Is the number of distinct prime factors of the positive integer X more

Question

Is the number of distinct prime factors of the positive integer X more than 4? 
(1) X is a multiple of 42. 
(2) X is a multiple of 98.

Bunuel · Answer

42 = 2*3*7.
98 = 2*7^2.

So, even when we combine the statements, X could have only three (2, 3 and 7) or more number (four, five, ...) of prime factors.

Answer: E.

ravigupta2912 · Answer

(1) X is a multiple of 42.

Prime factors of 42 are 2, 3 and 7. If x is 42, unique prime factors are less than 4, if x is 462, unique prime factors are 2,3,5,7 and 11 i.e. greater than 4. Therefore, not sufficient.

(2) X is a multiple of 98.

Prime factors of 98 are 2 and 7. A multiple of 98 can have more than or less than 4 unique prime factors. Not sufficient.

Merging them, we get that x is a multiple of both, 98 and 42. The prime factors of LCM are 2, 3 and 7 i.e. less than 4 but if we multiple the LCM itself by 55, then we would have more than 4 unique prime factors. Therefore, not sufficient.

E is the correct answer.

ueh55406 · Answer

Prime factorising statement 1 and 2, we get :

X= 42 (a) =  7*2*3*a . Now, we don't know what a is, if it a multiple of 2 then no, we'll be stuck with just 3 distinct prime number, but if it's something else, it could give us 4 or more than 4 prime factors.

X= 98(a)  =  7*7*2*(a) . here as well, a could be anything. it could be a multiple of 7 or 2, in this case, distinct prime factors will be <4 or it could be anything else, in that case, the # of distinct prime factor will be = > 4.

1 & 2 together  :

X= 7^3*2^2*3*a , again same issue, we have 3 distinct factors, but it's not possible to confirm if a will bring anymore distinct prime factors to X. hence correct answer is E.

bumpbot · Answer

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Is the number of distinct prime factors of the positive integer X more

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Is the number of distinct prime factors of the positive integer X more

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