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01 Nov 2019, 06:26
Kudos
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
66% (02:08) correct
34%
(02:08)
wrong
based on 701
sessions
History
Date
Time
Result
Not Attempted Yet
If \(x > y\) and \(\frac{1}{x} < \frac{1}{y}\), which of the following could be true:
I. \(0 < x < 1\) and \(0 < y < 1\)
II. \(xy < 0\)
III. \(-1 < x < 0\) and \(-1 < y < 0\)
A. I only
B. I only II only
C. II only III only
D. I only III only
E. I, II, and III
Are You Up For the Challenge: 700 Level Questions
I. \(0 < x < 1\) and \(0 < y < 1\)
II. \(xy < 0\)
III. \(-1 < x < 0\) and \(-1 < y < 0\)
A. I only
B. I only II only
C. II only III only
D. I only III only
E. I, II, and III
Are You Up For the Challenge: 700 Level Questions
01 Nov 2019, 08:54
Kudos
Bookmarks
Bunuel
If \(x > y\) and \(\frac{1}{x} < \frac{1}{y}\), which of the following could be true:
I. \(0 < x < 1\) and \(0 < y < 1\)
II. \(xy < 0\)
III. \(-1 < x < 0\) and \(-1 < y < 0\)
A. I only
B. I only II only
C. II only III only
D. I only III only
E. I, II, and III
Are You Up For the Challenge: 700 Level Questions
I. \(0 < x < 1\) and \(0 < y < 1\)
II. \(xy < 0\)
III. \(-1 < x < 0\) and \(-1 < y < 0\)
A. I only
B. I only II only
C. II only III only
D. I only III only
E. I, II, and III
Are You Up For the Challenge: 700 Level Questions
A very straight forward answer will be
\(x > y\) and \(\frac{1}{x} < \frac{1}{y}\), that is cross-multiplication is NOT changing the sign. MEANS both x and y have SAME sign or xy>0.
I. \(0 < x < 1\) and \(0 < y < 1\)...xy>0..YES
II. \(xy < 0\)...NO
III. \(-1 < x < 0\) and \(-1 < y < 0\)...xy>0..YES
I and III
D
OR
Choose values...
I. \(0 < x < 1\) and \(0 < y < 1\)..........x=0.9 and y=0.3...0.9>0.3 and \(\frac{1}{0.3}>\frac{1}{0.9}\)..\(\frac{10}{3}>\frac{10}{9}\)...YES
II. \(xy < 0\)....x=2 and y=-1...2>-1 but 1/2>1/-1...Eliminate
III. \(-1 < x < 0\) and \(-1 < y < 0\)....x=-0.3 and y=-0.9...-0.3>-0.9 and \(-\frac{1}{0.3}>-\frac{1}{0.9}\)..\(\frac{10}{3}>\frac{10}{9}\)...YES
General Discussion
02 Nov 2019, 03:15
Kudos
Bookmarks
for given condition
\(x > y\) and \(\frac{1}{x} < \frac{1}{y}\)
we can test with integers and fractions ; ( 2,3) ( 1/2,1/3) & ( -1/2,-1/3)
\(0 < x < 1\) and \(0 < y < 1\)
\(-1 < x < 0\) and \(-1 < y < 0\)
true
IMO D;
\(x > y\) and \(\frac{1}{x} < \frac{1}{y}\)
we can test with integers and fractions ; ( 2,3) ( 1/2,1/3) & ( -1/2,-1/3)
\(0 < x < 1\) and \(0 < y < 1\)
\(-1 < x < 0\) and \(-1 < y < 0\)
true
IMO D;
Bunuel
If \(x > y\) and \(\frac{1}{x} < \frac{1}{y}\), which of the following could be true:
I. \(0 < x < 1\) and \(0 < y < 1\)
II. \(xy < 0\)
III. \(-1 < x < 0\) and \(-1 < y < 0\)
A. I only
B. I only II only
C. II only III only
D. I only III only
E. I, II, and III
Are You Up For the Challenge: 700 Level Questions
I. \(0 < x < 1\) and \(0 < y < 1\)
II. \(xy < 0\)
III. \(-1 < x < 0\) and \(-1 < y < 0\)
A. I only
B. I only II only
C. II only III only
D. I only III only
E. I, II, and III
Are You Up For the Challenge: 700 Level Questions
