BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

GMAT past paper - Algebra

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 53
Joined: Sun May 06, 2007 5:03 am
by akay » Sat Aug 11, 2007 8:15 am
I am close but for some reason not being able to get this.

If the sum of two positive integers is 24 and the difference of their squares is 48, what is the product of the two integers

(A) 108
(B) 119
(C) 128
(D) 135
(E) 143
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
Senior | Next Rank: 100 Posts
Posts: 47
Joined: Sat Jun 16, 2007 10:58 pm

by RM » Sat Aug 11, 2007 9:52 am
Let the two positive integers be x and y.

Sum of two positive integers is 24, i.e. x + y = 24 ... (1)
Difference of their squares is 48, i.e. x2- y2 = 48
Or, x2-y2 = (x+y)(x-y) = 48 ... (2)

Solving equation (1) & (2):
(x+y)(x-y) = 24(x-y) = 48
(x-y) = 2 ... (3)

Solving equation (1) & (3):
x = 13
y = 11

Product of the two integers = x.y = 13x11 = 143, Choice E
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 53
Joined: Sun May 06, 2007 5:03 am

by akay » Sat Aug 11, 2007 9:33 pm
thanks RM appreciate your taking the time.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members
Location: New York, NY
Thanked: 39 times

by Jeff@TargetTestPrep » Fri Dec 22, 2017 10:01 am

If the sum of two positive integers is 24 and the difference of their squares is 48, what is the product of the two integers

(A) 108
(B) 119
(C) 128
(D) 135
(E) 143
We can let x = one integer and y = the other integer and create the following equations:

x + y = 24

and

x^2 - y^2 = 48

Notice that x^2 - y^2 = (x + y)(x - y), and so:

(x + y)(x - y) = 48

Since x + y = 24:

24(x - y) = 48

x - y = 2

So, we have x + y = 24 and x - y = 2. If we add these two equations together, we have 2x = 26 or x = 13. Once we know x = 13, y must be 11 since x + y = 24. Thus, xy = (13)(11) = 143.

Answer: E

Jeffrey Miller
Head of GMAT Instruction
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1