Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
May 1212:00 PM EDT
-11:59 PM EDT
Make the most of your break with the most realistic GMAT™ prep. Take up to $700 off select products.
Jun 1006:00 AM PDT
-06:15 PM PDT
Register for the GMAT Club Virtual MBA Spotlight Fair – the world’s premier event for serious MBA candidates. This is your chance to hear directly from Admissions Directors at nearly every Top 30 MBA program..
16 Sep 2014, 01:31
Kudos
Bookmarks
If \(x\) is not equal to 0 and \(x^y=1\), then which of the following must be true?
I. \(x=1\)
II. \(x=1\) and \(y=0\)
III. \(x=1\) or \(y=0\)
A. \(I\) only
B. \(II\) only
C. \(III\) only
D. \(I\) and \(III\) only
E. \(None\)
I. \(x=1\)
II. \(x=1\) and \(y=0\)
III. \(x=1\) or \(y=0\)
A. \(I\) only
B. \(II\) only
C. \(III\) only
D. \(I\) and \(III\) only
E. \(None\)
16 Sep 2014, 01:31
Kudos
Bookmarks
Official Solution:
If \(x\) is not equal to 0 and \(x^y=1\), then which of the following must be true?
I. \(x=1\)
II. \(x=1\) and \(y=0\)
III. \(x=1\) or \(y=0\)
A. \(I\) only
B. \(II\) only
C. \(III\) only
D. \(I\) and \(III\) only
E. \(None\)
\(x^y=1\) implies we have one of the following three cases:
1. The base is 1, because \(1^y=1\), for all \(y\);
2. The exponent is 0, because \(x^0=1\), for any nonzero \(x\);
3. The base is -1 and the exponent is even, because \((-1)^x=1\), for any even \(x\)
Notice that if we have case 3, so if \(x=-1\) and \(y\) is any even number, then \((-1)^{even}=1\), and in this case none of the options must be true.
Answer: E
If \(x\) is not equal to 0 and \(x^y=1\), then which of the following must be true?
I. \(x=1\)
II. \(x=1\) and \(y=0\)
III. \(x=1\) or \(y=0\)
A. \(I\) only
B. \(II\) only
C. \(III\) only
D. \(I\) and \(III\) only
E. \(None\)
\(x^y=1\) implies we have one of the following three cases:
1. The base is 1, because \(1^y=1\), for all \(y\);
2. The exponent is 0, because \(x^0=1\), for any nonzero \(x\);
3. The base is -1 and the exponent is even, because \((-1)^x=1\), for any even \(x\)
Notice that if we have case 3, so if \(x=-1\) and \(y\) is any even number, then \((-1)^{even}=1\), and in this case none of the options must be true.
Answer: E
09 Jul 2020, 11:25
Kudos
Bookmarks
I think this is a high-quality question and I agree with explanation. An excellent question
