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07 Jun 2015, 09:27
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If \(0 < x < 1 < y\), which of the following must be true?
A. \(1 < \frac{1}{x} < \frac{1}{y}\)
B. \(\frac{1}{x} < 1 < \frac{1}{y}\)
C. \(\frac{1}{x} < \frac{1}{y} < 1\)
D. \(\frac{1}{y} < 1 < \frac{1}{x}\)
E. \(\frac{1}{y} < \frac{1}{x} < 1\)
A. \(1 < \frac{1}{x} < \frac{1}{y}\)
B. \(\frac{1}{x} < 1 < \frac{1}{y}\)
C. \(\frac{1}{x} < \frac{1}{y} < 1\)
D. \(\frac{1}{y} < 1 < \frac{1}{x}\)
E. \(\frac{1}{y} < \frac{1}{x} < 1\)
07 Jun 2015, 09:27
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Official Solution:
If \(0 < x < 1 < y\), which of the following must be true?
A. \(1 < \frac{1}{x} < \frac{1}{y}\)
B. \(\frac{1}{x} < 1 < \frac{1}{y}\)
C. \(\frac{1}{x} < \frac{1}{y} < 1\)
D. \(\frac{1}{y} < 1 < \frac{1}{x}\)
E. \(\frac{1}{y} < \frac{1}{x} < 1\)
Since \(0 < x < 1\), then \(0 < 1 < \frac{1}{x}\) (dividing by \(x\)) and since \(0 < 1 < y\), then \(0 < \frac{1}{y} < 1\) (dividing by \(y\)).
So, we have that \(0 < \frac{1}{y} < 1 < \frac{1}{x}\).
Answer: D
If \(0 < x < 1 < y\), which of the following must be true?
A. \(1 < \frac{1}{x} < \frac{1}{y}\)
B. \(\frac{1}{x} < 1 < \frac{1}{y}\)
C. \(\frac{1}{x} < \frac{1}{y} < 1\)
D. \(\frac{1}{y} < 1 < \frac{1}{x}\)
E. \(\frac{1}{y} < \frac{1}{x} < 1\)
Since \(0 < x < 1\), then \(0 < 1 < \frac{1}{x}\) (dividing by \(x\)) and since \(0 < 1 < y\), then \(0 < \frac{1}{y} < 1\) (dividing by \(y\)).
So, we have that \(0 < \frac{1}{y} < 1 < \frac{1}{x}\).
Answer: D
shasadou
Joined: 12 Aug 2015
Last visit: 24 Nov 2022
Posts: 219
Given Kudos: 1,475
Concentration: General Management, Operations
Schools: Johnson '18 (WL) Duke '18 (M) Tuck '18 (D)
GMAT 1: 640 Q40 V37
GMAT 2: 650 Q43 V36
GMAT 3: 600 Q47 V27
GPA: 3.3
WE:Management Consulting (Consulting)
07 Sep 2015, 13:13
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i picked numbers and this approach is way too time consuming. algebra here is elegant
