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A is a set holding only all possible solutions of x, and B is a set ho
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25 Sep 2019, 23:23
(x−a)(x−b)(x−c)(x−d)=0
(|y|−a)(|y|−b)(|y|−c)(|y|−d)=0
set A represents only possible values of x
set B represents only possible values of y
STATEMENT (1)-- a and b are positive
but we don't have any information on c and d
set A =(a,b,c,d)
if c and d are positive -then set B = (a,-a,b,-b,c,-c,d,-d)
is the number of elements in set A equal to the number of elements in set B?---NO
if c and d are negative -then set B = (a,-a,b,-b) --(since c and d are negative let c = -2 d = -3--(|y|−a)(|y|−b)(|y|−c)(|y|−d)--(|y|−a)(|y|−b)(|y|+2)(|y|+3) = 0)
is the number of elements in set A equal to the number of elements in set B?---YES
INSUFFICIENT
STATEMENT (2)--c and d are negative
but we don't have any information on a and b
set A =(a,b,c,d)
if a and b are positive -then set B = (a,-a,b,-b,) --(since c and d are negative let c = -2 d = -3--(|y|−a)(|y|−b)(|y|−c)(|y|−d)--(|y|−a)(|y|−b)(|y|+2)(|y|+3) = 0)
is the number of elements in set A equal to the number of elements in set B?---YES
if a and b are negative -then set B = 0 solution -no element in set B (suppose a=-1 b=-4 then (|y|+1)(|y|+4)(|y|+2)(|y|+3) = 0--no solution )
is the number of elements in set A equal to the number of elements in set B?---NO
INSUFFICIENT
combining both statements
we know-- a and b are positive and c and d are negative
set A = (a,b,c,d)
set B = (a,-a,b,-b)--(since c and d are negative let c = -2 d = -3--(|y|−a)(|y|−b)(|y|−c)(|y|−d)--(|y|−a)(|y|−b)(|y|+2)(|y|+3) = 0--has 4 solutions)
is the number of elements in set A equal to the number of elements in set B?---YES
SUFFICIENT
C is the correct answer