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16 Sep 2014, 01:50
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If \(r\), \(s\), and \(t\) are nonzero numbers, is \(rt = 14\)?
(1) \(r^2st = 14rs\)
(2) \(\frac{t}{2} = \frac{7}{r}\)
(1) \(r^2st = 14rs\)
(2) \(\frac{t}{2} = \frac{7}{r}\)
16 Sep 2014, 01:50
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Official Solution:
We must determine if \(rt = 14\), given that \(r\), \(s\), and \(t\) are nonzero numbers.
Statement 1 says that \(r^2st = 14rs\). We can divide both sides of the equation by \(rs\), like so: \(\frac{r^2st}{rs} = \frac{14rs}{rs}\). The \(rs\) in the numerator and denominator on each side divide to 1, leaving us with \(rt = 14\). Therefore, statement 1 alone is sufficient to answer the question. Eliminate answer choices B, C, and E. The correct answer choice is either A or D.
Statement 2 says that \(\frac{t}{2} = \frac{7}{r}\). Cross-multiply to obtain \(t \times r = 7 \times 2\), or \(rt = 14\). Statement 2 alone is also sufficient to answer the question.
Answer: D
We must determine if \(rt = 14\), given that \(r\), \(s\), and \(t\) are nonzero numbers.
Statement 1 says that \(r^2st = 14rs\). We can divide both sides of the equation by \(rs\), like so: \(\frac{r^2st}{rs} = \frac{14rs}{rs}\). The \(rs\) in the numerator and denominator on each side divide to 1, leaving us with \(rt = 14\). Therefore, statement 1 alone is sufficient to answer the question. Eliminate answer choices B, C, and E. The correct answer choice is either A or D.
Statement 2 says that \(\frac{t}{2} = \frac{7}{r}\). Cross-multiply to obtain \(t \times r = 7 \times 2\), or \(rt = 14\). Statement 2 alone is also sufficient to answer the question.
Answer: D
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03 Aug 2017, 01:58
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Hi Bunuel, I was wondering how with statement 1, we can simply divide by 'rs' and conclude the answer. What if r is negative? In that case, there would be one negative sign remaining in the LHS post division by 'rs', leaving us with -> -rt=14.
Could you please clarify? Thanks a ton!
Could you please clarify? Thanks a ton!
