It is currently 18 Feb 2018, 23:38

### 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

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

# 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)

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 02 Jan 2017
Posts: 315
If p + q = 7 and pq = 12, then what is the value of (1/p^2) + (1/q^2) [#permalink]

### Show Tags

08 Mar 2017, 04:29
3
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

88% (01:21) correct 13% (01:24) wrong based on 48 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
[Reveal] Spoiler: OA
VP
Joined: 24 Jul 2011
Posts: 1358
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

08 Mar 2017, 06:38
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

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

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

Intern
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)
Re: If p + q = 7 and pq = 12, then what is the value of (1/p^2) + (1/q^2) [#permalink]

### Show Tags

08 Mar 2017, 07:11
2
This post was
BOOKMARKED
$$\frac{1}{p^2}$$+$$\frac{1}{q^2}$$
=$$\frac{p^2+q^2}{p^2q^2}$$
=$$\frac{(p+q)^2-2pq}{(pq)^2}$$
=$$\frac{7^2-2*12}{12^2}$$
=$$\frac{49-24}{144}$$
=$$\frac{25}{144}$$

Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3326
Location: India
GPA: 3.5
If p + q = 7 and pq = 12, then what is the value of (1/p^2) + (1/q^2) [#permalink]

### Show Tags

08 Mar 2017, 07:14
1
KUDOS
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 )

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1975
Re: If p + q = 7 and pq = 12, then what is the value of (1/p^2) + (1/q^2) [#permalink]

### Show Tags

10 Mar 2017, 09:38
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

_________________

Jeffery Miller

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

Manager
Joined: 16 Jan 2017
Posts: 64
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

23 Mar 2017, 10:05
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,

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, 10:05
Display posts from previous: Sort by