If m has the smallest prime number as its only prime factor, is

Question

If m has the smallest prime number as its only prime factor, is Cube√m an integer?

(1) m^2 is divisible by 32

(2) √m is divisible by 4

chetan2u · Answer

\sqrt {m} , where  m=2^x ..
So,  \sqrt {2^x}  will be an integer when x is multiple of 3..

(1)  m^2  is divisible by 32 or  2^5 .
So if x is 10, answer is no, but if x is 15 answer is yes.

(2) √m is divisible by 4
So m is multiple of 16 or 2^4..
So if x is 20, answer is no, but if x is 24 answer is yes

Combined..
So if x is 20, answer is no, but if x is 60, answer is yes
Insufficient

E

mangamma · Answer

Hope Statment 1 worngly mentioned.. please do correct.

kiran120680 · Answer

Edited.. Thank you

SPatel1992 · Answer

I didn't understand the question stem.Can someone explain this?

SaquibHGMATWhiz · Answer

Solution:      
  Pre Analysis:  
  m has the smallest prime number as its only prime factor 
 This means that upon prime factorizing, we can write  m=2^n  
 We are asked if  \sqrt {x}=\sqrt {2^n}=2^{\frac{n}{3}}  is integer or not 
 For  2^{\frac{n}{3}}  to be integer,  n has to be multiple of 3

Statement 1:   m^2 is divisible by 32
  According to this statement,  m^2=32k 
 ⇒(2^n)^2=2^5	imes k 
 ⇒2^{2n}=2^5 k 
 ⇒2^{2n-5}=k  
 The value of n can be 6 (multiple of 3) or 8 (not multiple of 3) as well 
 Thus,  statement 1 alone is not sufficient and we can eliminate options A and D

Statement 2:   √m is divisible by 4
  According to this statement,  \sqrt{m}=4q 
 ⇒\sqrt{2^n}=2^2 q 
 ⇒2^{\frac{n}{2}}=2^2 q 
 ⇒2^{\frac{n}{2}-2}=q  
 The value of n can be 6 (multiple of 3) or 8 (not multiple of 3) as well 
 Thus,  statement 2 alone is also not sufficient and we can eliminate option B

Combining:   
  Even after combining, we can still have the same 2 possible values n = 6 or 8

Hence the right answer is    Option E

If m has the smallest prime number as its only prime factor, is

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