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# How many prime factors of x are also prime factors of y?

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Math Expert
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How many prime factors of x are also prime factors of y?  [#permalink]

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25 Jul 2016, 10:17
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25% (medium)

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69% (00:55) correct 31% (00:51) wrong based on 114 sessions

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How many prime factors of x are also prime factors of y?

(1) x = 30
(2) y is a multiple of x

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Re: How many prime factors of x are also prime factors of y?  [#permalink]

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25 Jul 2016, 11:07
I picked C.

x=30 gives us the prime factors of x but does not establish a relationship with y. Insufficient.

y=kx means that y definitely shares all of x's prime factors. Pretty good but insufficient without a value for x.

Taking the two statements together, we know that x=30, and that y=k30, so y we can count how many prime factors 30 has. All of them y shares for sure. That's our answer.
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Re: How many prime factors of x are also prime factors of y?  [#permalink]

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26 Jul 2016, 00:48

1)insuff
2)ok. but what if x=0.then it shares 0 prime factors and if x=30 then 3, so This statement is insuff.

1+2,

yes it shares 3 factors(2,3,5)
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Re: How many prime factors of x are also prime factors of y?  [#permalink]

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26 Jul 2016, 02:44
hsbinfy wrote:

1)insuff
2)ok. but what if x=0.then it shares 0 prime factors and if x=30 then 3, so This statement is insuff.

1+2,

yes it shares 3 factors(2,3,5)

I will go for E.
it says y=kx
if k is a prime number then we wont be able to get any particular value for the number of prime numbers .
suppose k = 77 or k = 7*13*19 or etc
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How many prime factors of x are also prime factors of y?  [#permalink]

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26 Jul 2016, 06:18
Bunuel wrote:
How many prime factors of x are also prime factors of y?

(1) x = 30
(2) y is a multiple of x

(1) x = 30

We do not know y

$$y = 30 \implies \text{shared prime factors} = \{2,5,3\}\\ y = 10 \implies \text{shared prime factors} = \{2,5\}$$

Insufficient

(2) y is a multiple of x

Neither x or y are fixed. Prove by example:

$$x = y = 2 \implies \text{shared prime factors} = \{2\}\\ x = y = 6 \implies \text{shared prime factors} = \{2,3\}$$

Insufficient

(1 AND 2).
We have $$x$$ fixed, and know that $$y$$ is a multiple of $$x$$.

For some multiple $$k \in \mathbb{Z}$$
$$y = kx$$.

Note that (2) does not state that the multiple must be positive.

$$k = 0 \implies \text{shared prime factors} = \varnothing\\ k \neq 0 \implies \text{shared prime factors} = \text{prime factors of 30} = \{2,3,5\}$$

Insufficient

(E) statements 1 and 2 together are not sufficient, and additional data is needed to answer the question

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Re: How many prime factors of x are also prime factors of y?  [#permalink]

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21 Aug 2016, 08:53
here we arent asked the number of prime factors of y rather we are asked the number prime factors of that are also prime factors of x
statement 1 => insuff as there is no info on y
statement 2 => it tells us that all the prime factors of x must also be the prime factors of y (remember may contain additional prime factors as well but that isnt asked)
insuff
combining them as number od primes of x=3
hence y has all 3 primes of x and it may have even more
but it definitely has 2,3,5 as its prime factors
hence sufficient
SMASH that C
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Re: How many prime factors of x are also prime factors of y?  [#permalink]

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29 Jan 2019, 09:20
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Re: How many prime factors of x are also prime factors of y?   [#permalink] 29 Jan 2019, 09:20
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