GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 22 Jun 2018, 02:14

Close

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

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If p + q = 7 and pq = 12, then what is the value of (1/p^2) + (1/q^2)

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

1 KUDOS received
Senior Manager
Senior Manager
User avatar
D
Joined: 02 Jan 2017
Posts: 314
Location: Canada
Reviews Badge
If p + q = 7 and pq = 12, then what is the value of (1/p^2) + (1/q^2) [#permalink]

Show Tags

New post 08 Mar 2017, 05:29
1
3
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

88% (01:21) correct 12% (01:24) wrong based on 51 sessions

HideShow timer Statistics

If p + q = 7 and pq = 12, then what is the value of (1/p^2) + (1/q^2) ?

(A) 1/6

(B) 25/144

(C) 49/144

(D) 7/12

(E) 73/144
Top Contributor
VP
VP
User avatar
S
Status: Top MBA Admissions Consultant
Joined: 24 Jul 2011
Posts: 1370
GMAT 1: 780 Q51 V48
GRE 1: 1540 Q800 V740
Re: If p + q = 7 and pq = 12, then what is the value of (1/p^2) + (1/q^2) [#permalink]

Show Tags

New post 08 Mar 2017, 07:38
Top Contributor
(1/p^2) + (1/q^2) = (p^2 + q^2) / (pq)^2 = ((p+q)^2 - 2pq)/(pq)^2 = (7^2 - 2*12)/(12^2) = 25/144

(B) it is.
_________________

GyanOne | Top MBA Rankings and MBA Admissions Blog

Top MBA Admissions Consulting | Top MiM Admissions Consulting

Premium MBA Essay Review|Best MBA Interview Preparation|Exclusive GMAT coaching

Get a FREE Detailed MBA Profile Evaluation | Call us now +91 98998 31738

1 KUDOS received
Intern
Intern
avatar
S
Joined: 11 Aug 2016
Posts: 47
Location: India
Concentration: Operations, General Management
Schools: HBS '18, ISB '17, IIMA
GMAT 1: 710 Q49 V38
GPA: 3.95
WE: Design (Manufacturing)
GMAT ToolKit User
Re: If p + q = 7 and pq = 12, then what is the value of (1/p^2) + (1/q^2) [#permalink]

Show Tags

New post 08 Mar 2017, 08:11
1
1
\(\frac{1}{p^2}\)+\(\frac{1}{q^2}\)
=\(\frac{p^2+q^2}{p^2q^2}\)
=\(\frac{(p+q)^2-2pq}{(pq)^2}\)
=\(\frac{7^2-2*12}{12^2}\)
=\(\frac{49-24}{144}\)
=\(\frac{25}{144}\)

Answer B
1 KUDOS received
Board of Directors
User avatar
G
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3511
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member
If p + q = 7 and pq = 12, then what is the value of (1/p^2) + (1/q^2) [#permalink]

Show Tags

New post 08 Mar 2017, 08:14
1
vikasp99 wrote:
If p + q = 7 and pq = 12, then what is the value of (1/p^2) + (1/q^2) ?

(A) 1/6

(B) 25/144

(C) 49/144

(D) 7/12

(E) 73/144


\(p + q = 12\)

So, we can say \(p = 4\) and \(q =3\)

Hence, the value of \((\frac{1}{p^2}) + (\frac{1}{q^2})\) -

\(= (\frac{1}{3^2}) + (\frac{1}{4^2})\)

\(= (\frac{1}{9}) + (\frac{1}{16})\)

\(= \frac{25}{144}\)

Thus, answer must be (B) \(\frac{25}{144}\)
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Expert Post
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2570
Re: If p + q = 7 and pq = 12, then what is the value of (1/p^2) + (1/q^2) [#permalink]

Show Tags

New post 10 Mar 2017, 10:38
vikasp99 wrote:
If p + q = 7 and pq = 12, then what is the value of (1/p^2) + (1/q^2) ?

(A) 1/6

(B) 25/144

(C) 49/144

(D) 7/12

(E) 73/144



We can start by adding together (1/p^2) + (1/q^2) by first obtaining a common denominator:

(q^2/q^2)(1/p^2) + (p^2/p^2)(1/q^2)

q^2/[(q^2)(p^2)] + p^2/[(q^2)(p^2)]

(q^2 + p^2)/(pq)^2

Since pq =12, we have:

(q^2 + p^2)/(12)^2

(q^2 + p^2)/144

To determine the value of q^2 + p^2, we can do the following:

(p + q)^2 = (7)^2

p^2 + q^2 + 2pq = 49

Since pq = 12, we know:

p^2 + q^2 + 24 = 49

p^2 + q^2 = 25

Thus, (q^2 + p^2)/144 = 25/144

Answer: B
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Manager
Manager
avatar
B
Joined: 16 Jan 2017
Posts: 65
GMAT 1: 620 Q46 V29
Re: If p + q = 7 and pq = 12, then what is the value of (1/p^2) + (1/q^2) [#permalink]

Show Tags

New post 23 Mar 2017, 11:05
I used a different method, which was a bit over 2 minutes, but basically:

plug in p = 7 - p into th eequation pq = 12, (or we can plug in q = 7 - p).

Then we foil the formula which will end up being p^2 - 7p +12 = 0,
(p - 4)(p - 3),
p = 3 or = 4. And we know that we will get the same values for q,

Therefore there are 3 possible answer:

(1/3^3) + (1/3^2) = 2/9 - not available
(1/4^2) + (1/4^2) = 2/16 = 1/8 - not available
(1/4^2) + (1/3^2) = 1/16 + 1/9 = 25/144,

Thus, the answer is B.

I am still practicing hoping I can use more time efficient. Tapabrata's ways surely seems way faster!
Re: If p + q = 7 and pq = 12, then what is the value of (1/p^2) + (1/q^2)   [#permalink] 23 Mar 2017, 11:05
Display posts from previous: Sort by

If p + q = 7 and pq = 12, then what is the value of (1/p^2) + (1/q^2)

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.