Does the integer a have 4 or more distinct prime factors?

Question

Does the integer  a  have 4 or more distinct prime factors?

(1)  a  is divisible by 36. 
(2)  a  is divisible by 35.

GMATinsight · Answer

Question : Does the integer  a  have 4 or more distinct prime factors

Statement 1 :  a  is divisible by 36.  
 36 = 2^2*3^2 
i.e. a has min two prime factors which are 2 and 3

a may or may NOT have 4 distinct prime factors hence

NOT SUFFICIENT

Statement 2 :  a  is divisible by 35.  
 35 = 5*7 
i.e. a has min two prime factors which are 5 and 7

a may or may NOT have 4 distinct prime factors hence

NOT SUFFICIENT

Combining

a has 2, 3, 5, 7 factors i.e. min 4 distinct prime factors hence

SUFFICIENT
Answer: Option C

GMATWhizTeam · Answer

Solution 
 Step 1: Analyse Question Stem 
 • a is an integer.
• We need to find if the number of distinct prime factors of a are greater or equal to 4.

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE 
 Statement 1:  a is divisible by 36
 • So,  a = k*36 , where k is an integer.
 o Or,  a = k*2^2*3^2  
• We can see that a has at least 2 distinct prime factors. However, we can’t say if it has 4 or more distinct prime factors. For example, consider the following two simple cases:
 o Case 1: if  k = 5  (k is a prime other than 2 and 3)
  Then  a = 5*2^2*3^2  and number of distinct prime factors = 3 
o Case 2: if  k = 55  (k is a composite number consists of at least 2 primes other than 2 and 3)
  Then  a = 55*2^2*3^2 = 2^2*3^2*5*11  and number of distinct prime factors = 4   
From the above two cases we can see that we cannot decidedly say if a has 4 or more distinct prime factors.
Hence, statement 1 is NOT sufficient and we can eliminate answer Options A and D.

Statement 2:  a is divisible by 35.
 • So,  a = l*35 , where l is an integer.
 o Or,  a = l*5*7  
• We can see that a has at least 2 distinct prime factors. However, we can’t say if it has 4 or more distinct prime factors. For example, consider the following two simple cases:
 o Case 1: if  l = 2  (k is a prime other than 5 and 7)
  Then  a = 2*5*7  and number of distinct prime factors = 3 
o Case 2: if  l=6  (l is a composite number consists of at least 2 primes other than 5 and 7)
  Then  a = 6*5*7 = 2*3*5*7  and number of distinct prime factors = 4   
Again, looking at the above two cases we cannot decidedly say if a has 4 or more distinct prime factors.
Hence, statement 2 is also NOT sufficient and we can eliminate answer Option B.

Step 3: Analyse Statements by combining. 
 • From statement 1:  a = k*36 
• From statement 2 :  a = l*35 
• On combining both the statement, we can say,
 o a = m*(L.C.M. of 36 and 35) where m is an integer.
o Or,  a = m*2^2*3^2*5*7 
o Thus, m at least has 4 distinct prime factors (i.e. 2, 3, 5 and 7)  
Thus, the correct answer is  Option C

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Does the integer a have 4 or more distinct prime factors?

Prep Toolkit

Top 5 GMAT Debrief Videos

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

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

Does the integer a have 4 or more distinct prime factors?

Prep Toolkit

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

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards