Forum Home > GMAT > Quantitative > Problem Solving (PS)
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.
Sep 2001:00 PM EDT
-02:00 PM EDT
Have you ever wondered how to score a PERFECT 805 on the GMAT? Meet Julia, a banking professional who used the Target Test Prep course to achieve this incredible feat. Julia's story is nothing short of an inspiration.
Sep 2008:00 PM EDT
-11:59 PM EDT
For a limited time only, get 20% off our game-changing GMAT self-study plans and live online classes. Use the coupon code FLASH20 at checkout to save up to $320.
Sep 2105:30 AM PDT
-07:30 AM PDT
Not only the typical inference questions but also all other CR questions on the GMAT require the ability to deduce from the given information. Come master how to draw inferences accurately and efficiently with Verbal Expert-Sunita Singhvi. Limited Seats!
Sep 2111:00 AM IST
-01:00 PM IST
Attend this session to learn how to Deconstruct arguments, Pre-Think Author’s Assumptions, and apply Negation Test.
Sep 2108:00 PM PDT
-09:00 PM PDT
Full-length FE mock with insightful analytics, weakness diagnosis, and video explanations!
Sep 2205:30 AM PDT
-07:30 AM PDT
Unlock GMAT success! Join our webinar for exclusive insights on scoring V85+ in the Verbal section. Proven strategies, expert tips, and essential focus to elevate your GMAT game. Register now for the ultimate Verbal mastery!
Sep 2210:00 AM EDT
-11:00 AM EDT
More and more TTP students are earning impressive scores on the GMAT. Now is the perfect time to join the many GMAT students who made the switch to TTP and surpassed their wildest expectations on test day.- Sep 22
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. 
Sep 2701:00 PM EDT
-11:59 PM EDT
Save 20% on Target Test Prep and get a perfect score like Julia. Through Monday, September 30, get an EXTRA 20% OFF any Target Test Prep GMAT plan by using the coupon code FLASH20 at checkout.
If (r+1/r)^2 = 5, what is the value of (r^3+1/r^3)^2?
[#permalink]
21 Mar 2019, 12:50
21 Mar 2019, 12:50
6
Bookmarks
Expert Reply
Show timer
00:00
A
B
C
D
E
Difficulty:
75%
(hard)
Question Stats:
47% (02:30) correct
53%
(02:55)
wrong
based on 77
sessions
GMATH practice exercise (Quant Class 3)
If \({\left( {r + {1 \over r}} \right)^2} = 5\), what is the value of \(\,{\left( {{r^3} + {1 \over {{r^3}}}} \right)^2}\,\) ?
\(\eqalign{\\
& \left( A \right)\,\,7.75 \cr \\
& \left( B \right)\,\,10 \cr \\
& \left( C \right)\,\,12.25 \cr \\
& \left( D \right)\,\,15 \cr \\
& \left( E \right)\,\,20 \cr}\)
If \({\left( {r + {1 \over r}} \right)^2} = 5\), what is the value of \(\,{\left( {{r^3} + {1 \over {{r^3}}}} \right)^2}\,\) ?
\(\eqalign{\\
& \left( A \right)\,\,7.75 \cr \\
& \left( B \right)\,\,10 \cr \\
& \left( C \right)\,\,12.25 \cr \\
& \left( D \right)\,\,15 \cr \\
& \left( E \right)\,\,20 \cr}\)
Tutor
Joined: 04 Aug 2010
Posts: 1333
Given Kudos: 9
Schools:Dartmouth College
If (r+1/r)^2 = 5, what is the value of (r^3+1/r^3)^2?
[#permalink]
Updated on: 21 Mar 2019, 17:53
Updated on: 21 Mar 2019, 17:53
1
Kudos
1
Bookmarks
Expert Reply
fskilnik
GMATH practice exercise (Quant Class 3)
If \({\left( {r + {1 \over r}} \right)^2} = 5\), what is the value of \(\,{\left( {{r^3} + {1 \over {{r^3}}}} \right)^2}\,\) ?
\(\eqalign{\\
& \left( A \right)\,\,7.75 \cr \\
& \left( B \right)\,\,10 \cr \\
& \left( C \right)\,\,12.25 \cr \\
& \left( D \right)\,\,15 \cr \\
& \left( E \right)\,\,20 \cr}\)
If \({\left( {r + {1 \over r}} \right)^2} = 5\), what is the value of \(\,{\left( {{r^3} + {1 \over {{r^3}}}} \right)^2}\,\) ?
\(\eqalign{\\
& \left( A \right)\,\,7.75 \cr \\
& \left( B \right)\,\,10 \cr \\
& \left( C \right)\,\,12.25 \cr \\
& \left( D \right)\,\,15 \cr \\
& \left( E \right)\,\,20 \cr}\)
(r + 1/r)² = 5
r + 1/r = √5
(r + 1/r)² = 5
r² + 1/r² + 2(r)(1/r) = 5
r² + 1/r² + 2 = 5
r² + 1/r² = 3
Multiplying the blue equation and the red equation, we get:
(r² + 1/r²)(r + 1/r) = 3√5
r³ + (r²)(1/r) + (1/r²)(r) + 1/r³ = 3√5
r³ + (r + 1/r) + 1/r³ = 3√5
Substituting r + 1/r = √5 into the green equation above, we get:
r³ + √5 + 1/r³ = 3√5
r³ + 1/r³ = 2√5
(r³ + 1/r³)² = (2√5)²
(r³ + 1/r³)² = 20
.
Originally posted by GMATGuruNY on 21 Mar 2019, 13:54.
Last edited by GMATGuruNY on 21 Mar 2019, 17:53, edited 1 time in total.
Last edited by GMATGuruNY on 21 Mar 2019, 17:53, edited 1 time in total.
Re: If (r+1/r)^2 = 5, what is the value of (r^3+1/r^3)^2?
[#permalink]
21 Mar 2019, 14:23
21 Mar 2019, 14:23
1
Kudos
Expert Reply
fskilnik
GMATH practice exercise (Quant Class 3)
If \({\left( {r + {1 \over r}} \right)^2} = 5\), what is the value of \(\,{\left( {{r^3} + {1 \over {{r^3}}}} \right)^2}\,\) ?
\(\eqalign{\\
& \left( A \right)\,\,7.75 \cr \\
& \left( B \right)\,\,10 \cr \\
& \left( C \right)\,\,12.25 \cr \\
& \left( D \right)\,\,15 \cr \\
& \left( E \right)\,\,20 \cr}\)
\({\left( {r + {1 \over r}} \right)^2} = 5\,\,\,\,\,\left( * \right)\)If \({\left( {r + {1 \over r}} \right)^2} = 5\), what is the value of \(\,{\left( {{r^3} + {1 \over {{r^3}}}} \right)^2}\,\) ?
\(\eqalign{\\
& \left( A \right)\,\,7.75 \cr \\
& \left( B \right)\,\,10 \cr \\
& \left( C \right)\,\,12.25 \cr \\
& \left( D \right)\,\,15 \cr \\
& \left( E \right)\,\,20 \cr}\)
\(? = \,{\left( {{r^3} + {1 \over {{r^3}}}} \right)^2}\)
\(?\,\,\, = \,\,\,{\left[ {\left( {r + {1 \over r}} \right)\left( {{r^2} - r \cdot {1 \over r} + {1 \over {{r^2}}}} \right)} \right]^{\,2}} = {\left( {r + {1 \over r}} \right)^2}{\left( {{r^2} - 1 + {1 \over {{r^2}}}} \right)^2}\,\,\,\mathop = \limits^{\left( * \right)} \,\,\,5 \cdot {\left( {{r^2} - 1 + {1 \over {{r^2}}}} \right)^2}\,\,\,\mathop = \limits^{\left( {**} \right)} \,\,\,20\)
\(\left( {**} \right)\,\,{r^2} - 1 + {1 \over {{r^2}}} = \left( {{r^2} + 2 + {1 \over {{r^2}}}} \right) - 3 = {\left( {r + {1 \over r}} \right)^2} - 3\,\,\,\mathop = \limits^{\left( * \right)} \,\,\,2\)
The correct answer is (E).
We follow the notations and rationale taught in the GMATH method.
Regards,
Fabio.
