Is x divisible by 405 ? (1) 27 is a factor of x (2) x is a multiple o

Question

Is x divisible by 405 ?

(1) 27 is a factor of x
(2) x is a multiple of 15

stne · Answer

405 =3*3*3*3*5

(1)  27  is a factor of  x

x = 3*3*3  , NO 
 x= 3*3*3*3*5 , Yes

INSUFF.

(2)  x   is a multiple of  15

x = 3*5  , NO 
 x= 3*3*3*3*5 ,Yes

INSUFF.

1+2

x= 3*3*3*5 , NO

x= 3*3*3*3*5 , Yes

INSUFF .

Hope it's clear.

Ans E

SaquibHGMATWhiz · Answer

Solution:      
  Pre Analysis:  
  We are asked if x is divisible by 405 or not 
 In other words we are asked if x can be written as  x=3^4	imes 5	imes p  or not where p is a positive integer 
 This is a YES-NO question

Statement 1:   27 is a factor of x
  According to this statement,  x=3^3	imes q  where q is a positive integer 
 If  q=3	imes 5	imes 2 , then we can answer the question with a YES 
 If  q=3 , then the answer will be NO 
 Thus,  statement 2 alone is also not sufficient and we can eliminate options A and D

Statement 2:   x is a multiple of 15
  According to this statement,  x=3	imes 5	imes r  where r is a positive integer 
 If  r=3^3	imes 2 , then we can answer the question with a YES 
 If  r=3 , then the answer will be NO 
 Thus,  statement 1 alone is not sufficient and we can eliminate option B

Combining:   
  From statement 1, x is a multiple of 27 
 From statement 2, x is a multiple of 15  
 So, x is a mutliple of  LCM(27, 15) = 135 = 3^3	imes 5  
 After combining,  x=3^3	imes 5	imes s  where r is a positive integer 
 If  s=3 , then we can answer the question with a YES 
 If  s=2 , then the answer will be NO

Hence the right answer is    Option E

Fish181 · Answer

Each alone are insufficient and together it may or may not be true. It's true that 15*27 = 405 BUT that's just a multiple of those two numbers and x only has to be divisble by the LCM. The LCM of 15 and 27 is 135 which is not divisible by 405 (obviously).

E

E

ShreeyaV · Answer

I am definately missing something here so please help me out.

Question is asking, is x is divisible by 405. Since 15*27 = 405, can't I say based on statement (I) & (II), x = 15*27*g, where g can be any other number, divided by 405 yields a remainder of 0? Hence, x is divisble by 405 making option C as the solution?

I am not sure where my understanding is lacking...

Bunuel · Answer

x being divisible by 27 and 15 does not necessarily mean that it's divisible by 27*15; it means that it's divisible by the least common multiple of 27 and 15, which is 135. Hence, among many other options, x could be 135, giving a NO answer to the question, or 405, giving a YES answer to the question.

unraveled · Answer

Is x divisible by 405 ?

(1) 27 is a factor of x
a) 27*2 = 54, NO
b) 27*15 = 405, YES

INSUFFICIENT.

(2) x is a multiple of 15
a) 15*2 = 30, NO
b) 27*15 = 405, YES

INSUFFICIENT.

Together 1 and 2
a) 9*15 = 135, NO
b) 9*15*3 = 405, YES

Answer E.

bumpbot · Answer

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Is x divisible by 405 ? (1) 27 is a factor of x (2) x is a multiple o

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