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

Question

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

radi · Answer

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.

hsbinfy · Answer

answer is C

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)

SOHAM6185 · Answer

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

DAllison2016 · Answer

(1)  x = 30

We do not know y

y = 30 \implies 	ext{shared prime factors} = \{2,5,3\}\
y = 10 \implies 	ext{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 	ext{shared prime factors} = \{2\}\
x = y = 6 \implies 	ext{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 	ext{shared prime factors} = \varnothing\
k 
eq 0 \implies 	ext{shared prime factors} = 	ext{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

stonecold · Answer

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

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

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