Last visit was: 24 Jul 2024, 14:59 It is currently 24 Jul 2024, 14:59
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
SORT BY:
Date
Tags:
Show Tags
Hide Tags
VP
VP
Joined: 29 Oct 2019
Posts: 1361
Own Kudos [?]: 1540 [24]
Given Kudos: 582
Send PM
Most Helpful Reply
Retired Moderator
Joined: 19 Oct 2018
Posts: 1868
Own Kudos [?]: 6666 [7]
Given Kudos: 705
Location: India
Send PM
General Discussion
Senior Manager
Senior Manager
Joined: 14 Oct 2019
Status:Today a Reader; Tomorrow a Leader.
Posts: 344
Own Kudos [?]: 379 [0]
Given Kudos: 127
Location: India
GPA: 4
WE:Engineering (Energy and Utilities)
Send PM
Intern
Intern
Joined: 16 Oct 2019
Posts: 6
Own Kudos [?]: 2 [0]
Given Kudos: 3
Send PM
What is the greatest prime factor of 25^2 + 44^2 + 2200? [#permalink]
VeritasKarishma How can the problem above be recognized promptly? It is so tricky one. Could you please make an attempt to resolve the problem above? Thanks a ton in advance if anyone helps.
VP
VP
Joined: 29 Oct 2019
Posts: 1361
Own Kudos [?]: 1540 [0]
Given Kudos: 582
Send PM
Re: What is the greatest prime factor of 25^2 + 44^2 + 2200? [#permalink]
masuda wrote:
VeritasKarishma How can the problem above be recognized promptly? It is so tricky one. Could you please make an attempt to resolve the problem above? Thanks a ton in advance if anyone helps.



a solution to the problem above is in the link below:

https://www.youtube.com/watch?v=YuwaPxB3hes&t=572s
Tutor
Joined: 16 Oct 2010
Posts: 15148
Own Kudos [?]: 66848 [2]
Given Kudos: 436
Location: Pune, India
Send PM
Re: What is the greatest prime factor of 25^2 + 44^2 + 2200? [#permalink]
2
Kudos
Expert Reply
masuda wrote:
VeritasKarishma How can the problem above be recognized promptly? It is so tricky one. Could you please make an attempt to resolve the problem above? Thanks a ton in advance if anyone helps.


Doesn't matter if you don't recognise it instantly. To find the greatest prime factor, you need to break the whole expression down into its factors.

\(25^2 + 44^2 + 2200\)

The first obvious step would be to take common to ease the calculations. Let's see what we have common in the terms.

\(5^4 + 2^4*11^2 * 2^3*5^2*11\)

Note that the first term has 5s only, the second term has 11s and 2s and the third term has both. We can't take anything common. With the squares in the first two terms, you should think of a^2 + b^2 + 2ab. On inspection you see that the third term is 2ab.

\(= (25 + 44)^2\)

= 69^2 = (3*23)^2

It's now broken down into its factors. 23 is the greatest prime factor.
Intern
Intern
Joined: 24 Oct 2019
Posts: 14
Own Kudos [?]: 1 [0]
Given Kudos: 43
Send PM
Re: What is the greatest prime factor of 25^2 + 44^2 + 2200? [#permalink]
nick1816 Could you please explain how you have caught the tricky PS above is a reflection of a formula?
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6031
Own Kudos [?]: 13827 [1]
Given Kudos: 125
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Re: What is the greatest prime factor of 25^2 + 44^2 + 2200? [#permalink]
1
Kudos
Expert Reply
Turjoy98 wrote:
nick1816 Could you please explain how you have caught the tricky PS above is a reflection of a formula?


Turjoy98

Usually a hunch plays a role in such problems. Since we have first two terms as \(25^2+44^2\) so we try to see how much short or excess the number 2200 is than 2*25*44 which in this case, on checking, results in zero excess or short from 2200


If there was some short or excess even then we would have translated the expression in the algebraic formula to make it simpler.
Retired Moderator
Joined: 19 Oct 2018
Posts: 1868
Own Kudos [?]: 6666 [1]
Given Kudos: 705
Location: India
Send PM
What is the greatest prime factor of 25^2 + 44^2 + 2200? [#permalink]
1
Kudos
Turjoy98

Nice explanation by GMATinsight. My explanation is bit similar.

Most probably you get \((a+b)^2\) or \((a+b)^2-c^2\) = (a+b+c)(a+b-c) in such questions.

Or there is a direct observation- 2200= 22*100 = 22*(2*2*25) = 44*2*25




Turjoy98 wrote:
nick1816 Could you please explain how you have caught the tricky PS above is a reflection of a formula?
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 34079
Own Kudos [?]: 853 [0]
Given Kudos: 0
Send PM
Re: What is the greatest prime factor of 25^2 + 44^2 + 2200? [#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.
GMAT Club Bot
Re: What is the greatest prime factor of 25^2 + 44^2 + 2200? [#permalink]
Moderator:
Math Expert
94609 posts