Does the positive integer M have greater than 4 factors?

Question

(1) M/8 is an integer
(2) M/20 is an integer

GMATinsight · Answer

Question: Does M have greater than 4 factors?

Statement 1 : M/8 is an integer

i.e. M could be 8 (4 factors) NO or 16 (5 factors) YES

NOT SUFFICIENT

STatement 2 : M/20 is an integer

i.e. M could be 20 (6 Factors) or any other multiple of 20 (greater than 4 factors) YES hence

SUFFICIENT

Answer: Option B

GMATWhizTeam · Answer

Solution 
 Step 1: Analyse Question Stem 
 • M is a positive integer.
• We need to find if M has more than 4 factors.

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE 
 Statement 1:  M/8 is an integer
 • It means, M = k*8, where k is positive integer.
 o  ⟹ M = k*2^3 
  Now if  k = 1 , M will have exactly  (3 +1) = 4  factors.
 Else if  k > 1 , M will have more than 4 factors.  
• We are getting contradictory results. 
Hence, statement 1 is NOT sufficient and we can eliminate answer Options A and D.

Statement 2:  M/20 is an integer
 • It means,  M = l*20 , where l is positive integer.
 o  ⟹ M = l*2^2*5 
  Now if  l = 1 , M will have  (2 +1)*(1+1) = 6  factors.
 And if  l > 1 , M will have more than 6 factors.
 So, in all cases M will have more than 4 factors.   
Hence, statement 2 is sufficient.
Thus, the correct answer is  Option B.

Archit3110 · Answer

target are factors of +ve integer M >4

#1
M/8 is an integer
least M= 8 whose factors are 4 so insufficient
#2
M/20 is an integer
Least M= 20 ; whose factors are 2^2*5^1 ; 3*2 ; 6
sufficient
OPTION B

Does the positive integer M have greater than 4 factors?

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