Last visit was: 24 Apr 2026, 01:03 It is currently 24 Apr 2026, 01:03
Home
Messages
Tests
Schools
Events
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
605-655 (Medium)|   Algebra|            
User avatar
itspinky
User avatar
Joined: 22 Aug 2009
Last visit: 10 Sep 2009
Posts: 5
Own Kudos:
106
 [106]
Posts: 5
Kudos: 106
 [106]
What is the value of a^4 - b^4 ? 04 Sep 2009, 17:56
7
Kudos
Add Kudos
98
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

45% (medium)

Question Stats:

66% (01:41) correct 34% (01:44) wrong based on 2139 sessions

History

Date
Time
Result
Not Attempted Yet
What is the value of a^4 - b^4 ?

(1) a^2 - b^2 = 16
(2) a + b = 8
ShowHide Answer
Official Answer
C
Need more similar questions? Run a 5 to 10 question quiz in GMAT Club Forum Quiz →
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 23 Apr 2026
Posts: 109,802
Own Kudos:
810,909
 [21]
Given Kudos: 105,868
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,802
Kudos: 810,909
 [21]
What is the value of a^4 - b^4 ? 22 Sep 2010, 23:04
10
Kudos
Add Kudos
11
Bookmarks
Bookmark this Post
What is the value of a^4 - b^4 ?

\(a^4 - b^4 =(a^2-b^2)(a^2+b^2)\)

(1) a^2 - b^2 = 16 --> clearly not sufficient.
(2) a + b = 8 --> clearly not sufficient.

(1)+(2) As from (2) \(a + b = 8\) then \(a^2 - b^2 =(a-b)(a+b)=(a-b)*8 =16\) --> \(a-b=2\). Sum \(a-b=2\) and \(a + b = 8\) --> \(2a=10\) --> \(a=5\) --> \(b=3\) --> \(a^4 - b^4 =(a^2-b^2)(a^2+b^2)=16*34\). Sufficient.

Answer: C.
General Discussion
User avatar
jpr200012
User avatar
Joined: 30 May 2010
Last visit: 10 Oct 2011
Posts: 135
Own Kudos:
844
 [2]
Given Kudos: 32
Posts: 135
Kudos: 844
 [2]
What is the value of a^4 - b^4 ? 24 Sep 2010, 01:43
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Thanks Bunuel. I thought E, but had a feeling I was missing something!
User avatar
iliavko
User avatar
Joined: 08 Dec 2015
Last visit: 28 Apr 2019
Posts: 255
Own Kudos:
138
Given Kudos: 36
GMAT 1: 600 Q44 V27
Products:
My Reviews
GMAT 1: 600 Q44 V27
Posts: 255
Kudos: 138
What is the value of a^4 - b^4 ? 12 Mar 2016, 11:08
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel,

A question here, why can't we assume that since a+b=8 then a^2+b^2=64? same as a^2-b^2=16, then sq root both sides and get a-b=4

Thank you!
User avatar
ENGRTOMBA2018
User avatar
Joined: 20 Mar 2014
Last visit: 01 Dec 2021
Posts: 2,319
Own Kudos:
3,890
Given Kudos: 816
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
Products:
My Reviews
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
Posts: 2,319
Kudos: 3,890
What is the value of a^4 - b^4 ? 12 Mar 2016, 11:24
Kudos
Add Kudos
Bookmarks
Bookmark this Post
iliavko
Bunuel,

A question here, why can't we assume that since a+b=8 then a^2+b^2=64? same as a^2-b^2=16, then sq root both sides and get a-b=4

Thank you!
Show more

Let me try to answer.

If you are given \(a+b=8\), then you CAN NOT write it as \(a^2+b^2=64\). The reason is that you must square both sides COMPLETELY,

i.e.

\(a+b=8\) ---> squaring both sides ---> \((a+b)^2=8^2\) ---> \(a^2+2ab+b^2=64\)

Think of it this way, if I tell you that a+b=8 ----> I can have 1 case for (a,b) as a=7, b=1 , does \(a^2+b^2=64\)? NO.

Also, I dont know where you saw that then \(a^2-b^2=16\) --->\(a-b=4\) but this is again incorrect.

If you have \(a^2-b^2=16\) ---> the only correct manipulation for this expression is \((a+b)(a-b)=16\) and nothing else.

Again, if \(a^2-b^2=16\), I can have \(a= \sqrt{17}\) and \(b=1\), now does a-b = 4 ? NO

The formulae that I have used above are (learn these as they are one of the most used formulae in GMAT Quant):

\((a + b) = a^2 + 2ab + b^2\)

\((a - b) = a^2 - 2ab + b^2\)

\(a^2-b^2 = (a+b)*(a-b)\)

FYI,

1. If you are given a+b = 8 , then a^2+b^2=64 ONLY IF 2ab = 0 ---> ab=0 ---> either a or b=0 or even BOTH a,b =0. Thus the only case when if a+b = 8 , then a^2+b^2=64, is when either a OR b =0.

2. If you are given a^2-b^2 = 16 ---> a-b=4 , ONLY POSSIBLE when b=0 and a=4



Hope this helps.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 23 Apr 2026
Posts: 109,802
Own Kudos:
810,909
 [3]
Given Kudos: 105,868
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,802
Kudos: 810,909
 [3]
What is the value of a^4 - b^4 ? 12 Mar 2016, 11:25
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
iliavko
Bunuel,

A question here, why can't we assume that since a+b=8 then a^2+b^2=64? same as a^2-b^2=16, then sq root both sides and get a-b=4

Thank you!
Show more

Generally \((a+b)^2\neq a^2+b^2\) and \((a-b)^2 \neq a^2-b^2\). This is algebra 101. You need to brush up basics before attempting questions.

Please go through the following links:

ALL YOU NEED FOR QUANT ! ! !: all-you-need-for-quant-140445.html

Theory on Algebra: algebra-101576.html
Algebra - Tips and hints: algebra-tips-and-hints-175003.html

Factoring Quadratics: https://www.purplemath.com/modules/factquad.htm
Solving Quadratic Equations: https://www.purplemath.com/modules/solvquad.htm

DS Algebra Questions to practice: search.php?search_id=tag&tag_id=29
PS Algebra Questions to practice: search.php?search_id=tag&tag_id=50

Special algebra set: new-algebra-set-149349.html

Hope this helps.
User avatar
iliavko
User avatar
Joined: 08 Dec 2015
Last visit: 28 Apr 2019
Posts: 255
Own Kudos:
138
Given Kudos: 36
GMAT 1: 600 Q44 V27
Products:
My Reviews
GMAT 1: 600 Q44 V27
Posts: 255
Kudos: 138
What is the value of a^4 - b^4 ? 12 Mar 2016, 11:39
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Great explanations, actually now I get the special cases much better :)

Yeah you are right, I am still discovering "what can be done and what can't be done" in algebra.

Thank you for the quick reply!
User avatar
qazi11
User avatar
Joined: 14 Dec 2016
Last visit: 10 May 2020
Posts: 6
Own Kudos:
2
 [1]
Given Kudos: 7
Posts: 6
Kudos: 2
 [1]
What is the value of a^4 - b^4 ? 27 Feb 2018, 09:31
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
What is the value of a^4 - b^4 ?

\(a^4 - b^4 =(a^2-b^2)(a^2+b^2)\)

(1) a^2 - b^2 = 16 --> clearly not sufficient.
(2) a + b = 8 --> clearly not sufficient.

(1)+(2) As from (2) \(a + b = 8\) then \(a^2 - b^2 =(a-b)(a+b)=(a-b)*8 =16\) --> \(a-b=2\). Sum \(a-b=2\) and \(a + b = 8\) --> \(2a=10\) --> \(a=5\) --> \(b=3\) --> \(a^4 - b^4 =(a^2-b^2)(a^2+b^2)=16*34\). Sufficient.

Answer: C.
Show more

Hello,

Can we not take the first equation a^2-b^2= 16 as straight away as (a+b) (a-b)=16. Clearly a^2 has to be Greater than b^2
To satisfy this, a has to be 5 and b has to be 3 . Eventually 5^4- 3^4 can be easily found.(625-81). so only the first should suffice
User avatar
pushpitkc
User avatar
Joined: 26 Feb 2016
Last visit: 19 Feb 2025
Posts: 2,800
Own Kudos:
6,235
 [1]
Given Kudos: 47
Location: India
GPA: 3.12
Posts: 2,800
Kudos: 6,235
 [1]
What is the value of a^4 - b^4 ? 27 Feb 2018, 09:41
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
qazi11
Bunuel
What is the value of a^4 - b^4 ?

\(a^4 - b^4 =(a^2-b^2)(a^2+b^2)\)

(1) a^2 - b^2 = 16 --> clearly not sufficient.
(2) a + b = 8 --> clearly not sufficient.

(1)+(2) As from (2) \(a + b = 8\) then \(a^2 - b^2 =(a-b)(a+b)=(a-b)*8 =16\) --> \(a-b=2\). Sum \(a-b=2\) and \(a + b = 8\) --> \(2a=10\) --> \(a=5\) --> \(b=3\) --> \(a^4 - b^4 =(a^2-b^2)(a^2+b^2)=16*34\). Sufficient.

Answer: C.

Hello,

Can we not take the first equation a^2-b^2= 16 as straight away as (a+b) (a-b)=16. Clearly a^2 has to be Greater than b^2
To satisfy this, a has to be 5 and b has to be 3 . Eventually 5^4- 3^4 can be easily found.(625-81). so only the first should suffice
Show more

Hi qazi11

It is not necessary that both a and b are integers

Imagine a case when a=\(\sqrt{18}\) and b=\(\sqrt{2}\), here \(a^2 - b^2 = 16\)
Now, you will have a different value when you find \(a^4 - b^4\)

Hope this helps you!
User avatar
ritikajain1988
User avatar
Joined: 09 May 2016
Last visit: 30 Oct 2018
Posts: 6
Given Kudos: 11
Posts: 6
Kudos: 0
What is the value of a^4 - b^4 ? 03 May 2018, 11:32
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
What is the value of a^4 - b^4 ?

\(a^4 - b^4 =(a^2-b^2)(a^2+b^2)\)

(1) a^2 - b^2 = 16 --> clearly not sufficient.
(2) a + b = 8 --> clearly not sufficient.

(1)+(2) As from (2) \(a + b = 8\) then \(a^2 - b^2 =(a-b)(a+b)=(a-b)*8 =16\) --> \(a-b=2\). Sum \(a-b=2\) and \(a + b = 8\) --> \(2a=10\) --> \(a=5\) --> \(b=3\) --> \(a^4 - b^4 =(a^2-b^2)(a^2+b^2)=16*34\). Sufficient.

Answer: C.
Show more


Can I use the following:

(a^2-b^2= (a+b) (a-b))
(a+b) (a-b)=16
(a+b)=8 and a-b=2
which gives the value of a as 5 and b as 3??
Doesn't it make 1 sufficient alone?
User avatar
niks18
User avatar
Retired Moderator
Joined: 25 Feb 2013
Last visit: 30 Jun 2021
Posts: 862
Own Kudos:
1,805
Given Kudos: 54
Location: India
GPA: 3.82
Products:
My Reviews
Posts: 862
Kudos: 1,805
What is the value of a^4 - b^4 ? 03 May 2018, 11:42
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ritikajain1988
Bunuel
What is the value of a^4 - b^4 ?

\(a^4 - b^4 =(a^2-b^2)(a^2+b^2)\)

(1) a^2 - b^2 = 16 --> clearly not sufficient.
(2) a + b = 8 --> clearly not sufficient.

(1)+(2) As from (2) \(a + b = 8\) then \(a^2 - b^2 =(a-b)(a+b)=(a-b)*8 =16\) --> \(a-b=2\). Sum \(a-b=2\) and \(a + b = 8\) --> \(2a=10\) --> \(a=5\) --> \(b=3\) --> \(a^4 - b^4 =(a^2-b^2)(a^2+b^2)=16*34\). Sufficient.

Answer: C.


Can I use the following:

(a^2-b^2= (a+b) (a-b))
(a+b) (a-b)=16
(a+b)=8 and a-b=2
which gives the value of a as 5 and b as 3??
Doesn't it make 1 sufficient alone?
Show more

Hi ritikajain1988

from the equation (a+b)(a-b)=16, you cannot assume that a+b=8 & a-b=2, it could also be a+b=16 & a-b=1 or a+b=-8 & a-b=-2 etc.

Essentially you have two variable and one equation, hence it cannot be solved
User avatar
amanvermagmat
User avatar
Retired Moderator
Joined: 22 Aug 2013
Last visit: 28 Mar 2025
Posts: 1,142
Own Kudos:
2,973
Given Kudos: 480
Location: India
Posts: 1,142
Kudos: 2,973
What is the value of a^4 - b^4 ? 03 May 2018, 23:27
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ritikajain1988
Bunuel
What is the value of a^4 - b^4 ?

\(a^4 - b^4 =(a^2-b^2)(a^2+b^2)\)

(1) a^2 - b^2 = 16 --> clearly not sufficient.
(2) a + b = 8 --> clearly not sufficient.

(1)+(2) As from (2) \(a + b = 8\) then \(a^2 - b^2 =(a-b)(a+b)=(a-b)*8 =16\) --> \(a-b=2\). Sum \(a-b=2\) and \(a + b = 8\) --> \(2a=10\) --> \(a=5\) --> \(b=3\) --> \(a^4 - b^4 =(a^2-b^2)(a^2+b^2)=16*34\). Sufficient.

Answer: C.


Can I use the following:

(a^2-b^2= (a+b) (a-b))
(a+b) (a-b)=16
(a+b)=8 and a-b=2
which gives the value of a as 5 and b as 3??
Doesn't it make 1 sufficient alone?
Show more

Hello

You have taken a+b = 8, but that is given in the second statement. Since you have taken data from second statement and used it in first statement, the answer becomes C here.
User avatar
Basshead
User avatar
Joined: 09 Jan 2020
Last visit: 07 Feb 2024
Posts: 906
Own Kudos:
323
Given Kudos: 431
Location: United States
Posts: 906
Kudos: 323
What is the value of a^4 - b^4 ? 23 Nov 2020, 19:33
Kudos
Add Kudos
Bookmarks
Bookmark this Post
itspinky
What is the value of a^4 - b^4 ?

(1) a^2 - b^2 = 16
(2) a + b = 8
Show more

\(a^4 - b^4 = (a^2+b^2)(a^2-b^2)\)

(1) \(a^2 - b^2 = 16\)

We don't know what a^2 + b^2 equals. Insufficient.

(2) \(a + b = 8\)

Clearly insufficient.

(1&2) \((a+b)(a-b) = 16\)

\(8(a-b) = 16\)

\(a - b = 2\)

\(2a = 10\)

\(a = 5\)

\(b = 3\)

\(a^2 + b^2 = 25 + 9 = 34\)

\(34 * 16 \)

SUFFICIENT.

Answer is C.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,965
Own Kudos:
1,117
Posts: 38,965
Kudos: 1,117
What is the value of a^4 - b^4 ? 25 Apr 2025, 01:44
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109802 posts
kingbucky
498 posts
Gmat860sanskar
212 posts