = 3.4\); less than \(5\) --> Sufficient
Option D
--> Let the Center be C = \((0, 0)\) & A = \((3, p)\); radius = \(4\)
Note that, distance of point A from center C is less than radius
--> \(\sqrt{(3 - 0)^2 + (p - 0)^2} < 4\)
--> \(9 + p^2 < 16\)
--> \(p^2 < 7\)
--> \(-\sqrt{7} < p < \sqrt{7}\)
\(p\) is definitely less than \(5\) --> Sufficient
(2) In the coordinate plane, the point \((p,3)\) lies on the line \(5x − 3y = 8\)
--> \((p, 3)\) satisfies the equation
--> \(5*p - 3*3 = 8\)
--> \(5p = 17\)
--> \(p = 3.4\); less than \(5\) --> Sufficient
Option D
Updated on: 03 Apr 2020, 17:55
Originally posted by freedom128 on 20 Mar 2020, 02:12.
Last edited by freedom128 on 03 Apr 2020, 17:55, edited 4 times in total.
Last edited by freedom128 on 03 Apr 2020, 17:55, edited 4 times in total.
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(1) sufficient
x^2+y^2=16 is circle at origin and r^2=16, r=4
since r=4, and p is inside the circle, then p<5
(2) sufficient
5x-3y=8…(3,p)…5x-3(3)=8…5x=17…x=p=17/5=3.4
FINAL ANSWER IS (D)
x^2+y^2=16 is circle at origin and r^2=16, r=4
since r=4, and p is inside the circle, then p<5
(2) sufficient
5x-3y=8…(3,p)…5x-3(3)=8…5x=17…x=p=17/5=3.4
FINAL ANSWER IS (D)
