Last visit was: 18 Dec 2024, 07:04 It is currently 18 Dec 2024, 07:04
Decision Tracker
My Rewards
New comers' posts
New posts
Unanswered

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.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel
PREVIOUS TOPIC
NEXT TOPIC

m is a positive integer less than 300 and has exactly two e

Tags :
Find Similar Topics  About  Add a Tag

Show Tags
Hide Tags

User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 30355
Own Kudos [?]: 36751 [19]
Given Kudos: 26080
Send PM
m is a positive integer less than 300 and has exactly two e [#permalink] New post   09 Aug 2017, 15:26
3
Expert Reply
16
Bookmarks
00:00

Question Stats:

34% (02:09) correct 65% (02:14) wrong based on 107 sessions

Hide Show timer Statistics



m is a positive integer less than 300 and has exactly two even and two odd prime factors in its prime factorization. What is the maximum possible value of m ?

enter your value

Show: :: OA
276
Most Helpful Expert Reply
User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 30355
Own Kudos [?]: 36751 [5]
Given Kudos: 26080
Send PM
Re: m is a positive integer less than 300 and has exactly two e [#permalink] New post   31 Aug 2017, 09:03
5
Expert Reply
OE

Quote:
Because the only even prime number is 2, m must be the product of 2 × 2 = 4 and two odd primes. Further, due to the restriction that m be less than 300, the product of those two odd primes must be less than \(\frac{300}{4} = 75\). Thus, you need to find the largest number smaller than 75 that is the product of exactly two odd prime numbers. You can rule out even numbers, and you have 73, which is prime, as is 71; 69 is the product of two prime numbers (3 and 23). Thus, the maximum possible value for m is 2 × 2 × 3 × 23 = 276.

General Discussion
avatar
Raj95
Intern
Intern
Joined: 17 Feb 2017
Posts: 11
Own Kudos [?]: 11 [1]
Given Kudos: 0
Send PM
Re: m is a positive integer less than 300 and has exactly two e [#permalink] New post   30 Aug 2017, 08:33
1
any explanation??
avatar
ajudd22
Intern
Intern
Joined: 21 Jul 2020
Posts: 3
Own Kudos [?]: 3 [1]
Given Kudos: 0
Send PM
Re: m is a positive integer less than 300 and has exactly two e [#permalink] New post   05 Sep 2020, 11:42
1
How does something have two even prime factors? Is 2 not the only even prime factor? Every other even number is divisible by 2.
avatar
pranab223
Retired Moderator
Joined: 20 Apr 2016
Posts: 1307
Own Kudos [?]: 2280 [2]
Given Kudos: 251
WE:Engineering (Energy and Utilities)
Send PM

Top Member of the Month
Re: m is a positive integer less than 300 and has exactly two e [#permalink] New post   05 Sep 2020, 23:20
2
ajudd22 wrote:
How does something have two even prime factors? Is 2 not the only even prime factor? Every other even number is divisible by 2.


Hi, that's how GRE put a trap ques.

Plz see the ques "m is a positive integer less than 300 and has exactly two even and two odd prime factors in its prime factorization."

The sentence marked as bold, provides you a criteria. Your approach should satisfy the criteria. i.e the number must have 2 even prime factors and 2 odd prime factors
User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 30355
Own Kudos [?]: 36751 [0]
Given Kudos: 26080
Send PM
Re: m is a positive integer less than 300 and has exactly two e [#permalink] New post   06 Sep 2020, 01:05
Expert Reply
ajudd22 wrote:
How does something have two even prime factors? Is 2 not the only even prime factor? Every other even number is divisible by 2.


I think you are having a confusion between prime numbers and prime factorization

Here more on number properties of the numbers on our math book

https://gre.myprepclub.com/forum/gre-quant ... tml#p51913

Regards
avatar
S
void
Senior Manager
Senior Manager
Joined: 03 Dec 2020
Posts: 440
Own Kudos [?]: 61 [0]
Given Kudos: 68
Send PM
Re: m is a positive integer less than 300 and has exactly two e [#permalink] New post   09 Dec 2020, 05:03
1
why it can't be 288?
it has two even and two odd prime factor...
288=2*2*3*3*8
and for the record, question don't mention prime factor has to be distinct....
User avatar
P
GreenlightTestPrep
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12225 [0]
Given Kudos: 136
Send PM

Top Member of the Month
Re: m is a positive integer less than 300 and has exactly two e [#permalink] New post   09 Dec 2020, 10:10
1
void wrote:
why it can't be 288?
it has two even and two odd prime factor...
288=2*2*3*3*8
and for the record, question don't mention prime factor has to be distinct....

288 = (2)(2)(2)(2)(2)(3)(3)
So, 288 has five (not two) even primes (2's) in its prime factorization.
avatar
B
lavebder
Intern
Intern
Joined: 05 Jul 2022
Posts: 34
Own Kudos [?]: 31 [2]
Given Kudos: 13
Send PM
Re: m is a positive integer less than 300 and has exactly two e [#permalink] New post   15 Jul 2022, 22:07
2
So two even primes means that the number must be a multiple of 4 and must be less than 300. This means the number must be less than 300/4 = 75.
Now we need to find the product of two primes closest to 75. It comes out to be 3*23=69.
Hence the number is 4*69 = 276
avatar
B
emmar
Intern
Intern
Joined: 26 Dec 2023
Posts: 44
Own Kudos [?]: 16 [1]
Given Kudos: 4
Send PM
Re: m is a positive integer less than 300 and has exactly two e [#permalink] New post   27 Dec 2023, 18:08
1
Carcass wrote:
OE

Quote:
Because the only even prime number is 2, m must be the product of 2 × 2 = 4 and two odd primes. Further, due to the restriction that m be less than 300, the product of those two odd primes must be less than \(\frac{300}{4} = 75\). Thus, you need to find the largest number smaller than 75 that is the product of exactly two odd prime numbers. You can rule out even numbers, and you have 73, which is prime, as is 71; 69 is the product of two prime numbers (3 and 23). Thus, the maximum possible value for m is 2 × 2 × 3 × 23 = 276.



A slightly faster was to get to 69. Once you know that you need to find the largest number smaller than 75 that is the product of exactly two odd prime numbers, it's fair to guess one of the prime factors is 3.* What is the other prime factor? The largest prime number smaller than 75/3, aka largest prime < 25. That's 23. 23*3 is 69.

Multiply 69 by 4, and you get the answer.

*This is just an intuition I have, but I checked it against other possibilities and it seemed to be true. Like, if I guessed the prime factor was 5 or 13, that wouldn't work. Could someone explain why 3 is a reasonable guess here? My guess is something to do with, you want to find a number whose product is close to 75, and generally the product of two numbers far apart on the number line is going to be more than the product of numbers closer? But that seems wrong? It seems like there's something generalizable here.
Prep Club for GRE Bot
gmatclubot
Re: m is a positive integer less than 300 and has exactly two e [#permalink]
27 Dec 2023, 18:08
Moderators:
adewale223
GRE Instructor
88 posts
bronaugust
GRE Forum Moderator
37 posts
BrushMyQuant
Moderator
1115 posts
VibhuAnurag
GRE Instructor
234 posts

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

Main navigation

Partners

GRE Resources

www.ets.org/gre | About | Terms and Conditions and Privacy Policy | Prep Club for GRE Rules | Contact