If rt ≠ 0, is qt sr? (1) q/r

Question

If  rt ≠ 0 , is  qt > sr ?

(1)  \frac{q}{r} < \frac{s}{t}

(2)  rt < 0

IanOuellette · Answer

I assume that the 1 and 2 under the question are the conditions? If so:
since rt < 0, rt /= 0, we know that r and t must not be 0. There will be 2 possibilities:
1. r < 0 , t > 0
2. r > 0, t < 0
Since we know that q/r < s/t
For 1: since t > 0, qt/r < s (no sign flipping), then since r < 0, qt > sr (sign flipped)
For 2: Since r > 0, q < rs/t (no sign flipping), then since t < 0, qt > sr (sign flipped)
And this is how you solve inequalities related problem

Bunuel · Answer

If rt ≠ 0 , is qt > sr ? (1) \frac{q}{r} < \frac{s}{t} If r and s have the same sign, then after cross-multiplying we'll get qt > sr (if r and s are both positive then after cross-multiplying we won't flip the sign and if r and s are both negative then after cross-multiplying we'll flip the sign twice, so still will get the same one). If r and s have different signs, then after cross-multiplying we'll get qt < sr (after cross-multiplying we'll flip the sign once). Not sufficient. (2) rt < 0 . This statement tells us that r and t have different signs but we still know nothing about q and s. Not sufficient. (1)+(2) Since from (2) r and t have different signs, then from (1) we'll get the second case: qt < sr. Sufficient. Answer: C. Hope it's clear.

Raksat · Answer

From statement 1 qt-sr/rt <0 Hence either rt<0 or qt-sr<0 Therefore we cannot prove from statement 1 that qt>sr Insufficient. From statement 2 rt<0 either r or t is less than 0. but still we donot know anything about s or q hence insufficient Combining both the statements we get , rt<0 then qt-sr must be positive , hence qt>sr Hence the solution should be C

push12345 · Answer

Hi 
  Bunuel

We don't know sign of q and s so how only on basis of r and t we infer the answer...

Could you please explain

Posted from my mobile device

Hero8888 · Answer

When you multiply both sides of inequality on number <0, you have to flip sign (don't care about other numbers, because you are given the inequality as a fact, it must work with any those variables)
q/r<s/t (* both sides qt<0), so qt > sr

push12345 · Answer

Thanks for explanation.I got it now.

GyMrAT · Answer

Statement 1: \frac{q}{r} < \frac{s}{t} \frac{q}{r} - \frac{s}{t} < 0 \frac{(qt - sr)}{rt} < 0 Hence, Case 1 (qt - sr) > 0 , rt < 0 or Case 2 (qt - sr) < 0 , rt > 0 Statement 1 alone is Not Sufficient. Statement 2: rt < 0 , no information about other variables, Hence, Statement 2 alone is Not Sufficient. Combining both statements, we get Case 1. Combining the 2 statements is sufficient. Answer C. Thanks, GyM

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If rt ≠ 0, is qt > sr? (1) q/r < s/t (2) rt < 0

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