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## Comment on

6 a divisor of x## Brent,

I have some doubts about the OG17 questions:

#168: I did not understand what is the question ansking?

#365: I did not understand what is 2-height, hence I did not understand the whole question.

#389: I do not know how to solve this question.

Could you help me please?

Thanks,

Pedro

## You bet, Pedro. You'll find

You bet, Pedro.

#168: If 3 < x < 100, for how many values of x is x/3 the square of a prime number?

Prime numbers: 2, 3, 5, 7, 11, 13, etc

So, SQUARES of prime numbers = 4, 9, 25, 49, 121, etc.

We want x/3 to equal the square of a prime number

So, for example, if x/3 = 4, then x = 12. In other words, when x = 12, x/3 = 4 (which is the square of a prime)

Likewise, if x/3 = 9, then x = 27. In other words, when x = 27, x/3 = 9, which is the square of a prime.

etc.

Here's my solution: https://gmatclub.com/forum/if-3-x-100-for-how-many-values-of-x-is-x-3-th...

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#365: For any positive integer x, the 2-height of x is defined to be the greatest nonnegative integer n such that 2^n is a factor of x.

Let's look at some examples:

EXAMPLE #1: What is the 2-height of 12?

In other words, what's the biggest non-negative integer (n) so that 2^n is a factor of 12?

2^0 = 1, and 1 IS a factor of 12

2^1 = 2, and 2 IS a factor of 12

2^2 = 4, and 4 IS a factor of 12

2^3 = 8, but 8 is NOT a factor of 12

So, 2 is the biggest value of n so that 2^n is a factor of 12

In other words, the 2-height of 12 is 2

EXAMPLE #2: What is the 2-height of 40?

In other words, what's the biggest non-negative integer (n) so that 2^n is a factor of 40?

2^0 = 1, and 1 IS a factor of 40

2^1 = 2, and 2 IS a factor of 40

2^2 = 4, and 4 IS a factor of 40

2^3 = 8, and 8 IS a factor of 40

2^4 = 16, but 16 is NOT a factor of 80

So, 3 is the biggest value of n so that 2^n is a factor of 40

In other words, the 2-height of 40 is 3

EXAMPLE #3: What is the 2-height of 11?

In other words, what's the biggest non-negative integer (n) so that 2^n is a factor of 11?

2^0 = 1, and 1 IS a factor of 11

2^1 = 2, but 2 is NOT a factor of 11

So, 0 is the biggest value of n so that 2^n is a factor of 11

In other words, the 2-height of 11 is 0

Does that help?

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#389: here's my step-by-step solution: https://gmatclub.com/forum/a-school-administrator-will-assign-each-stude...

Cheers,

Brent

## Thank you Brent, that help me

## Definitely 700+

Definitely 700+

## But can't it be the case that

## I think you're interpreting

I think you're interpreting statement 1 as saying "n is a divisor of 18". This is not what it says though.

Statement 1 says that 18 is a divisor of x. In other words, x is a MULTIPLE of 18. So, some possible values of x include: 18, 36, 54, 72, etc

Does that help?

Cheers,

Brent

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