Which of the following are/is prime?

Question

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

In order to handle questions like this without a calculator, it is very helpful to know
(a) divisibility tricks = https://magoosh.com/gmat/2012/gmat-divis ... shortcuts/
(b) factoring tricks = https://magoosh.com/gmat/2012/advanced-n ... -the-gmat/

Mike :-)

mikemcgarry · Accepted Answer

Dear joondez , I'm happy to help. :-)

My friend, one of the most important skills on the GMAT Quant is developing number sense . For example, when I look at 147, I notice that 147 = 140 + 7. Well, 140 is divisible by 7--it's equal to 20*7. Of course 7 is divisible by 7. Therefore: 147 = 140 + 7 = 20*7 + 7 = (20 + 1)*7 = 21*7 Part of number sense is being able to "chop up" numbers to see what is divisible by what. Here's a video that explains more. Multiples For 143, we use another trick. You may be familiar with the algebraic formula know as " Difference of Two Squares ." P^2 - Q^2 = (P + Q)(P - Q) Well, we can use this for algebra, but we also can use this for numbers. See: Advanced (Non-Calculator!) Factoring on the GMAT We know that 12^2 = 144 , and 143 = 144 - 1 . Therefore 143 = 144 - 1 = 12^2 - 1^2 = (12 + 1)(12 - 1) = 13*11 BTW, another trick we can use: suppose we have a three-digit number abc , where those are the three digits. If it's true that b = a + c , then it has to be true that the number is divisible by 11. For example, consider the number 473. Any number of this kind we can write in the form (10*N) + N for some positive integer N. For this number, 473 = 430 + 43 = 43*10 + 43 = 43(10 + 1) = 43*11 Don't just memorize these patterns: really make sure you understand them. Does all this make sense? Mike :-)

CarlMtl · Answer

Step 1, look over the three numbers quickly, realize 147 is divisible by 3. We know II is not prime.
Step 2, look at the answer choices. Realize the answer is (B) or (D). Therefore III must be prime.
Step 3, Verify if I is prime. Build a division table with other prime numbers and get your answer!

shelrod007 · Answer

An interesting way to solve these kind of problems is to eliminate the obvious answers 
1) 143 = 13*11 so we know it is not prime quickly eliminate all options having 1 as a choice 
which leaves us with 2 ) and 3) as possible answers 
From here on we find 147 = 3* 49 so we eliminate 147 which leaves us with 149 as the only possible solution

johnwesley · Answer

Which of the following are/is prime?

I. 143: 
 - sum of digits multiple of 3? NO
 - divisible by 7? NO
 - divisible by 11? YES, 13x11=143 --> Not prime
II. 147
 - sum of digits multiple of 3? YES, 1+4+7=12 --> Not prime

III. 149
 - sum of digits multiple of 3? NO
 - divisible by 7? NO
 - divisible by 11? NO
 - divisible by 13? NO

B is the only possible solution

Abhishek009 · Answer

I. 143 = 13*11
II. 147 = 21*7 
 III. 149

Among the given options 149 is a prime number...

Thus, answer must be (III) 149

joondez · Answer

How did you find this out?

abhishekdadarwal2009 · Answer

Show timer Statistics 
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

143= 11*13
147=3*49
149= prime

IdiomSavant · Answer

B.

III only.

Another way is to remember all higher prime numbers will by 6X-1 or 6X+1. Since 6 goes into 144 and 150 the potential primes around that area are 143,145,149 and 151.

joondez · Answer

Your explanation was extremely clear and helped me a lot. Thank you! I have a lot to improve in my number sense

Shiv2016 · Answer

(1) 143
Not divisible by 3 as the sum of the digits (1+4+3=8) which is not divisible by 3.
It ends in 3, thus not divisible by 2. (not even)
It ends in 3, thus not divisible by 5. (the number should end in 0 or 5)
Not divisible by 7 either as leaves a remainder of 3.
Divisible by 11: 1+3-4=0 which is divisible by 11.
 Thus not prime.

(2) 147
Sum of digits is 12 which is divisible by 3.
Thus not prime.

(3) 149
Its a prime number as it is not divisible by any of the prime numbers less than sq. root of 149.

How to know by what all prime numbers we should check its divisibility?

e.g. 149 lies between square of 144 (12^2) and 169 (13^2)
Square root of 149: 12<sq.root 149<13
Therefore we have to check its divisibility by all the prime numbers less than the lower limit i.e. 12.

Prime numbers less than 12 are 2,3,5,7, and 11

ScottTargetTestPrep · Answer

Since 143 = 11 x 13, 143 is not a prime.

Since 147 = 7 x 21, 147 is not a prime.

149 is a prime since there is no multiplication of two numbers that equals 149 other than 1 x 149.

Answer: B

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Which of the following are/is prime?

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Which of the following are/is prime?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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