NEW HERE? LEARN MORE
closeclose
Last visit was: 24 Apr 2024, 22:24 It is currently 24 Apr 2024, 22:24
Decision Tracker
My Rewards
New posts
New comers' posts

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

There are two positive integers a and b, where a > b.

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
GMATNinja
GMAT Club Verbal Expert
Joined: 13 Aug 2009
Status: GMAT/GRE/LSAT tutors
Posts: 6920
Own Kudos [?]: 63658 [17]
Given Kudos: 1773
Location: United States (CO)
GMAT 1: 780 Q51 V46
GMAT 2: 800 Q51 V51
GRE 1: Q170 V170

GRE 2: Q170 V170
Send PM
There are two positive integers a and b, where a > b. [#permalink] New post   Updated on: 17 Apr 2022, 23:56
4
Kudos
13
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

75% (02:50) correct 25% (02:54) wrong based on 169 sessions
Hide Show timer Statistics
There are two positive integers \(𝑎\) and \(𝑏\), where \(𝑎 > 𝑏\). The sum of the squares of these integers is equal to 5 times their sum. The difference of the squares of these integers is equal to 9 times their difference. What is the value of \(𝑎 − 𝑏\)?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
ShowHide Answer
Official Answer
A

Originally posted by GMATNinja on 17 Apr 2022, 23:14.
Last edited by GMATNinja on 17 Apr 2022, 23:56, edited 2 times in total.
Formatting
Most Helpful Reply
User avatar
L
PyjamaScientist
Admitted - Which School Forum Moderator
Joined: 25 Oct 2020
Posts: 1131
Own Kudos [?]: 1047 [5]
Given Kudos: 630
Schools: Ross '25 (M$)
GMAT 1: 740 Q49 V42 (Online)
Send PM
Reviews Badge
Re: There are two positive integers a and b, where a > b. [#permalink] New post   18 Apr 2022, 05:48
5
Kudos
Posted from my mobile device
Attachments

image.jpg
image.jpg [ 2.26 MiB | Viewed 4929 times ]

General Discussion
User avatar
L
Archit3110
GMAT Club Legend
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 8019
Own Kudos [?]: 4096 [1]
Given Kudos: 242
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Send PM
GMAT ToolKit User CAT Tests
Re: There are two positive integers a and b, where a > b. [#permalink] New post   18 Apr 2022, 02:15
1
Kudos
GMATNinja wrote:
There are two positive integers \(𝑎\) and \(𝑏\), where \(𝑎 > 𝑏\). The sum of the squares of these integers is equal to 5 times their sum. The difference of the squares of these integers is equal to 9 times their difference. What is the value of \(𝑎 − 𝑏\)?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7


given
a>b
a^2+b^2 = 5*( a+b)
a^2-b^2= 9* (a-b)
add both
2*a^2 = 14a-4b
a^2 = 7a-2b
plugin values we see at a = 6 and b = 3 expression is valid
a-b= 3 correct option a
User avatar
B
samarth1222
Manager
Manager
Joined: 30 Dec 2021
Posts: 52
Own Kudos [?]: 8 [0]
Given Kudos: 71
Send PM
Re: There are two positive integers a and b, where a > b. [#permalink] New post   05 Aug 2022, 20:56
Archit3110 wrote:
GMATNinja wrote:
There are two positive integers \(𝑎\) and \(𝑏\), where \(𝑎 > 𝑏\). The sum of the squares of these integers is equal to 5 times their sum. The difference of the squares of these integers is equal to 9 times their difference. What is the value of \(𝑎 − 𝑏\)?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7


given
a>b
a^2+b^2 = 5*( a+b)
a^2-b^2= 9* (a-b)
add both
2*a^2 = 14a-4b
a^2 = 7a-2b
plugin values we see at a = 6 and b = 3 expression is valid
a-b= 3 correct option a


hi
In this question how did you plug in the value? I didn't understand the last step can you please explain that again
User avatar
B
anuja3a
Intern
Intern
Joined: 03 May 2020
Posts: 1
Own Kudos [?]: 0 [0]
Given Kudos: 45
Send PM
Re: There are two positive integers a and b, where a > b. [#permalink] New post   23 Oct 2022, 02:56
Please explain how you plugged in the values

Posted from my mobile device
User avatar
B
Alexabisaad
Intern
Intern
Joined: 10 Oct 2023
Posts: 8
Own Kudos [?]: 4 [1]
Given Kudos: 4
Send PM
Re: There are two positive integers a and b, where a > b. [#permalink] New post   15 Dec 2023, 02:22
1
Kudos
we have:

1. a^2 + b^2 = 5 ( a + b )
2. a^2 - b^2 = 9 ( a - b )

If we expand 2. we will have ( a + b )( a - b ) = 9 ( a - b )
we can cancel out (a-b) from both sides, then we will have (a+b) = 9

Replace it in 1. we will have a^2 + b^2 = 5 (9) = 45

Also a>b, so the possible combinations are either a=5,b=4 / a=6,b=3 / a=7,b=2 / a=7,b=1

See each one that satisfies both equations a+b = 9 and a^2 + b^2 = 45

We can see that 6^2+3^2=45 and 6+3=9.
GMAT Club Bot
gmatclubot
Re: There are two positive integers a and b, where a > b. [#permalink]
15 Dec 2023, 02:22
Moderators:
Bunuel
Math Expert
92900 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions