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 0510:00 AM PDT
-11:00 AM PDT
GMAT Inequalities is a high-frequency topic in GMAT Quant, but many students struggle because the concepts behave differently from standard algebra. Understanding the right rules, patterns, and edge cases can significantly improve both speed and accuracy.- May 06
08:30 AM PDT
-09:30 AM PDT
In Episode 3 of our GMAT Ninja Critical Reasoning series, we tackle Discrepancy, Paradox, and Explain an Oddity questions. You know the feeling: the passage gives you two facts that seem completely contradictory.... - May 08
08:00 AM PDT
-08:30 AM PDT
Join the special YouTube live-stream for selecting the winners of GMAT Club MBA Scholarships sponsored by Juno live. Watch who gets these coveted MBA scholarships offered by GMAT Club and Juno.
16 Sep 2014, 01:28
Kudos
Bookmarks
What is the value of \(xy\)?
(1) \(3^x*5^y=75\)
(2) \(3^{(x-1)(y-2)}=1\)
(1) \(3^x*5^y=75\)
(2) \(3^{(x-1)(y-2)}=1\)
16 Sep 2014, 01:28
Kudos
Bookmarks
Official Solution:
What is the value of \(xy\)?
Notice that we are not told that \(x\) and \(y\) are integers.
(1) \(3^x*5^y=75\).
\(3^x5^y=75\), can be rewritten as \(3^x5^y=3^15^2\). If \(x\) and \(y\) are integers, then \(x=1\) and \(y=2\). However, if they are not integers, an infinite number of solutions would exist, since any value of \(x\) would have a corresponding non-integer value of \(y\) that would satisfy the equation and vice versa. For example, if \(y=1\), then \(3^x5^y=3^x5=75\), hence \(3^x=15\) and \(x\) would be some irrational number, approximately equal to \(2.5\). Therefore, statement (1) alone is not sufficient to determine the value of \(xy\).
(2) \(3^{(x-1)(y-2)}=1\).
This above implies that \((x-1)(y-2)=0\). Thus, either \(x=1\) and \(y\) can be any number (including \(2\)), or \(y=2\) and \(x\) can be any number (including \(1\)). However, this statement alone does not give us a unique solution for \(xy\). Therefore, statement (2) alone is not sufficient.
(1)+(2) If from (2) \(x=1\), then from (1) we have \(3^x5^y=3*5^y=75\), which gives us \(y=2\). If from (2) \(y=2\), then from (1) we have \(3^x5^y=3^x*25=75\), which gives us \(x=1\). Thus, we have a unique solution of \(x=1\) and \(y=2\), and the value of \(xy\) is \(1*2=2\). Sufficient.
Answer: C
What is the value of \(xy\)?
Notice that we are not told that \(x\) and \(y\) are integers.
(1) \(3^x*5^y=75\).
\(3^x5^y=75\), can be rewritten as \(3^x5^y=3^15^2\). If \(x\) and \(y\) are integers, then \(x=1\) and \(y=2\). However, if they are not integers, an infinite number of solutions would exist, since any value of \(x\) would have a corresponding non-integer value of \(y\) that would satisfy the equation and vice versa. For example, if \(y=1\), then \(3^x5^y=3^x5=75\), hence \(3^x=15\) and \(x\) would be some irrational number, approximately equal to \(2.5\). Therefore, statement (1) alone is not sufficient to determine the value of \(xy\).
(2) \(3^{(x-1)(y-2)}=1\).
This above implies that \((x-1)(y-2)=0\). Thus, either \(x=1\) and \(y\) can be any number (including \(2\)), or \(y=2\) and \(x\) can be any number (including \(1\)). However, this statement alone does not give us a unique solution for \(xy\). Therefore, statement (2) alone is not sufficient.
(1)+(2) If from (2) \(x=1\), then from (1) we have \(3^x5^y=3*5^y=75\), which gives us \(y=2\). If from (2) \(y=2\), then from (1) we have \(3^x5^y=3^x*25=75\), which gives us \(x=1\). Thus, we have a unique solution of \(x=1\) and \(y=2\), and the value of \(xy\) is \(1*2=2\). Sufficient.
Answer: C
General Discussion
10 Oct 2016, 00:56
Kudos
Bookmarks
Bunuel
Please clarify .
in condition B. if x=1, then y must have to be 2, or if y =2, x is 1. so why not B sufficient? What did i miss?
