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26 May 2017, 04:41
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If x and y are positive numbers, is \(\frac{y}{x} < \frac{6}{11}\) ?
(1) \(\frac{y}{x} < 0.545\)
(2) \(\frac{x}{y} > 1.834\)
(1) \(\frac{y}{x} < 0.545\)
(2) \(\frac{x}{y} > 1.834\)
26 May 2017, 04:41
Kudos
Bookmarks
Official Solution:
One of the most important things when solving an inequality question is that if the range of the question includes the range of the condition, the condition is sufficient.
If you take the 1st step of the variable approach and modify the original condition and the question,
the question becomes "\(\frac{y}{x} < \frac{6}{11} = 0.54545454 \ldots\)?"
In the case of con 1),\(\frac{y}{x} < 0.545\), then \(0.545 < 0.54545454...\) , so the range of the question includes the range of the condition, hence it is sufficient.
In the case of con 2), it is very difficult to change \(\frac{x}{y} > 1.834\) into \(\frac{y}{x} < \frac{1}{1.834}\) . Therefore, what you need here is CMT 4(B: if you get A or B too easily, consider D). If you apply this, the condition is sufficient. The answer is D.
If you modify the question in order to prove this, you get
"\(\frac{y}{x} < \frac{6}{11} \rightarrow \frac{x}{y} > \frac{11}{6} = 1.8333333 \ldots\ldots\ldots\)", and then from con 2), it becomes \(\frac{x}{y} > 1.834 > 1.8333333 \ldots\ldots\ldots\) Thus, in this case, the range of the question includes the range of the condition, hence it is sufficient. The answer is D. For reference,\(\frac{y}{x} < \frac{6}{11} \rightarrow \frac{x}{y} > \frac{11}{6}\), because the reason that the sign of inequality changes is that both \(x\) and \(y\) are positive.
Answer: D
One of the most important things when solving an inequality question is that if the range of the question includes the range of the condition, the condition is sufficient.
If you take the 1st step of the variable approach and modify the original condition and the question,
the question becomes "\(\frac{y}{x} < \frac{6}{11} = 0.54545454 \ldots\)?"
In the case of con 1),\(\frac{y}{x} < 0.545\), then \(0.545 < 0.54545454...\) , so the range of the question includes the range of the condition, hence it is sufficient.
In the case of con 2), it is very difficult to change \(\frac{x}{y} > 1.834\) into \(\frac{y}{x} < \frac{1}{1.834}\) . Therefore, what you need here is CMT 4(B: if you get A or B too easily, consider D). If you apply this, the condition is sufficient. The answer is D.
If you modify the question in order to prove this, you get
"\(\frac{y}{x} < \frac{6}{11} \rightarrow \frac{x}{y} > \frac{11}{6} = 1.8333333 \ldots\ldots\ldots\)", and then from con 2), it becomes \(\frac{x}{y} > 1.834 > 1.8333333 \ldots\ldots\ldots\) Thus, in this case, the range of the question includes the range of the condition, hence it is sufficient. The answer is D. For reference,\(\frac{y}{x} < \frac{6}{11} \rightarrow \frac{x}{y} > \frac{11}{6}\), because the reason that the sign of inequality changes is that both \(x\) and \(y\) are positive.
Answer: D
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