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 2007:30 AM PST
-08:30 AM PST
Learn what truly sets the UC Riverside MBA apart and how it helps in your professional growth
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 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.
18 Jan 2022, 09:15
Kudos
Bookmarks
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
49% (02:09) correct
51%
(02:13)
wrong
based on 146
sessions
History
Date
Time
Result
Not Attempted Yet
If P*R = Q*S = 3, then the sum of squares of P, Q, R and S is ?
A. at most 18
B. at most 12
C. at least 12
D. at least 18
E. at least 23
Are You Up For the Challenge: 700 Level Questions
A. at most 18
B. at most 12
C. at least 12
D. at least 18
E. at least 23
Are You Up For the Challenge: 700 Level Questions
18 Jan 2022, 11:49
Kudos
Bookmarks
Bunuel
STRATEGY: As with all GMAT Problem Solving questions, we should immediately ask ourselves, Can I use the answer choices to my advantage?
In this case, we COULD test values of P, R, Q and S that satisfy the given equation.
Now we should give ourselves about 20 seconds to identify a faster approach......
.......time's up! If you can't see a faster approach, start testing....
If PR = QS = 3, then it could be the case that P = 1, R = 3, Q = 1 and S = 3
So, P² + R² + Q² + S² = 1² + 3² + 1² + 3² = 1 + 9 + 1 + 9 = 20
Since the sum of the squares in this case is 20, we can eliminate answer choices A, B and E, since they all state that of the sum of the squares CANNOT be 20.
So, by testing these very easy values (in a matter of seconds), we're down to just two answer choices, C and D
Now let's test another set of values...
If PR = QS = 3, then it could be the case that P = √3, R = √3, Q = √3 and S = √3
So, P² + R² + Q² + S² = (√3)² + (√3)² + (√3)² + (√3)² = 3 + 3 + 3 + 3 = 12
Since the sum of the squares in this case is 12, we can eliminate answer choice D, since it states that of the sum of the squares CANNOT be 12.
By the process of elimination, the correct answer is C
General Discussion
15 Aug 2025, 07:27
Kudos
Bookmarks
If P*R = Q*S = 3, then the sum of squares of P, Q, R and S is ?
Let us assume that P = Q = x; R = S = 3/x
\(P^2 + Q^2 + R^2 + S^2 = x^2 + x^2 + \frac{9}{x^2} + \frac{9}{x^2} = 2x^2 + \frac{18}{x^2} = 2 (x^2 + \frac{9}{x^2})\)
Since AM >= GM
\(P^2 + Q^2 + R^2 + S^2 = 2(x^2 + 9/x^2) >= 4 \sqrt{x^2*\frac{9}{x^2}} = 4*3 = 12\)
IMO C
Let us assume that P = Q = x; R = S = 3/x
\(P^2 + Q^2 + R^2 + S^2 = x^2 + x^2 + \frac{9}{x^2} + \frac{9}{x^2} = 2x^2 + \frac{18}{x^2} = 2 (x^2 + \frac{9}{x^2})\)
Since AM >= GM
\(P^2 + Q^2 + R^2 + S^2 = 2(x^2 + 9/x^2) >= 4 \sqrt{x^2*\frac{9}{x^2}} = 4*3 = 12\)
IMO C
