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## Comment on

Prime Numbers## Hi Brent,

Do you have the video slides for this lesson available for download? I know you have some available in linkedin.

Thanks!

## Hi bcc123,

Hi bcc123,

We don't have slides for each individual video lesson. However, we do have slides that cover all of GMAT math here: https://www.gmatprepnow.com/content/free-content (see the flashcard section)

## sir doubt

https://gmatclub.com/forum/if-x-y-y-1-and-y-is-a-prime-number-less-than-11-which-of-the-f-223453.html

## Happy to help!

Happy to help!

My step-by-step solution can be found here: https://gmatclub.com/forum/if-x-y-y-1-and-y-is-a-prime-number-less-than-...

Cheers,

Brent

## Is the positive integer x

(1) (x - 1) is a prime number

(2) (x^2 - 1) is a prime number

statement 1 = if x = 3 then x-1 is prime

if x = 6 then x-1 is prime

so insuff

statement 2

x^2-1 = prime

only 2 satisfies this

so suff

is this approach correct???

## Perfect approach!

Perfect approach!

Cheers,

Brent

## Hi Brent, could you please

https://gmatclub.com/forum/how-many-positive-integers-less-than-30-are-either-a-multiple-of-2-an-127362.html

## Hi Jalaj,

Hi Jalaj,

Here's my solution: https://gmatclub.com/forum/how-many-positive-integers-less-than-30-are-e...

Cheers,

Brent

## Hi Brent here's another one I

https://gmatclub.com/forum/set-s-consists-of-more-than-two-integers-are-all-the-numbers-in-set-s-152717.html

## Here's my solution: https:/

Here's my solution: https://gmatclub.com/forum/set-s-consists-of-more-than-two-integers-are-...

## https://gmatclub.com/forum/if

sir in statement 1 how to know which values to test?

## Question link: https:/

Question link: https://gmatclub.com/forum/if-p-is-a-positive-integer-is-p-a-prime-numbe...

In this question, we're asked whether p is a prime number.

The GMAT loves to test whether students are aware that 2 is a prime number (in fact 2 is the ONLY prime number that's even). In fact, 2, 3 are the ONLY two consecutive primes.

So, that's why I tested p = 2

Notice that 2 and 3 (aka, p and p+1) have TWO factors each (making them both prime)

So, at that point, I started looking for 2 consecutive integers that each have FOUR factors each, which would make those values NOT prime numbers (aka composite numbers).

Do 3 & 4 work? No, 3 has two factors, and 4 has three factors.

Do 4 & 5 work? No, 4 has three factors, and 5 has two factors.

Do 5 & 6 work? No, 5 has two factors, and 6 has four factors.

.

.

.

Do 14 & 15 work? YES! 14 has FOUR factors, and 15 has FOUR factors.

Cheers,

Brent

## https://gmatclub.com/forum

I'm not sure if the approach I used is right:

Number of multiples of 2 between 2 and 30:

2(1) ... 2(15) 15 - 1 + 1 = 15

Take away 1 as its integers below 30

So total is 14

Number of odd prime numbers below 30:

9

Sum of positive multiples of 2 and odd prime numbers:

2 + 19 = 21

2 + 23 = 25

4 + 23 = 27

Any other calculations would have resulted in overlap and repetition. So total numbers that satisfied the statement was: 14+9+3 = 26

Where am I going wrong and how could this have been done much much more simpler in under 2 mins?

## Question link: https:/

Question link: https://gmatclub.com/forum/how-many-positive-integers-less-than-30-are-e...

Your list is missing 9 and 15

9 = 2 + 7

15 = 2 + 13

Here's m full solution: https://gmatclub.com/forum/how-many-positive-integers-less-than-30-are-e...

## In your approach, what's the

## Choosing 3 ensures that I don

Choosing 3 ensures that I don't miss any values.

That said, in this particular example, I could have chosen 5 or 7 and still reached the correct answer, but it's still best to start with the smallest odd prime.

For example, if I had chosen 11, then I would have missed the opportunity to get 9 as one of the possible values.

Cheers,

Brent

## https://gmatclub.com/forum

i did not get the 30 second approach given by Bunuel

## Question link: https:/

Question link: https://gmatclub.com/forum/how-many-positive-integers-less-than-30-are-e...

Bunuel's solution is pretty much the same as my 30-second solution (at https://gmatclub.com/forum/how-many-positive-integers-less-than-30-are-e...). The main difference is that Bunuel uses fewer words :-)

Cheers,

Brent

## https://gmatclub.com/forum/if

would you please give your approch?

## Here's my full solution:

Here's my full solution: https://gmatclub.com/forum/if-the-integer-n-is-greater-than-1-is-n-equal...

Cheers,

Brent

## The product of all the prime

(A) 10^9

(B) 10^8

(C) 10^7

(D) 10^6

(E) 10^5

The answer is D right?

Prime numbers are 2,3,5,7,11,13,17,19.

To approximate the product of those prime numbers we can do the following:

2*5=10

3*7=20

11*19=200

13*17=200

Now lets multiply 10*20*200*200=8000000 and according to scientific notation the result should be written as 8*10^6.

If to take calculator and make a precise calculation the answer is also 10^6. Do I understand it correctly? Please help me out. Thank you.

## Your approach is great.

Your approach is great.

However, you need to recognize that your approximations are all a bit smaller than than the actual products.

For example, 11 x 19 = 209 (not 200), and 13 x 17 = 221 (not 200) etc.

So, your product of 8 x 10^6 is a bit LESS THAN the actual answer.

If we round UP, we get: 8 x 10^6 ≈ 10 x 10^6 ≈ 10^7

Here's my full solution: https://gmatclub.com/forum/the-product-of-all-the-prime-numbers-less-tha...

Does that help?

Cheers,

Brent

## Question link: https:/

Hi Brent, I don't see how this explanation holds good for a set with, say, 4 or 5 numbers. Could you please help on this?

Thanks!

Kashaf

## Question link: https:/

Question link: https://gmatclub.com/forum/set-s-consists-of-more-than-two-integers-are-...

This is a crazy tricky question!!

The solution wouldn't hold up if there were 4 or 5 numbers. However, since we're not told how many numbers there are, it's possible that there are 3 numbers (if we knew there were 4 or 5 numbers in the set, statement 1 would be sufficient. So, the only way statement 1 is not sufficient is when there are only 3 numbers in the set).

However, when we combine the two statements, we can be certain that all of the numbers are negative.

Does that help?

Cheers,

Brent

## Was hoping this was asked.

## Statement 2: The product of

Statement 2: The product of the smallest and largest integers in the list is a prime number.

The product of two prime numbers is composite (e.g., 3 x 5 = 15, and 15 is composite)

The product of a prime number and a composite number is composite (i.e., non-prime).

The product of two composite numbers is composite.

So, the are two ways for the product of two integers to be prime

- One number is 1 and the other number is prime (e.g., 1 x 7 = 7, and 7 is prime)

- One number is -1 and the other number is the negative of a prime number (e.g., -1 x -3 = 3, and 3 is prime)

I hope that helps.

## Question: https://gmatclub

Hi Brent,

For this question, I spent over 1 minute to confirm if 97 and 79 are primes. Do we need to memorize primes till 100 for the GMAT? Thanks.

## Question link: https:/

Question link: https://gmatclub.com/forum/if-each-of-the-two-digits-x-and-y-is-distinct...

It's pretty rare for official GMAT questions to ask about primes greater than 70.

That said, even though this isn't an official question, there's certainly no harm in memorizing all of the primes up to 97.