Does x have at least 3 prime factors? (1) x = 5b, where b is a positiv

Question

Does x have at least 3 prime factors?

(1) x = 5b, where b is a positive integer.
(2) b = 2c, where c is a positive integer.

thyagi · Answer

Statement 1 - x = 5b
From this we know that X has atleast one prime factor... But we don't know anything about "b".. not sufficient..

Statement 2 - not sufficient.

Combining both
We know that x = 5b, 
And b = 2c. 
Therefore x = 5 * 2c
Now we know that x atleast has 2 prime factors i.e 5 &2, but "c" can take any value. For e.g if c = 7, then x will have atleast 3 prime factors.. but if c = 2, then x will not have three prime factors.... Combining both statements is still not sufficient to get to the conclusion... Option E is the right answer...

Am I right??

Posted from my mobile device

leomanna10 · Answer

IMO C

1) clearly insufficient. For example
 
 if b= 1. ----> x has 2 prime factors 1 and 5;
 if b= 3 -----> x has 3 prime factor 1, 3 and 5;

2) claearly insufficient

1 + 2) x= 5*2C = 10c. If we multiply 10 for any positive integer, we always have at list 3 prime factors: 1,2,5

for example

if c= 1 -----> X = 10*1 = 10 in this case x has 3 prime factors 1,2,5
if c=19 -----> X = 190 in this case has at least 3 positive factors 1,2,5

Is my answer right? O someone can give an explanation?

Archit3110 · Answer

#1
x=5b
x=5; no
x=50;no
x=60 ; yes 3 prime factors 2^2*3*5
in sufficient
#2
b=2c
no info of x in sufficeint
from1 &2
@ b= 2-10 ; no 3 prime factors i.e x=50
but @b>12 ; >=3 prime factors i.e x=60 onwards
in sufficient
IMO E

lily123400 · Answer

I agree with this even though the answer says E. I feel like even if c=2, then we still have 2,5, and 1 as prime factors

Bunuel · Answer

Does x have at least 3 prime factors?

(1) x = 5b, where b is a positive integer. 
 (2) b = 2c, where c is a positive integer.

No, the correct answer is E, not C. When combining the statements we get x = 2 * 5 * c.

If c = 1, x = 2 * 5, which has only two primes 2 and 5 (1 is NOT a prime number). 
 If c = 7, x = 2 * 5 * 7, which has three primes 2, 5 and 7.

Rishm · Answer

Suppose C is 1, then b=2c then B is 2, and then x=5b where b is 2, which is 10, which has 2 prime factors. Hence it is possible to have 2 and ofc more than 2. Hence E, it is insufficient to answer.

Does x have at least 3 prime factors? (1) x = 5b, where b is a positiv

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