Last visit was: 28 Apr 2026, 19:03 It is currently 28 Apr 2026, 19:03
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
Events & Promotions
Back to Forum
Create Topic
505-555 (Easy)|   Algebra|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 28 Apr 2026
Posts: 109,950
Own Kudos:
811,815
 [5]
Given Kudos: 105,927
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: 109,950
Kudos: 811,815
 [5]
If x - y = 2 and x^2 - y^2 = 16, then x^3 - y^3 = ? 26 May 2022, 06:00
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

15% (low)

Question Stats:

83% (01:43) correct 17% (02:25) wrong based on 103 sessions

History

Date
Time
Result
Not Attempted Yet
If x - y = 2 and x^2 - y^2 = 16, then x^3 - y^3 = ?

A. 97
B. 98
C. 99
D. 100
E. 152
ShowHide Answer
Official Answer
B
User avatar
genericUser
User avatar
Joined: 31 Jan 2022
Last visit: 22 Dec 2023
Posts: 111
Own Kudos:
99
Given Kudos: 35
Location: Italy
Schools: SDA Bocconi "24 (M)
GMAT 1: 670 Q49 V33
GMAT 2: 690 Q47 V37
GPA: 3.9
Schools: SDA Bocconi "24 (M)
GMAT 2: 690 Q47 V37
Posts: 111
Kudos: 99
If x - y = 2 and x^2 - y^2 = 16, then x^3 - y^3 = ? 26 May 2022, 06:07
Kudos
Add Kudos
Bookmarks
Bookmark this Post
If x - y = 2 and x^2 - y^2 = 16, then x^3 - y^3 = ?

A. 97
B. 98
C. 99
D. 100
E. 152

n^2=1, 4, 9, 16, 25, 36
25-9=16
5-3=2
5^3-3^3=125-27=98
User avatar
Kinshook
User avatar
Major Poster
Joined: 03 Jun 2019
Last visit: 28 Apr 2026
Posts: 5,989
Own Kudos:
5,862
Given Kudos: 163
Location: India
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Products:
My Reviews
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
Posts: 5,989
Kudos: 5,862
If x - y = 2 and x^2 - y^2 = 16, then x^3 - y^3 = ? 26 May 2022, 06:15
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Asked: If x - y = 2 and x^2 - y^2 = 16, then x^3 - y^3 = ?

x^2 - y^2 = (x+y)(x-y) = 2(x+y) = 16
x + y = 8
x = 5
y = 3
x^3 - y^3 = (x-y)(x^2+y^2+xy) = 2 (64 - 15) = 2*49 = 98

IMO B
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 31 Oct 2025
Posts: 6,733
Own Kudos:
36,476
 [3]
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,733
Kudos: 36,476
 [3]
If x - y = 2 and x^2 - y^2 = 16, then x^3 - y^3 = ? Updated on: 26 May 2022, 06:40
Originally posted by BrentGMATPrepNow on 26 May 2022, 06:18.
Last edited by BrentGMATPrepNow on 26 May 2022, 06:40, edited 1 time in total.
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If x - y = 2 and x² - y² = 16, then x³ - y³ = ?

A. 97
B. 98
C. 99
D. 100
E. 152
Show more

Take: x² - y² = 16
Factor: (x + y)(x - y) = 16
Substitute to get: (x + y)(2) = 16
Divide both sides of the equation by 2 to get: x + y = 8

We now have the following system of equations:
x - y = 2
x + y = 8
Add the two equations to get: 2x = 10, which means x = 5
Once we know x = 5, we can plug this value into one of the two equations to learn that y = 3

Now that we know the values of x and y, x³ - y³ = 5³ - 3³ = 125 - 27 = 98

Answer: B
User avatar
genericUser
User avatar
Joined: 31 Jan 2022
Last visit: 22 Dec 2023
Posts: 111
Own Kudos:
99
 [1]
Given Kudos: 35
Location: Italy
Schools: SDA Bocconi "24 (M)
GMAT 1: 670 Q49 V33
GMAT 2: 690 Q47 V37
GPA: 3.9
Schools: SDA Bocconi "24 (M)
GMAT 2: 690 Q47 V37
Posts: 111
Kudos: 99
 [1]
If x - y = 2 and x^2 - y^2 = 16, then x^3 - y^3 = ? 26 May 2022, 06:35
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
BrentGMATPrepNow
Bunuel
If x - y = 2 and x² - y² = 16, then x³ - y³ = ?

A. 97
B. 98
C. 99
D. 100
E. 152

Take: x² - y² = 16
Factor: (x + y)(x - y) = 16
Substitute to get: (x + y)(2) = 16
Divide both sides of the equation by 2 to get: x + y = 8

We now have the following system of equations:
x - y = 2
x + y = 8
Add the two equations to get: 2x = 10, which means x = 5
Once we know x = 5, we can plug this value into one of the two equations to learn that y = -3

Now that we know the values of x and y, x³ - y³ = 5³ - (-3)³ = 125 - (-27) = 152

Answer: E
Show more


Hi BrentGMATPrepNow
if x=5 and y=-3
x-y=5-(-3)=8, the stem mention x-y=2. Am I missing something?

Regards,
R
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 31 Oct 2025
Posts: 6,733
Own Kudos:
36,476
 [2]
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,733
Kudos: 36,476
 [2]
If x - y = 2 and x^2 - y^2 = 16, then x^3 - y^3 = ? 26 May 2022, 06:41
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
rseglia

Hi BrentGMATPrepNow
if x=5 and y=-3
x-y=5-(-3)=8, the stem mention x-y=2. Am I missing something?

Regards,
R
Show more

No, you're absolutely right.
Once I'd determined x = 5, I have no idea how I then concluded y = -3, when y actually equals 3.
I have edited my response accordingly.

Thanks for the heads up!
Kudos for you!!!
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,987
Own Kudos:
1,119
Posts: 38,987
Kudos: 1,119
If x - y = 2 and x^2 - y^2 = 16, then x^3 - y^3 = ? 20 Jan 2024, 04:11
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
109950 posts
Krunaal
Tuck School Moderator
852 posts