Question: 6 a divisor of x

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
gmat-admin's picture

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 a lot. Just a question, do you consider the exercise #389 a 700+ question on GMAT?
gmat-admin's picture

Definitely 700+

But can't it be the case that for statement 1, x is 2 or 9, since (2)(9) = 18? How can we say for sure that x is or isn't divisible by 6? Hmm..
gmat-admin's picture

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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