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

 It is currently 13 Dec 2019, 03:05 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If a+b=−8, and a=20/b, what is the value of a^2+b^2?

Author Message
TAGS:

### Hide Tags

Retired Moderator Joined: 29 Apr 2015
Posts: 816
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
If a+b=−8, and a=20/b, what is the value of a^2+b^2?  [#permalink]

### Show Tags

1
6 00:00

Difficulty:   45% (medium)

Question Stats: 62% (01:35) correct 38% (02:44) wrong based on 136 sessions

### HideShow timer Statistics

If a+b=−8, and a=20/b, what is the value of a^2+b^2?

A. 24
B. 32
C. 34
D. 40
E. 104
Intern  Joined: 02 Jun 2015
Posts: 32
Location: United States
Concentration: Operations, Technology
GMAT Date: 08-22-2015
GPA: 3.92
WE: Science (Other)
Re: If a+b=−8, and a=20/b, what is the value of a^2+b^2?  [#permalink]

### Show Tags

3
This one threw me off as my original method dealt with complex numbers and even though it is solvable that way I knew there had to be a more efficient way:

a^2 + b^2 should make you think of these formulas:
(a+b)(a+b) = a^2+b^2+2ab
(a+b)(a-b) = a^2-b^2
(a-b)(a-b) = a^2+b^2 - 2ab

The first formula is the key here. We already know (a+b) = -8 and a*b = 20
(a+b)(a+b) = (-8)(-8) = a^2+b^2+2*(20)
a^2+b^2 = 64 - 40 = 24.

Honestly, this question will sure mess up a lot of people who can't see this shortcut, because everyone will say "hell no this can't be right" if they start getting complex numbers. =)
Senior Manager  Joined: 15 Sep 2011
Posts: 305
Location: United States
WE: Corporate Finance (Manufacturing)
Re: If a+b=−8, and a=20/b, what is the value of a^2+b^2?  [#permalink]

### Show Tags

4
Sum of squares is the most efficient way to solve the problem.

Given: $$a^{2}+b^{2}$$
Solve via sum of squares:
$$(a+b)^{2}-2ab$$
$$(-8)^{2}-2(20) = 24$$

A.
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4145
Re: If a+b=−8, and a=20/b, what is the value of a^2+b^2?  [#permalink]

### Show Tags

Top Contributor
reto wrote:
If a+b=−8, and a=20/b, what is the value of a^2+b^2?

A. 24
B. 32
C. 34
D. 40
E. 104

Given: a + b = −8 and a = 20/b

Take a = 20/b and multiply both sides by b to get: ab = 20

Take a + b = −8 and SQUARE both sides to get (a+b)² = (−8)²
Expand and simplify left side to get: a² + 2ab + b² = 64
Now replace ab with 20 to get: a² + 2(20)+ b² = 64
Simplify: a² + 40 + b² = 64
Subtract 40 from both sides to get: a² + b² = 24

RELATED VIDEO FROM OUR COURSE

_________________
Target Test Prep Representative G
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2809
Re: If a+b=−8, and a=20/b, what is the value of a^2+b^2?  [#permalink]

### Show Tags

1
reto wrote:
If a+b=−8, and a=20/b, what is the value of a^2+b^2?

A. 24
B. 32
C. 34
D. 40
E. 104

We can square the first equation and we have:

a^2 + b^2 + 2ab = 64

Simplifying the second equation, we have:

ab = 20

Thus:

a^2 + b^2 + 40 = 64

a^2 + b^2 = 24

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Non-Human User Joined: 09 Sep 2013
Posts: 13742
Re: If a+b=−8, and a=20/b, what is the value of a^2+b^2?  [#permalink]

### Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: If a+b=−8, and a=20/b, what is the value of a^2+b^2?   [#permalink] 22 Nov 2019, 15:30
Display posts from previous: Sort by

# If a+b=−8, and a=20/b, what is the value of a^2+b^2?  