Last visit was: 09 Aug 2024, 06:06 It is currently 09 Aug 2024, 06:06
Toolkit
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

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.

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

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94837
Own Kudos [?]: 648121 [23]
Given Kudos: 86892
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 30986 [8]
Given Kudos: 799
Math Expert
Joined: 02 Sep 2009
Posts: 94837
Own Kudos [?]: 648121 [0]
Given Kudos: 86892
General Discussion
Intern
Joined: 29 Aug 2015
Posts: 7
Own Kudos [?]: 20 [1]
Given Kudos: 8
Re: If the sum of two positive integers is 24 and the difference of their [#permalink]
1
Kudos
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
Retired Moderator
Joined: 08 Dec 2013
Status:Greatness begins beyond your comfort zone
Posts: 2090
Own Kudos [?]: 9028 [1]
Given Kudos: 171
Location: India
Concentration: General Management, Strategy
GPA: 3.2
WE:Information Technology (Consulting)
Re: If the sum of two positive integers is 24 and the difference of their [#permalink]
1
Bookmarks
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

Board of Directors
Joined: 11 Jun 2011
Status:QA & VA Forum Moderator
Posts: 6047
Own Kudos [?]: 4782 [2]
Given Kudos: 463
Location: India
GPA: 3.5
Re: If the sum of two positive integers is 24 and the difference of their [#permalink]
1
Kudos
1
Bookmarks
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)

$$2a$$ $$=$$ $$26$$
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

GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21835
Own Kudos [?]: 11821 [1]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If the sum of two positive integers is 24 and the difference of their [#permalink]
1
Kudos
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.

GMAT assassins aren't born, they're made,
Rich
BSchool Moderator
Joined: 08 Dec 2013
Posts: 685
Own Kudos [?]: 525 [0]
Given Kudos: 227
Location: India
Concentration: Nonprofit, Sustainability
Schools: ISB '23
GMAT 1: 630 Q47 V30
WE:Operations (Non-Profit and Government)
Re: If the sum of two positive integers is 24 and the difference of their [#permalink]
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 x and y >0 where x+y= 24, substituting x in second equation:

x^2 - y^2 = 48
(24-y)^2 = 48 + y^2
so, y=11 and x is 13.
Intern
Joined: 11 Oct 2021
Posts: 1
Own Kudos [?]: 0 [0]
Given Kudos: 1
Re: If the sum of two positive integers is 24 and the difference of their [#permalink]
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

in which book i can find this question?
Non-Human User
Joined: 09 Sep 2013
Posts: 34309
Own Kudos [?]: 859 [0]
Given Kudos: 0
Re: If the sum of two positive integers is 24 and the difference of their [#permalink]
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.
Re: If the sum of two positive integers is 24 and the difference of their [#permalink]
Moderator:
Math Expert
94837 posts