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# The integers r and s are distinct, r#0, and s#0. If r^2s^2 =

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The integers r and s are distinct, r#0, and s#0. If r^2s^2 = [#permalink]

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16 Sep 2010, 18:22
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25% (medium)

Question Stats:

72% (01:18) correct 28% (01:23) wrong based on 221 sessions

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The integers r and s are distinct, r#0, and s#0. If r^2s^2 = -rs, which of the following must be true?

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
[Reveal] Spoiler: OA

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16 Sep 2010, 18:34
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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).

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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16 Sep 2010, 18:37
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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.

Since $$r^2s^2 = -rs$$

=> $$r^2s^2 + rs = 0$$,

=> $$rs*(rs+1) = 0$$, since it is given that r and s are not equal to 0

=> $$rs+1 = 0$$ => $$rs= -1$$

Since r and s are integers, rs =-1 is only possible when one of them is 1 and other -1.

A and B are wrong because either of them could be -1 and 1.
C is wrong because r and s can not be equal because if they are, then rs =-1 can not be true.

Hence answer is I - None
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17 Sep 2010, 02:25
rs(rs+1)=0
rs = -1
either r or s can be -1 so B,C , E eliminated

say r = -1 and s= 1 or r=1 or s= -1
r-s can never be 0 since opposite signs.
option D eliminated

Only A

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Re: The integers r and s are distinct, r#0, and s#0. If r^2s^2 = [#permalink]

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14 Oct 2013, 21:40
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Re: The integers r and s are distinct, r#0, and s#0. If r^2s^2 = [#permalink]

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15 Dec 2014, 23:28
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Re: The integers r and s are distinct, r#0, and s#0. If r^2s^2 = [#permalink]

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20 May 2016, 21:56
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Re: The integers r and s are distinct, r#0, and s#0. If r^2s^2 = [#permalink]

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25 Jun 2017, 13:44
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Re: The integers r and s are distinct, r#0, and s#0. If r^2s^2 =   [#permalink] 25 Jun 2017, 13:44
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