Is r negative?

Question

Is  r  negative?

a)  r < s

b)  r = -s

Salsanousi · Answer

r < s doesn't tell us anything specific.

if s = 0 then r < 0

if s = 1 then r < 1 so it could be anything. Insufficient.

r = -s

if s = 1 then r = -1

if s = -1 then r = 1 also insufficient.

Combined we substitute in the inequality.

-s < s
0 < 2s
0 < s

that means s is positive.

given that s is positive then yes r is negative.

C is sufficient.

souvikgmat1990 · Answer

1. Not sufficient as we have no info about S
2. Not sufficient either as we have no info about S

Now combining 1 and 2 
We know r=-s therefore s=-r
So plugging it in eqn. 1 r<s
r<-r
r+r<0
2r<0
Dividing by 2
r<0

Hence C is sufficient

fskilnik · Answer

r\,\,\mathop < \limits^? \,\,0

\left( 1 ight)\,\,\,\,r < s\,\,\,\,\left\{ \begin{gathered}
 \,{	ext{Take}}\,\,\left( {r,s} ight) = \left( {0,1} ight)\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{	ext{NO}}} ightangle \,\, \hfill \
 \,{	ext{Take}}\,\,\left( {r,s} ight) = \left( { - 1,0} ight)\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{	ext{YES}}} ightangle \,\, \hfill \ 
\end{gathered} ight.

\left( 2 ight)\,\,\,\,r = - s\,\,\,\,\left\{ \begin{gathered}
 \,{	ext{Take}}\,\,\left( {r,s} ight) = \left( {1, - 1} ight)\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{	ext{NO}}} ightangle \,\, \hfill \
 \,{	ext{Take}}\,\,\left( {r,s} ight) = \left( { - 1,1} ight)\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{	ext{YES}}} ightangle \,\, \hfill \ 
\end{gathered} ight.

\left( {1 + 2} ight)\,\,\,\,\left\{ \begin{gathered}
 \,\,r = 0\,\,\,\,\mathop \Rightarrow \limits^{\left( 2 ight)} \,\,\,\,s = 0\,\,\,\, \Rightarrow \,\,\,\,\,\left( 1 ight)\,\,\,{	ext{contradicted}} \hfill \
 \,\,r > 0\,\,\,\,\,\mathop \Rightarrow \limits^{\left( 2 ight)} \,\,\,\,s < 0\,\,\,\, \Rightarrow \,\,\,\,\,\left( 1 ight)\,\,\,{	ext{contradicted}} \hfill \ 
\end{gathered} ight.\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,r \geqslant 0\,\,\,{	ext{impossible}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{	ext{YES}}} ightangle \,\,\,\,\,\,

This solution follows the notations and rationale taught in the GMATH method.

Regards, 
Fabio.

QuantMadeEasy · Answer

(1) r can be positive or negative. Insufficient

(2) When r is positive, s is negative and vice versa. Insufficient

(1)+(2), r is smaller than s; r is negative and s is positive. C is correct.

CrackverbalGMAT · Answer

Since the question stem does not give us any information, let us go straight to the statements.

From statement I alone,  we can only gather that r is smaller than s . But, this  does not tell us anything about the sign of r .  r may be positive, negative or ZERO . 
Statement I alone is insufficient. Answer options A and D can be eliminated. Possible answer options at this stage are B, C or E.

From statement II alone, r = -s.  From this , we see that  the sign of r depends on the sign of s . If s is positive, r is negative and vice versa. Additionally, if s = 0, then r = 0. Clearly insufficient to answer whether r is negative.

Answer option B can be eliminated. The possible answer options are C or E.

Combining the data from statements I and II, we have the following:
From statement II, if s is positive, r is negative. This satisfies the data given in the first statement that r<s.
 
But  if s is negative, r becomes positive . But, according to statement I, r has to be less than s. Therefore,  we can conclude that s cannot be negative and hence r cannot be positive if it has to satisfy the combination of statements. 
 
Similarly, s cannot be ZERO as well since that would make both r and s equal, which is not allowed.

So, from the combination of statements, we can answer that r is definitely negative. The combination of statements is sufficient. Answer option E can be eliminated.
 The correct answer option is C .

Hope that helps!

bumpbot · Answer

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Is r negative?

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Is r negative?

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