It is currently 20 May 2024, 12:04
Register
GMAT Focus Tests
Decision Tracker
My Rewards
Unanswered
Active Topics
New posts
New comers' posts
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

If x is a prime number, what is the number of factors of 75x?

7 posts Go to First Unread Post
Print view
NEW TOPIC
POST REPLY
Question banks

GMAT Question Banks

Downloads
My Bookmarks
Reviews
SORT BY:
Date
Kudos
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93351
CAT Tests Forum Quiz Mode
If x is a prime number, what is the number of factors of 75x? [#permalink] If x is a prime number, what is the number of factors of 75x?  22 May 2023, 09:30
2
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

75% (hard)

Question Stats:

48% (01:45) correct 52% (01:41) wrong based on 79 sessions
Hide Show timer Statistics
If x is a prime number, what is the number of factors of 75x?

(1) x^2 has 3 factors
(2) x > 5
ShowHide Answer
Official Answer
Official Answer and Stats are available only to registered users. Register/Login.

_________________
New to the GMAT CLUB Forum?

My Signature Questions' Collection:


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
request expert reply
User avatar
swapnils123
Intern
Intern
Joined: 25 Feb 2023
Posts: 8
Re: If x is a prime number, what is the number of factors of 75x? [#permalink] If x is a prime number, what is the number of factors of 75x?  25 May 2023, 00:19
Bunuel is the question correct?
I can find no of factors even without statements 1 and 2.
See this: If x is a prime number, then we can write: 75x = 3 * 5^2 * x which is 3^1 * 5^2 * x^1. So no of factors = (1+1) * (2+1) * (1+1) = 12.

Correct me if I am wrong.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93351
CAT Tests Forum Quiz Mode
Re: If x is a prime number, what is the number of factors of 75x? [#permalink] If x is a prime number, what is the number of factors of 75x?  25 May 2023, 00:26
Expert Reply
swapnils123 wrote:
Bunuel is the question correct?
I can find no of factors even without statements 1 and 2.
See this: If x is a prime number, then we can write: 75x = 3 * 5^2 * x which is 3^1 * 5^2 * x^1. So no of factors = (1+1) * (2+1) * (1+1) = 12.

Correct me if I am wrong.


How do you know that x is not 3 or 5?
_________________
New to the GMAT CLUB Forum?

My Signature Questions' Collection:


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
User avatar
swapnils123
Intern
Intern
Joined: 25 Feb 2023
Posts: 8
Re: If x is a prime number, what is the number of factors of 75x? [#permalink] If x is a prime number, what is the number of factors of 75x?  25 May 2023, 00:31
hmm ..okay. I see my mistake. Thanks for clarifying.
User avatar
mayankchamp1703
Intern
Intern
Joined: 08 Dec 2020
Posts: 1
Re: If x is a prime number, what is the number of factors of 75x? [#permalink] If x is a prime number, what is the number of factors of 75x?  25 May 2023, 00:57
Only when prime no 2 is involved..

Posted from my mobile device
User avatar
G
RahulJain293
Manager
Manager
Joined: 24 Apr 2022
Posts: 191
Location: India
Concentration: General Management, Nonprofit
GMAT Focus 1:
585 Q81 V80 DI76
Re: If x is a prime number, what is the number of factors of 75x? [#permalink] If x is a prime number, what is the number of factors of 75x?  07 Nov 2023, 05:23
Good one.. I got it wrong but quickly realized where I went wrong..

Answer is B

If x is a prime number, what is the number of factors of 75x?

(1) x^2 has 3 factors
(2) x > 5

Question - 75 has 5.5.3.x
We know - x = 2,3,5,7,11.... (prime numbers ONLY)

1. Square any number from set X.. we get many squares but we do not know if X is 3 or 5..
IF X = 3, then we get number of factors as 3.3 = 9
If X = 7, then we get number of factors as 3.2.2 = 12
Hence insufficient

2. Since X is greater than 5, any prime number can be plugged in with power 1 and we will get # of factors as 3.2.2 = 12
Hence sufficient
User avatar
G
SaquibHGMATWhiz
GMATWhiz Representative
Joined: 23 May 2022
Posts: 640
Location: India
GMAT 1: 760 Q51 V40
Re: If x is a prime number, what is the number of factors of 75x? [#permalink] If x is a prime number, what is the number of factors of 75x?  09 Nov 2023, 08:45
Expert Reply
Bunuel wrote:
If x is a prime number, what is the number of factors of 75x?
(1) x^2 has 3 factors
(2) x > 5


Solution:
Pre Analysis:
  • Given that x is a prime number
  • \(75x=3\times 5^2\times x\)
  • 3 cases possible here:
    • Case 1: If \(x=3\), then \(75x=3^2\times 5^2\). Ann the number of factors \(=(2+1)\times (2+1)=9\)
    • Case 2: If \(x=5\), then \(75x=3\times 5^3\). Ann the number of factors \(=(1+1)\times (3+1)=8\)
    • Case 3: If \(x=\) any other prime, then \(75x=3\times 5^2\times x^1\). Ann the number of factors \(=(1+1)\times (2+1)\times (1+1)=12\)

Statement 1: \(x^2\) has 3 factors
  • We know that x is a prime number
  • So, \(x^2\) will obviously have \((2+1)=3\) factors
  • Thus, statement 1 alone is not only insufficient but also redundant and we can eliminate options A, C and D

Statement 2: \(x > 5\)
  • This aligns with case 3 of our pre analysis step.
  • So, total factors \(=12\)
  • Thus, statement 2 alone is sufficient


Hence the right answer is Option B
_________________


Register for Free GMAT Live Sessions

Every week we conduct 3 FREE live sessions on various topics in Quant, Verbal, Strategy and Admission Consulting. You can register for the webinars - HERE

GMATWhiz FREE Trial: Prepare from an application driven course that serves real-time improvement modules along with a well-defined adaptive study plan. Start a free trial to experience it yourself and get access to 25 videos and 300 GMAT styled questions.

Score Improvement Strategy: How to score Q50+ on GMAT | 5 steps to Improve your Verbal score
Signature Read More
GMAT Club Bot
gmatclubot
Re: If x is a prime number, what is the number of factors of 75x? [#permalink]
09 Nov 2023, 08:45
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
Moderator:
Bunuel
Math Expert
93351 posts