• NEW! FREE Beat The GMAT Quizzes
Hundreds of Questions Highly Detailed Reporting Expert Explanations
• 7 CATs FREE!
If you earn 100 Forum Points

Engage in the Beat The GMAT forums to earn
100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Which of the following are/is prime? tagged by: VJesus12 ##### This topic has 3 expert replies and 0 member replies ### Top Member ## Which of the following are/is prime? Which of the following are/is prime? I. 143 II. 147 III. 149 (A) II only (B) III only (C) I & II (D) I & III (E) I, II, & III The OA is B. How can I find the prime number quickly? ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 VJesus12 wrote: Which of the following are/is prime? I. 143 II. 147 III. 149 (A) II only (B) III only (C) I & II (D) I & III (E) I, II, & III The OA is B. How can I find the prime number quickly? Break the numbers down into more manageable/recognizable values. I: 143 = 130 + 13 --> clearly divisible by 13, as both 130 and 13 are multiples of 13, so 143 is not prime. II: 147 --> 1 + 4 + 7 = 12. If the sum of the digits of the number is a multiple of 3, then the number itself is a multiple of 3. 147 is not prime. Since we don't have an option of NONE, we don't even have to test III. It has to be prime. The answer is B _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!

### GMAT/MBA Expert

GMAT Instructor
Joined
04 Oct 2017
Posted:
551 messages
Followed by:
11 members
180
Quote:
Which of the following are/is prime?

I. 143
II. 147
III. 149

(A) II only
(B) III only
(C) I & II
(D) I & III
(E) I, II, & III

The OA is B.

How can I find the prime number quickly?
Hi VJesus12,
Let's take a look at your question.

We are asked to find the prime number from the options given. We know that a prime number has only two divisors 1 and the number itself.
So to find if a number is a prime number or not we will check if it has any divisor other than 1 and the number itself.

We will look for two shortcuts to reach the solution.
Shortcut 1:
We will test the given numbers for the prime divisors only i.e. 2, 3, 5, 7, 11, 13, ...

Shortcut 2:
We will find the nearest perfect square to the number given. Find its square root and will limit testing till that number.
For example, for 143, the nearest perfect square is 144 and its square root is 12.
So we will limit the testing till 11 because 11 is the last prime number below 12.

It means we need to test 143 for 2, 3, 5, 7 and 11. If 143 is not divisible by any of these it will be a prime number.
Let's check 143.
143 is not divisible by 2.
143 is not divisible by 3.
143 is not divisible by 5.
143 is not divisible by 7
143 is divisible by 11.
Therefore, 143 is not a prime number.

Lets check 147 now.
Nearest perfect square is 169 and its square root is 13.
Therefore we will check 147 for 2, 3, 5, 7 and 11
147 is not divisible by 2.
147 is divisible by 3.
Therefore, 147 is not a prime number.

Let's check 149 now.
Nearest perfect square is 169 and its square root is 13.
Therefore we will check 149 for 2, 3, 5, 7 and 11
149 is not divisible by 2.
149 is not divisible by 3.
149 is not divisible by 5.
149 is not divisible by 7.
149 is not divisible by 11.
149 is not divisible by any of the prime number in the list.
Therefore, 149 is a prime number.

Therefore Option B is correct.

Hope it helps.
I am available if you'd like any follow up.

_________________
GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now.

### GMAT/MBA Expert

GMAT Instructor
Joined
12 Sep 2012
Posted:
2635 messages
Followed by:
116 members
625
Target GMAT Score:
V51
GMAT Score:
780
Piggybacking on David's answer, one neat way of finding a composite number is noticing that it consists of multiples of the same number glued together, so to speak. For example, say we have the number 28144977. We could illuminate that as 28144977, or four multiples of 7. That might not seem like much, but noticing that allows me to break the number down into

28144977 =
28000000 +
140000 +
4900 +
77

or

7 * (4000000 + 20000 + 700 + 11)

So the whole thing must divide by 7.

This won't help you find ANY composite number, but it's a neat trick nonetheless.

Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!
• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• FREE GMAT Exam
Know how you'd score today for $0 Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

Available with Beat the GMAT members only code

### Top First Responders*

1 Brent@GMATPrepNow 39 first replies
2 Ian Stewart 37 first replies
3 Jay@ManhattanReview 32 first replies
4 GMATGuruNY 26 first replies
5 Scott@TargetTestPrep 17 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 Scott@TargetTestPrep

Target Test Prep

188 posts
2 Max@Math Revolution

Math Revolution

84 posts
3 Brent@GMATPrepNow

GMAT Prep Now Teacher

71 posts
4 Ian Stewart

GMATiX Teacher

45 posts
5 GMATGuruNY

The Princeton Review Teacher

45 posts
See More Top Beat The GMAT Experts