It is currently 24 Feb 2018, 10:07

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If the sum of two positive integers is 24 and the difference of their

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43896
If the sum of two positive integers is 24 and the difference of their [#permalink]

Show Tags

New post 26 Nov 2015, 05:33
1
This post received
KUDOS
Expert's post
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

90% (01:19) correct 10% (01:39) wrong based on 221 sessions

HideShow timer Statistics

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
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Joined: 29 Aug 2015
Posts: 12
Re: If the sum of two positive integers is 24 and the difference of their [#permalink]

Show Tags

New post 26 Nov 2015, 06:16
Let the two numbers be X and Y.
As given in the problem.
X+Y=24---------(1)
Also, (X+Y) (X-Y)=48----------(2)
Solving (1) in (2), we get
X-Y=2-----(3)

Solving (1) and (3), we get X=13 and Y=11.

Hence XY=143.....Option E
Verbal Forum Moderator
User avatar
V
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 1914
Location: India
Concentration: General Management, Strategy
Schools: Kelley '20, ISB '19
GPA: 3.2
WE: Information Technology (Consulting)
GMAT ToolKit User Reviews Badge CAT Tests
Re: If the sum of two positive integers is 24 and the difference of their [#permalink]

Show Tags

New post 26 Nov 2015, 06:26
Let the 2 positive numbers x and y

x+ y = 24 -- 1
x^2 - y^2 = 48
=> (x+y)(x-y)=48 -- 2
Using equation 1 in 2 , we get
=> x-y = 2 -- 3

Solving equation 1 and 3 , we get
x= 13
y= 11
Product = 13*11 = 143

Answer E
_________________

When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long
+1 Kudos if you find this post helpful

Board of Directors
User avatar
G
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3326
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member
Re: If the sum of two positive integers is 24 and the difference of their [#permalink]

Show Tags

New post 26 Nov 2015, 11:45
1
This post was
BOOKMARKED
Bunuel wrote:
If the sum of two positive integers is 24


\(a\) \(+\) \(b\)\(=\) \(24\)-------->(I)

Bunuel wrote:
difference of their squares is 48


\(a^{2} - b^{2}\) \(=\) \(48\)

\(a^{2} - b^{2}\) = \(( a + b )(a - b)\)

Or, 48 = 24 \((a - b)\)

Or, \(a - b\) = 2 -------->(II)

Adding (I) & (II)

\(2a\) \(=\) \(26\)
or, \(a\) \(=\) \(13\)

Substituting \(a\) \(=\) \(13\) in (II) we get \(b\) \(=\)\(11\)


Bunuel wrote:
If what is the product of the two integers?


Product of the integers is \(a\) x \(b\)

13 x 11 =>143

hence answer is (E)
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Expert Post
2 KUDOS received
SVP
SVP
User avatar
P
Joined: 11 Sep 2015
Posts: 2066
Location: Canada
Re: If the sum of two positive integers is 24 and the difference of their [#permalink]

Show Tags

New post 26 Nov 2015, 11:50
2
This post received
KUDOS
Expert's post
Bunuel wrote:
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

Let the values = x and y

The sum of two positive integers is 24
So, x + y = 24


The difference of their squares is 48
So, x² - y² = 48
Factor to get: (x + y)(x - y) = 48
Replace to get: (24)(x - y) = 48
So, (x - y) = 2

We now have:
x + y = 24
x - y = 2
Add these equations to get: 2x = 26, which means x = 13
If x = 13, then y = 11

So, xy = (13)(11) = 143 = E

Cheers,
Brent
_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Expert Post
1 KUDOS received
EMPOWERgmat Instructor
User avatar
D
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11070
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: If the sum of two positive integers is 24 and the difference of their [#permalink]

Show Tags

New post 26 Nov 2015, 15:33
1
This post received
KUDOS
Expert's post
Hi All,

This question can be solved with 'brute force' and a bit of logic.

We're given a few facts about 2 numbers:
1) They're both POSITIVE INTEGERS.
2) Their sum is 24.
3) The difference in their squares is 48.

We're asked for the product of the two integers.

Let's see what happens when we TEST a couple of options...

IF the numbers are 1 and 23
The difference in their squares is 529-1 = 528, which is TOO BIG.

IF the numbers are 4 and 20
The difference in their squares is 400 - 16 = 384, which is still TOO BIG.

This proves that the two numbers are likely fairly close to one another...

IF... the numbers are 11 and 13
The difference in their squares is 169 - 121 = 48, which is a MATCH for what we were told.

The PRODUCT of 11 and 13 is 143.

Final Answer:
[Reveal] Spoiler:
E


GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13764
Premium Member
Re: If the sum of two positive integers is 24 and the difference of their [#permalink]

Show Tags

New post 22 Oct 2017, 00:39
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: If the sum of two positive integers is 24 and the difference of their   [#permalink] 22 Oct 2017, 00:39
Display posts from previous: Sort by

If the sum of two positive integers is 24 and the difference of their

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.