Last visit was: 10 Sep 2025, 02:56 It is currently 10 Sep 2025, 02:56

Close

GRE Prep 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 GRE 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
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Own Kudos [?]: 3509 [37]
Given Kudos: 172
Location: India
WE:Education (Education)
Send PM
Most Helpful Community Reply
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Own Kudos [?]: 3509 [6]
Given Kudos: 172
Location: India
WE:Education (Education)
Send PM
General Discussion
Manager
Manager
Joined: 26 Nov 2020
Posts: 110
Own Kudos [?]: 104 [3]
Given Kudos: 31
Send PM
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Own Kudos [?]: 3509 [3]
Given Kudos: 172
Location: India
WE:Education (Education)
Send PM
Re: 2 sides in both the triangles ABC and DEF are 5 and 10 respectively. [#permalink]
3
KarunMendiratta wrote:
2 sides in both the triangles ABC and DEF are 5 and 10 respectively.

Quantity A
Quantity B
The greatest possible integer difference between the parameters of two triangles
9



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.


Shortcut Method:

\(5 < x < 15\) and \(5 < y < 15\)

We have assumed that Perimeter or ABC > Perimeter of DEF
So, Maximum possible integer difference = \(x − y\)

Take Maximum value of \(x = 15\)
Take Minimum value of \(y = 5\)
integer difference = 10


Since, we cannot have 15 and 5 as the sides here, the difference of 10 is not possible.

So, what is the next possible integer value? It is 1 less than 10 = \(10 - 1 = 9\)

Hence, option C
Manager
Manager
Joined: 26 Nov 2020
Posts: 110
Own Kudos [?]: 104 [0]
Given Kudos: 31
Send PM
Re: 2 sides in both the triangles ABC and DEF are 5 and 10 respectively. [#permalink]
I only considered integer values !! My bad !!
Intern
Intern
Joined: 14 Feb 2025
Posts: 7
Own Kudos [?]: 2 [0]
Given Kudos: 44
Send PM
Re: 2 sides in both the triangles ABC and DEF are 5 and 10 respectively. [#permalink]
KarunMendiratta
what if the difference is greater than 9. if the unknown sides are 5.01 and 14.99 shall not A be the answer?
Verbal Expert
Joined: 18 Apr 2015
Posts: 33300
Own Kudos [?]: 39714 [0]
Given Kudos: 26509
Send PM
Re: 2 sides in both the triangles ABC and DEF are 5 and 10 respectively. [#permalink]
Expert Reply
For example, with third sides of 14.99 and 5.01 , the difference would be 9.98 . However, the question asks for the greatest possible integer difference.



The perimeter of a triangle with sides 5 and 10 is $P=15+x$, where $\(5<x<15\)$.

The difference in perimeters is $\(\left|P_1-P_2\right|=\left|\left(15+x_1\right)-\left(15+x_2\right)\right|=\left|x_1-x_2\right|\)$.
To maximize this difference, we need to choose values for the two third sides, $\(x_1\)$ and $\(x_2\)$, that are as far apart as possible.
- $\(x_1\)$ must be a number very close to 15 , but not 15 itself. For example, $\(x_1=14.999 \ldots\)$
- $\(x_2\)$ must be a number very close to 5 , but not 5 itself. For example, $\(x_2=5.001 \ldots\)$

The difference $\(\left|x_1-x_2\right|\)$ will be a number that is less than 10 but can be arbitrarily close to 10 . The set of all possible differences is the interval $\((0,10)\)$.

The question asks for the greatest possible integer value in this interval. The integers in the interval $\((0,10)\)$ are $\(\{1,2,3,4,5,6,7,8,9\}\)$. The largest of these is 9 .

So, while the numerical difference can be a decimal like 9.99 , the greatest integer difference is 9 .
Prep Club for GRE Bot
Re: 2 sides in both the triangles ABC and DEF are 5 and 10 respectively. [#permalink]
Moderators:
GRE Instructor
123 posts
GRE Forum Moderator
37 posts
Moderator
1141 posts
GRE Instructor
234 posts
Moderator
35 posts

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