ezhilkumarank wrote:
Question: The integers r and s are distinct, r <> 0, and s <> 0. If r^2s^2 = -rs, which of the following must be true? [<> -- Not equals]
A. r=-1
B. s=1
C. r-s=0
I - None
II - A alone
III - B alone
IV - C alone
V - A, B and C
Could not follow the explanation given in the book. Help appreciated.
r^2s^2=-rs --> as neither of unknowns equal to 0 we can safely reduce this equation by
rs (as
rs\neq{0}) -->
rs=-1.
A. r=-1 --> must not be true as
r could be 1 and
s could be -1;
B. s=1 --> the same here: must not be true as
r could be 1 and
s could be -1;
C. r-s=0 --> and again the same example works: must not be true as
r could be 1 and
s could be -1 -->
r-s=1-(-1)=2\neq{0} (in fact this statement is never true).
Answer: A (None).
The question asks which of the following
MUST be true, or which of the following is
ALWAYS true no matter what set of numbers you choose. For such kind of questions
if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.
As for "COULD BE TRUE" questions:
The questions asking which of the following
COULD be true are different:
if you can prove that a statement is true for one particular set of numbers, it will mean that this statement could be true and hence is a correct answer.
Hope it helps.
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83% (02:07) correct
