If n is a positive integer, is n divisible by at least six positive in

Question

If n is a positive integer, is n divisible by at least six positive integers?

(1) n is the product of three different prime numbers
(2) n = 30

DS20556

GMATWhizTeam · Accepted Answer

Solution 
 Step 1: Analyse Question Stem 
 • n is a positive integer. 
We need to find if n has at least 6 factors.
 Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE 
 Statement 1:  n is the product of three different prime numbers.
 •  n =p*q*r , here p, q, and r are distinct prime integers
• Total number of factors of n =  (1+1)(1+1)(1+1)=2*2*2 =8  
Hence, statement 1 is sufficient, we can eliminate the answer options B, C, and E.
 Statement 2:  n = 30
Upon prime factorization of 30, we get
 • n= 2*3*5
• Total number of factor of  n = (1+1)(1+1)(1+1) 
 o We can find the number of factors of n.  
Hence, statement 2 is also sufficient, the correct answer is  Option D

Archit3110 · Answer

#1
n is the product of three different prime numbers
a prime number has 2 +ve factors so 3 prime will have 6 factors sufficient
#2
n=30
n=2*3*5 ; total factors ; 6
sufficient
IMO D

zerotohero · Answer

(1) n is the product of three different prime numbers

n = a*b*c (where a,b,c are prime)

Now number of factors of n 
 i) choose any 1 of (a/b/c) = 3C1 = 3
 ii) choose any 2 of (a/b/c) = 3C2 = 3
 iii) choose all 3 of (a/b/c) = 3C3 = 1
 
So n can be written as a combination of a,b,c in (3+3+1)=7 ways

So (1) is sufficient

(2) 30 = 2*3*5 (prime factors)

if 1 is sufficient, 2 is sufficinet as well

D is correct !

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If n is a positive integer, is n divisible by at least six positive in

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GMAT Data Sufficiency (DS) Questions

If n is a positive integer, is n divisible by at least six positive in

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