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Re: 7x^2 has two different prime factors [#permalink]
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KarunMendiratta wrote:

\(7x^2\) has two different prime factors
This means \(x\) must have prime factors too

For example;
If \(x = 2\)
\(7(2)^2 = (7)(2)(2)\) has 2 different prime factors \(2\) and \(7\)
So, number of different prime factors of \(x\) is one wiz. \(2\)

But WAIT, what if \(x\) is a multiple of \(7\)??

For example;
If \(x = 14\)
\(7(14)^2 = (7)(14)(14) = (7)(7)(7)(2)(2)\) also has 2 different prime factors \(2\) and \(7\)
But the number of different prime factors of \(x\) is two wiz. \(2\) and \(7\)

Col. A: \(2\)
Col. B: \(1\)

Hence, option A



In that case then, shouldn't the answer be option D as there two different cases where in one case they are equal (option C) and in another case the first quantity is greater (option A)
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Re: 7x^2 has two different prime factors [#permalink]
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habush wrote:
KarunMendiratta wrote:

\(7x^2\) has two different prime factors
This means \(x\) must have prime factors too

For example;
If \(x = 2\)
\(7(2)^2 = (7)(2)(2)\) has 2 different prime factors \(2\) and \(7\)
So, number of different prime factors of \(x\) is one wiz. \(2\)

But WAIT, what if \(x\) is a multiple of \(7\)??

For example;
If \(x = 14\)
\(7(14)^2 = (7)(14)(14) = (7)(7)(7)(2)(2)\) also has 2 different prime factors \(2\) and \(7\)
But the number of different prime factors of \(x\) is two wiz. \(2\) and \(7\)

Col. A: \(2\)
Col. B: \(1\)

Hence, option A



In that case then, shouldn't the answer be option D as there two different cases where in one case they are equal (option C) and in another case the first quantity is greater (option A)


No dear, because you have been asked about the Maximum number of different prime factors of x

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7x^2 has two different prime factors [#permalink]
here in this case isnt the question talking about just 'x' and not '7x' ? so if x = 2 in 7x^2 then (x) will only have one prime number and that is 2 and '7' wont be included.
Could you confirm here Carcass
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7x^2 has two different prime factors [#permalink]
Expert Reply
No In this case 7x^2 based on the stem we do know that we have two different prime factors. This implies that we have to assess the maximum number of primes in the composite number 7x^2

But because we have two different prime numbers we must have a number > 1 otherwise the stem would contradict itself

The question looks like tricky but indeed it is a question of logic

For example x cannot be 7

7x^2= 7*7^2=7*49=7*7*7 but this is not possible from the stem

A is the answer
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7x^2 has two different prime factors [#permalink]
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