Divisibility and primes - Expert opinion

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I'm really struggling on the divisibility and primes questions. Specifically, the wording of the questions. I fully understand how to factor, primes etc, and I understand the Manhattan GMAT chapter on it and did well on the practice questions, but when I get to the OG I can't wrap my head around the wording. A lot of the time I don't understand what they are asking and spend so much time trying to figure it out. For example question 127, 155


Needing expert help on how I can better understand (simple technique) and translate the question, as well as and any additional sources online that I can practice doing more questions.

Thank-you!
B

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Hi Beth,

I'd like to know more about the specific issue/problem that you're facing. Can you post any of the prompts that you're referring to AND go into more detail about where you get 'stuck' in the question?

GMAT assassins aren't born, they're made,
Rich

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Hey Rich,
The issue is when I try read the question. I get confused at what they are asking, for example; If 3<x<100, for how many values of x is x/3 the square of a prime?

I don't know how to understand this, and quickly. I keep getting stuck on the wording and I am confused at what is being asked.

Or

If y is the smallest positive integer such that 3150 multiplied by y is the square of an integer, then y must be?

I read, reread and I am not clear on what the question is asking to begin with. This happens for multiple divisibility and prime questions. I keep getting frustrated at not being able to understand the prompt. I look at the answer and I get how they arrived at the numbers, but it's not clear on what the question was asking. Does that make sense? I may not be doing the best at explaining the issue...let me know if you need more examples.

Thanks for your help!

[Brent@GMATPrepNow]

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

Here's one approach: https://www.beatthegmat.com/og-127-t276321.html

If y is the smallest positive integer such that 3150 multiplied by y is the square of an integer, then y must be?

Several solutions here: https://qa.www.beatthegmat.com/factor-qu ... 70495.html


Cheers,
Brent

[theCEO]

Hi Beth,

At times I fall into the same spot. Here is what works for me. Break the problem up into smaller pieces as oppose to trying to do the problem as one whole for example

If 3<x<100, for how many values of x is x/3 the square of a prime?
I would start with x/3 the square of a prime
x/3 = (prime)^2
x = 3 (prime)^2

Then reanalyze the question
When is 3 < 3 (prime)^2 < 100 or
when is 1 < (prime)^2 < 33.3

This occurs when prime = 2,3,5, hence answer = 3

[[email protected]]

Hi Beth,

Every question that you face on the GMAT can be broken down into pieces (much in the way that theCEO described). How YOU choose to break them down is up to you, but it helps to take notes and stay organized.

Here's how I'd approach your first example:

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

Primes: 2, 3, 5, 7, 11, etc.
(Primes)^2: 4, 9, 25, 49, 121, etc.

X/3 = square of a prime, so X would equal...

4 --> X=12
9 --> X = 27
25 --> X = 75
49 --> X = 147 TOO BIG

GMAT assassins aren't born, they're made,
Rich

[nikhilgmat31]

If y is the smallest positive integer such that 3150 multiplied by y is the square of an integer, then y must be?

First We need to find in factors of = sqrt ( 3150 *y) = sqrt(3*7*3*5*5*2*y)
to be able to find a perfect square root - y must be 7*2= 14

Ans: 14

[theCEO]

If y is the smallest positive integer such that 3150 multiplied by y is the square of an integer, then y must be?

First We need to find in factors of = sqrt ( 3150 *y) = sqrt(3*7*3*5*5*2*y)
to be able to find a perfect square root - y must be 7*2= 14

Ans: 14

Eventhough your answer is correct, the question asked for "square" and not "square root". Did you purposely meant to use "sqrt" in your solution?

[Brent@GMATPrepNow]

If y is the smallest positive integer such that 3150 multiplied by y is the square of an integer, then y must be?

Here's a similar question to practice with: https://www.beatthegmat.com/which-of-the ... 83100.html

Cheers,
Brent

[nikhilgmat31]

answer asked for square of y so we did sqrt of 3150, Find prime factors of 3150 & make pairs.

integers not able to make pairs will be value of y.