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

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Math Expert
Joined: 02 Sep 2009
Posts: 61288
Does x have at least 3 prime factors? (1) x = 5b, where b is a positiv  [#permalink]

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05 Mar 2019, 04:21
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Difficulty:

35% (medium)

Question Stats:

71% (01:20) correct 29% (01:10) wrong based on 48 sessions

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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.

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Joined: 19 Jan 2019
Posts: 110
Re: Does x have at least 3 prime factors? (1) x = 5b, where b is a positiv  [#permalink]

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05 Mar 2019, 04:32
1
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??

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Joined: 11 Dec 2018
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Re: Does x have at least 3 prime factors? (1) x = 5b, where b is a positiv  [#permalink]

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05 Mar 2019, 09:02
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?
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Re: Does x have at least 3 prime factors? (1) x = 5b, where b is a positiv  [#permalink]

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05 Mar 2019, 10:43
Bunuel wrote:
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.

#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
Re: Does x have at least 3 prime factors? (1) x = 5b, where b is a positiv   [#permalink] 05 Mar 2019, 10:43
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