If k is an integer, is k prime? Statement #1: k has fewer than four

Question

If k is a positive integer, is k prime?

Statement #1: k has fewer than four positive factors
Statement #2: 150 ≤ k ≤ 200

For a set of challenging GMAT DS practice problems with solutions, including the OE for this particular question, see:
https://magoosh.com/gmat/2015/gmat-data- ... questions/

Mike :-)

apolo · Answer

But on the page that you mentioned the answer is E. :?:

chetan2u · Answer

hi all,
lets look at the rules of factors....
1)a prime factor will have 2 factors.. 1 and itself..
2) square of prime factor will have three factors ... 1, number itself and the prime factor..
3) all squares will have odd numbers of factors ...
4) all other number even factors...

now lets see the two statements..
1)k has fewer than four positive factors....
if it is two, its a prime number .. ans is yes
if it is three.. ans is no..... insufficient..

2) 150 ≤ k ≤ 200... clearly insufficient as there are prime numbers , and non prime numbers both within the range...

combined.. we can remove all numbers and look for all numbers having less than 4 factors..
it means any number with three factors , which means square of a prime number.. do we have any in this range?
 (a)  169.. factors 1,13,169…..Answer is NO
But for the prime factors within the range ..…Answer is YES..
as we get 'yes' and 'no' as the answer insufficient..

ans E..

Bunuel · Answer

Yes, the OA is E, not C. Edited. Thank you for noticing!

rajatbanik · Answer

Hello  chetan2u  Sir, could you explain me the rules of factors that you mentioned with examples. It would be of great help

mikemcgarry · Answer

Dear rajatbanik , I'm happy to respond. :-)

My friend, first of all, I am going to have you read this very carefully: Asking Excellent Questions One of the best habits a GMAT student can have is the habit of asking excellent questions. Your question was not a high quality question. You barely make clear which rules you want to understand. You don't make clear at all what you do and don't understand. Do you understand what a prime number is? Do you understand the idea of the prime factorization of a number? etc. etc. What do you understand about the number of factors that I number has? You see, when you put very little effort into the question, inevitably it's not going to help you that much. Part of the point of asking a high quality question is to provide the experts here with information so that we can give you a targeted answer. A larger part, though, is that when you review and articulate what you already understand, your force your brain to make new connections, and this "primes" your brain to receive an answer more deeply. Few students appreciate how their own engagement impacts their own understand. Many student have all the material available to get 700+, but comparably few assimilate enough to do so. Remember, if you want excellent results, you have to have bring excellence to everything you do. How you do anything is how you do everything. I am going to challenge you to write the highest quality question you can, and then I will be happy to answer it. Mike :-)

Mo2men · Answer

Dear Mike,

While I was solving this question, I got confused about something.

Does 196 fit as an example to prove insufficiency?

I had two solutions in mind as follows

196 consists of 1, 14, 196

Or

196 consists of 1, 2, 7 14, 28, 98, 196

Thanks in advance

mikemcgarry · Answer

Dear Mo2men , How are you, my friend? I'm happy to respond! :-)

The statement " k has fewer than four positive factors " has to mean that the total number of factors of k is less than 4. Otherwise, it would be meaningless: if we could just pick a few factors, picking fewer than 4, then every single natural number would fit the bill. If you interpret a restriction so that it's true for every single positive integer, then it's no longer a restriction! Does this make sense? Mike :-)

rickyric395 · Answer

chetan2u , Thanks for the explanation, in your explanation for statement 2, there is a typo, only 13 satisfy the square of prime condition, only 169 will have 3 factors, 196 will have >4 factors

If k is an integer, is k prime? Statement #1: k has fewer than four

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GMAT Data Sufficiency (DS) Questions

If k is an integer, is k prime? Statement #1: k has fewer than four

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