If positive integer A = m^3*n^2, where m and n are distinct prime

Question

If positive integer A = m^3*n^2, where m and n are distinct prime numbers, is A divisible by 72?

(1) 25mn is a multiple of 15
(2) 6m^2 is divisible by 12

Priyankajaismali · Answer

My ans. is  'C' 
prime factor of 72=2^3*3^2

IN STAT 1.
25mn is a multiple of 15 = 15 factor is 3*5, so we know the above statement is divisible by 5, but cannot predict the which value between m and n is 3 = Insuff.

IN STAT 2.
6m^2 is divisible by 12=from this we get the value of ' m '=2, but no value of n =Insuff.
  combine 1&2  
from statement 2 we know m=2 and n=3=  sufficient .

gmatophobia · Answer

Given  :  A = m^3n^2  ; m and n are distinct prime numbers

72 = 8 * 9 = 2^3 * 3^2

Given  : Does A consist of  2^3 * 3^2

In other words, we want to know if m = 2 and n = 3

Statement 1

25mn is a multiple of 15

5^2 * m * n = 5 * 3  * (some integer)

We don't have sufficient information at this stage whether the integer consists of 2. If so is m = 2 and n = 3 or vice versa.

Hence this statement is not sufficient. Eliminate A and D.

Statement 2

6m^2 is divisible by 12

2 * 3 * m^2 = 2^2 * 3  * some integer

We can conclude that m = 2, however we do not have any information on the value of n. Hence the statement is not sufficient.

Combined

From statement 2, we know that m = 2

Thus in statement 1, n = 3.

Sufficient.

Option C

SaquibHGMATWhiz · Answer

Solution:      
  Pre Analysis:  
  We are given  A = m^3	imes n^2  where m and n are prime numbers  
 And we know  72=2^3	imes 3^2  
 So, if A is divisible by 72,  m and n has to be 2 and 3 respectively  
 Thus, in other words,  we are asked if m = 2 and n = 3 or not

Statement 1:   25mn is a multiple of 15 
  According to this statement,  \frac{25mn}{15}=k  where k is a positive integer integer
 ⇒\frac{5^2	imes m	imes n}{3	imes 5}=k 
 ⇒\frac{5mn}{3}=k  
 However, this doesn't help us get if m = 2 and n = 3 or not 
 It might happen that m = 5 and n = 3  
 Thus,  statement 1 alone is not sufficient and we can eliminate options A and D

Statement 2:    6m^2  is divisible by 12
  According to this statement,  \frac{6m^2}{12}=q  where q is a positive integer integer
 ⇒\frac{m^2}{2}=q  
 From this, we can infer that  m = 2  
 However, we do not get any idea of the value of n  
 Thus,  statement 2 alone is also not sufficient    
 
  Combining:   
  From statement 1, we get  \frac{5mn}{3}=k  
 FRom statement 2, we get  m=2  which when we plug in  \frac{5mn}{3}=k  we get  n=3  
 So, after combining we get m = 2 and n = 3

Hence the right answer is    Option C

Bunuel · Answer

If positive integer A = m^3*n^2, where m and n are distinct prime numbers, is A divisible by 72?

For  m^3*n^2  to be a multiple of  72 = 2^3*3^2 , m must be 2 and n must be 3 (notice that we are told that both m and n are primes).

(1) 25mn is a multiple of 15 -->  5^2mn  is a multiple of 3*5 --> either m or n is 3. Not sufficient.
(2) 6m^2 is divisible by 12 --> 6m^2 is a multiple of 6*2 --> m = 2. Not sufficient.

(1)+(2) Since from (2) m = 2, then from (1) n = 3. Sufficient.

Answer: C.

Hope it's clear.

bumpbot · Answer

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If positive integer A = m^3*n^2, where m and n are distinct prime

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