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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.