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.
Nov 1912:30 PM EST
-01:30 PM EST
Learn how Keshav, a Chartered Accountant, scored an impressive 705 on GMAT in just 30 days with GMATWhiz's expert guidance. In this video, he shares preparation tips and strategies that worked for him, including the mock, time management, and more
Nov 2001:30 PM EST
-02:30 PM IST
Learn how Kamakshi achieved a GMAT 675 with an impressive 96th %ile in Data Insights. Discover the unique methods and exam strategies that helped her excel in DI along with other sections for a balanced and high score.
Nov 2211:00 AM IST
-01:00 PM IST
Do RC/MSR passages scare you? e-GMAT is conducting a masterclass to help you learn – Learn effective reading strategies Tackle difficult RC & MSR with confidence Excel in timed test environment- Nov 23
11:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease. 
Nov 2407:00 PM PST
-08:00 PM PST
Full-length FE mock with insightful analytics, weakness diagnosis, and video explanations!
Nov 2510:00 AM EST
-11:00 AM EST
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors.
13 Jul 2022, 08:00
Kudos
Bookmarks
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
35% (02:21) correct
65%
(02:15)
wrong
based on 195
sessions
History
Date
Time
Result
Not Attempted Yet
If \(a + b + c + d = 12\), what is the value of \(\sqrt{a^2+b^2+c^2+d^2}\) ?
(1) \(ab = cd = ad\)
(2) \(|a| = |b| = |c| = |d|\)
M38-09
(1) \(ab = cd = ad\)
(2) \(|a| = |b| = |c| = |d|\)
|
M38-09
Experience GMAT Club Test Questions
Yes, you've landed on a GMAT Club Tests question
Craving more? Unlock our full suite of GMAT Club Tests here
Want to experience more? Get a taste of our tests with our free trial today
Rise to the challenge with GMAT Club Tests. Happy practicing!
19 Aug 2022, 07:41
Kudos
Bookmarks
Bunuel
GMAT CLUB Official Explanation:
If \(a + b + c + d = 12\), what is the value of \(\sqrt{a^2+b^2+c^2+d^2}\) ?
(1) \(ab = cd = ad\)
It's so tempting to think that \(a=b=c=d=3\). In this case \(\sqrt{a^2+b^2+c^2+d^2}=\sqrt{36}=6\) It's certainly a possibility but is it the only one? Let's check:
Well, notice that if any three of the unknowns is 0, then \(ab = cd = ad\) holds and from \(a + b + c + d = 12\) it would follow that the fourth unknown must be 12. For example, \(a=b=c=0\) and \(d=12\). In this case \(\sqrt{a^2+b^2+c^2+d^2}=\sqrt{12^2}=12\)
So, this statement is not sufficient.
(2) \(|a| = |b| = |c| = |d|\)
We can have the following two ases:
I. If all four of the unknowns are positive, then we'd have \(a = b = c = d\). In this case \(a + b + c + d = 4a=12\), which gives \(a = b = c = d=3\) and thus \(\sqrt{a^2+b^2+c^2+d^2}=\sqrt{36}=6\).
II. If three of the unknowns are positive and the fourth one is negative, then we'd have \(a = b = c = -d\) (it does not matter which three are positive, so we can assign any). In this case \(a + b + c + d = 2a=12\), which gives \(a = b = c = -d=6\) and thus \(\sqrt{a^2+b^2+c^2+d^2}=\sqrt{4*36}=12\).
Two different answers. Not sufficient.
FYI: If two of the unknowns are positive and the remaining two are negative, then we'd have \(a = b = -c = -d\). In this case \(a + b + c + d = 0 \neq {12}\). So, this case is NOT possible. Also, all four of the unknowns cannot be negative because the sum of four negative numbers cannot be 12.
(1)+(2) Case II from (2) cannot be true because if one of the unknowns is negative and the other three are positive, then \(ab = cd = ad\) won't hold true: in this case \(ab\), \(cd\), or \(ad\) will be negative and the remaining two expressions will be positive. Thus, we have case I from (2), which means that \(a = b = c = d=3\) and thus \(\sqrt{a^2+b^2+c^2+d^2}=\sqrt{36}=6\). Sufficient.
Answer: C
General Discussion
13 Jul 2022, 09:25
Kudos
Bookmarks
Bunuel
\(a + b + c + d = 12\) - Given Statement
Statement 1 only -
\(ab = cd = ad\)
\(b = d\)
\(a = c\)
\(2 * (a + b) = 12\)
\(a + b = 6\)
\(\sqrt{a^2+b^2+c^2+d^2} = \sqrt{2 * (a^2+b^2)}\)
If a = 1, b = 5
\(\sqrt{2 * (a^2+b^2)} = \sqrt{2 * (1 + 25)} = \sqrt{52}\)
If a = 2, b = 3
\(\sqrt{2 * (a^2+b^2)} = \sqrt{2 * (4 + 9)} = \sqrt{26}\)
Different answers. Hence, INSUFFICIENT
Statement 2 only -
\(|a| = |b| = |c| = |d|\)
From the given statement and Statement 2, we can infer that there can be 2 types of sets.
Set 1 -
{|a|, |a|, |a|, |a|} -> all +ve
\(4|a| = 12\). Therefore, \(a = 3\)
\(\sqrt{a^2+b^2+c^2+d^2}= \sqrt{4*9} = 6\)
Set 2 -
{|a|, |a|, |a|, -|a|} -> 3 +ve and 1 -ve
\(2|a| = 12\). Therefore, \(a = 6\)
\(\sqrt{a^2+b^2+c^2+d^2}= \sqrt{4*36} = 12\)
Different answers. Hence, INSUFFICIENT
1 & 2 Together -
Since a = c & b = d, Set 2 is not possible.
Only Set 1 is possible. Hence \(a = 3\) & \(\sqrt{a^2+b^2+c^2+d^2}= \sqrt{4*9} = 6\)
SUFFICIENT
Hence, the answer is C.
