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integer r and s are distinct

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integer r and s are distinct

by Nijeesh » Sun Feb 21, 2010 7:45 pm
The integer r and s are distinct and each one not equal to 0. if (r^2)(S^2)=-rs which of the following must be true?

i. r=-1
ii. s=1
iii. r-s=0

a) None
b) i only
c) ii only
d) iii only
e) i, ii and iii
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by harsh.champ » Sun Feb 21, 2010 7:55 pm
Nijeesh wrote:The integer r and s are distinct and each one not equal to 0. if (r^2)(S^2)=-rs which of the following must be true?

i. r=-1
ii. s=1
iii. r-s=0

a) None
b) i only
c) ii only
d) iii only
e) i, ii and iii
(r^2)(S^2)=-rs
Hence,rs=-1.
Alos,since both are distinct either can be 1 or -1.Hence,i and ii not surely true.
For iii, r-s = 0(can not be )either -2 or +2.
Answer would be A.

I hope the explanation is helpful.
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by ajith » Sun Feb 21, 2010 8:01 pm
Nijeesh wrote:The integer r and s are distinct and each one not equal to 0. if (r^2)(S^2)=-rs which of the following must be true?

i. r=-1
ii. s=1
iii. r-s=0

a) None
b) i only
c) ii only
d) iii only
e) i, ii and iii
s= -1; r = +1 r-s = 2

satisfies r^2*s^2 = -rs

Hence none of I, II or III must be true.

A
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by shashank.ism » Sun Feb 21, 2010 8:34 pm
Nijeesh wrote:The integer r and s are distinct and each one not equal to 0. if (r^2)(S^2)=-rs which of the following must be true?

i. r=-1
ii. s=1
iii. r-s=0

a) None
b) i only
c) ii only
d) iii only
e) i, ii and iii
(r^2)(S^2)=-rs --> rs(rs+1)=0 --> rs=0 or rs=-1

so none fits the given expression and hence A
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by ashforgmat » Sun Feb 21, 2010 9:34 pm
None Will be my guess since r=-1, s=1 and r=1, s=-1 are the 2 solutions. And none of the choices give this as the answer.
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