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7x^2 has two different prime factors

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KarunMendiratta
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7x^2 has two different prime factors [#permalink] New post   02 Sep 2021, 04:06
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\(7x^2\) has two different prime factors

Quantity A
Quantity B
Maximum number of different prime factors of \(x\)
1


A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
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A
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Re: 7x^2 has two different prime factors [#permalink] New post   03 Sep 2021, 04:44
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arjunbir wrote:
KarunMendiratta sir can you please explain provide explanation?
thank you


\(7x^2\) 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
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arjunbir
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Re: 7x^2 has two different prime factors [#permalink] New post   03 Sep 2021, 03:12
KarunMendiratta sir can you please explain provide explanation?
thank you
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habush
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Re: 7x^2 has two different prime factors [#permalink] New post   05 Sep 2021, 10:41
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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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KarunMendiratta
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Re: 7x^2 has two different prime factors [#permalink] New post   05 Sep 2021, 10:43
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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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raghav4202
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7x^2 has two different prime factors [#permalink] New post   05 Mar 2024, 09:43
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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Carcass
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7x^2 has two different prime factors [#permalink] New post   05 Mar 2024, 11:32
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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