While solving GMAT quant questions, always remember that your one goal is to identify the correct answer as efficiently as possible, and not to please your former math teachers.
- Video Course
- Video Course Overview
- General GMAT Strategies - 7 videos (free)
- Data Sufficiency - 16 videos (free)
- Arithmetic - 38 videos
- Powers and Roots - 36 videos
- Algebra and Equation Solving - 73 videos
- Word Problems - 48 videos
- Geometry - 42 videos
- Integer Properties - 38 videos
- Statistics - 20 videos
- Counting - 27 videos
- Probability - 23 videos
- Analytical Writing Assessment - 5 videos (free)
- Reading Comprehension - 10 videos (free)
- Critical Reasoning - 38 videos
- Sentence Correction - 70 videos
- Integrated Reasoning - 17 videos
- Study Guide
- Blog
- Philosophy
- Office Hours
- Extras
- Prices
Comment on Prime Factorization
hi
would you plz help me with this
If K is an integer and 2 < k < 8, what is the value of k?
1) k is a factor of 30
2) k is a factor of 12.
my answer was c
the prime factorization for 30 is 2-3-5
for 12 is 2-2-3
so just 3 between them so it is c
what is the wrong here?
Be careful, the question does
Be careful. The question does not say that "k is a PRIME factor of 30." It just says "k is a factor of 30."
Statement 1: The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30.
Since we're told that 2 < k < 8, we can conclude that k = 3, 5 or 6
INSUFFICIENT
Statement 2: The factors of 12 are: 1, 2, 3, 4, 6, 12.
Since we're told that 2 < k < 8, we can conclude that k = 3, 4 or 6
INSUFFICIENT
The two statements COMBINED
Statement 1 tells us that k = 3, 5 or 6
Statement 2 tells us that k = 3, 4 or 6
Since both statements must be true, we can see that k can still equal 3 or 6.
INSUFFICIENT
Answer: E
Hi Brent,
Hi Brent,
I think the last answer choice has a mistake? "332" has "2" distinct primes.
Which of the following numbers has the greatest number of distinct prime factors?
A. 165
B. 192
C. 228
D. 330
E. 332
This requires us to find the prime factorization of each answer choice
A. 165 = (3)(5)(11) --- 3 distinct prime factors
B. 192 = (2)(2)(2)(2)(2)(2)(3) --- 2 distinct prime factors
C. 228 = (2)(2)(3)(19) --- 3 distinct prime factors
D. 330 = (2)(3)(5)(11) --- 4 distinct prime factors
E. 332 = (2)(2)(83) --- 3 distinct prime factor
Hi Brent,
This was one of the links posted for this vid: https://gmatclub.com/forum/stonecold-s-mock-test-217160.html
Are there any questions from here that you suggest we focus on? Or should we just save the set for further refining post answering the other links?
Many thanks,
Neel
Hi Neel,
Hi Neel,
I don't see a link to https://gmatclub.com/forum/stonecold-s-mock-test-217160.html from any of the above links.
With the links in the Reinforcement Activities boxes, I suggest that you answer as many as you feel are necessary to get to the level of expertise you need to achieve your target score.
For some students, this will mean answering a handful of questions in the 500-650 range. For others, it will mean answering all of the questions in the 650 range, etc.
Does that help?
Cheers,
Brent
Oops! In that case I must
Definitely, thank you for clarifying!
Best,
Neel
Hi Brent,
Could you please help me with the below question:
Does the integer k have a factor p such that 1 < p <k?
(1) k > 4!
(2) 13! + 2 ≤ k ≤ 13! + 13
Here's my full solution:
Here's my full solution: https://gmatclub.com/forum/does-the-integer-k-have-a-factor-p-such-that-...
Cheers,
Brent
Hi Brent,
Can you please explain this below mentioned question solution in
details
!https://gmatclub.com/forum/if-x-is-the-product-of-the-positive-integers-from-1-to-8-in-146157.html#p1171891
Thanks
Fatima-Zahra
Hi Fatima-Zahra,
Hi Fatima-Zahra,
Here's my full solution: https://gmatclub.com/forum/if-x-is-the-product-of-the-positive-integers-...
Cheers,
Brent
Hi,
Would like to know if my approach is good on the following problem https://gmatclub.com/forum/a-number-is-said-to-be-prime-saturated-if-the-product-of-all-the-diffe-106511.html
Let a,b,c be different prime factors of n. As per question a*b*c < square root of n, if we square both sides we get (a*b*c)^2 < n
Now on to checking numbers:
99= 3*3*11=> (3*11)^2 must be less than 99, which it is not
98=7*7*2 => (7*2)^2 must be less than 98, not true
97 is a prime number 97^2 is more than 97
96= 3*2*2*2*2*2 => (3*2)^2 must be less than 96, 36<96, true.
Answer 96
Question link: https:/
Question link: https://gmatclub.com/forum/a-number-is-said-to-be-prime-saturated-if-the...
Your approach is perfect - nice work!
Cheers,
Brent
Hi Brent,
Can you help with this problem https://gmatclub.com/forum/if-x-y-and-z-are-integers-and-2-x-5-y-z-0-00064-what-is-the-188182.html
I am completely stuck. I represented 0.00064 as 64*10^-5, which can be represented as 2^6*10^-5, I do not know what to do from here. Or maybe the whole approach is wrong?
Question link: https:/
Question link: https://gmatclub.com/forum/if-x-y-and-z-are-integers-and-2-x-5-y-z-0-000...
That's a good start.
The trick now is to recognize that there are many different ways to rewrite (2^6)(10^-5)
For example, we know that (2^-5)(5^-5) = 10^-5
So, we can write: (2^6)(10^-5) = (2^6)(2^-5)(5^-5)
Or we can combine the two powers of 2 to get: (2^6)(2^-5)(5^-5) = (2^1)(5^-5)
And so on.
Here's my full solution: https://gmatclub.com/forum/if-x-y-and-z-are-integers-and-2-x-5-y-z-0-000...
Cheers,
Brent
Hi Brent
could you please help me
from times to times in this topic i found a question like:
"how many different prime factors does n have?"
"n is divisible by how many positive integers?"
the problem is that it's not clear for me what I need to find. Should I found how many different factors N has OR should I found how many different numbers/quantity factors N has.
examples below
for me both of these questions sound the same, but they are different. how to dedicate\understand those differences?
https://gmatclub.com/forum/if-n-is-the-product-of-the-integers-from-1-to-8-inclusive-135542.html
https://gmatclub.com/forum/if-n-is-an-integer-then-n-is-divisible-by-how-many-positive-164964.html
Question links:
Question links:
https://gmatclub.com/forum/if-n-is-the-product-of-the-integers-from-1-to...
https://gmatclub.com/forum/if-n-is-an-integer-then-n-is-divisible-by-how...
If we're asked to find the number of DIFFERENT PRIME factors, we are counting ONLY prime factors, and we cannot count repeated primes more than once.
For example, 18 = (2)(3)(3)
So, 18 has TWO DIFFERENT prime factors: 2 and 3
Next, asking "n is divisible by how many positive integers?" is the same as asking "How many POSITIVE FACTORS does n have?"
In this case, we are counting ALL factors (prime and not prime)
Example: How many POSITIVE FACTORS does 18 have?
Factors of 18: 1, 2, 3, 6, 9, 12
So, 18 has 6 positive factors.
Does that help?
Cheers,
Brent
Question link: https:/
Hi Brent, can you please share your solution to this problem?
Thanks!
Kashaf
Here's my full solution:
Here's my full solution: https://gmatclub.com/forum/if-60-is-written-out-as-an-integer-with-how-m...
Cheers,
Brent
Hi Brent, can you please
(A school will assign each student in a group of n students to one of m classrooms. If 3<m<13<n, is it possible to assign each of n students to m classrooms so that each class has same number of students?)
According to me the answer is D. But correct answer is B, which I couldn't understand from OG's solution.
Thanks!
Kashaf
Here's my full solution:
Here's my full solution: https://gmatclub.com/forum/a-school-administrator-will-assign-each-stude...
Cheers,
Brent
https://gmatclub.com/forum/if
Approach plz
Here's my full solution:
Here's my full solution: https://gmatclub.com/forum/if-q-is-a-positive-integer-is-300-a-factor-of...
f x is a prime number greater
(A) x^2
(B) x/2
(C) 3x
(D) x−4
(E) x^2 + 1
Check the answer choices.....
Answer: D
But here what if 13 -4 =9 pls explain 9 is not a prime
The key word here is COULD.
Question link: https://gmatclub.com/forum/if-x-is-a-prime-number-greater-than-2-which-o...
The key word here is COULD. So, we need just ONE instance in which x - 4 is prime in order for D to be correct.
If x = 11 (which is prime), then x - 4 is prime.
So, x - 4 CAN be prime.
Your example (using x = 13) simply shows that x - 4 isn't always prime (but the correct answer is still D, since x - 4 CAN be prime)
If, on the other hand, the question asked, "...which of the following MUST be a prime number?", then answer choice D would not be correct.
How many prime numbers
factors of 7150 ...whats the shortest trick pls explain
Hi, is there a less time
If 60! is written out as an integer, with how many consecutive 0’s will that integer end?
https://gmatclub.com/forum/if-60-is-written-out-as-an-integer-with-how-many-101752.html
The key concept here is: For
The key concept here is: For every pair of one 2 and one 5, we get a product of 10, which accounts for one zero at the end of the integer.
Since there are A LOT more 2's than 5's "hiding" in 60!, it all comes down to counting the number of 5's hiding in 60!
We have 5, 10, 15, 20, 25 (there are two 5's hiding in 25), etc.
The entire process shouldn't take longer than 1 minute.
Here's my full solution: https://gmatclub.com/forum/if-60-is-written-out-as-an-integer-with-how-m...
Hi Brent, Can you explain me
https://gmatclub.com/forum/in-a-certain-game-a-large-container-is-filled-with-red-yel-144902.html
Here's my full solution:
Here's my full solution: https://gmatclub.com/forum/in-a-certain-game-a-large-container-is-filled...
Thank you
Hi Brent, could you please
1) https://gmatclub.com/forum/in-n-is-a-positive-integer-and-14n-60-is-an-integer-then-n-has-how-ma-224145.html
2) https://gmatclub.com/forum/if-n-is-a-positive-integer-less-than-200-and-14n-60-is-an-100763.html
I am struggling to understand the difference as in Question 2, it says " In N is a positive integer less than 200 ", here N not necessarily has to be 30 right, it can also be 40 as well.
Question #1: https://gmatclub
Question #1: https://gmatclub.com/forum/in-n-is-a-positive-integer-and-14n-60-is-an-i...
Question #2: https://gmatclub.com/forum/if-n-is-a-positive-integer-less-than-200-and-...
Question #2 says "N is a positive integer less than 200"
Given: 14N/60 is an integer
Simplify to get: 7N/30 is an integer.
This means N must be divisible by 30.
So, N can equal 30, 60, 90, 120, etc.
In fact, N can be any multiple of 30. So, the possible values of N range from 30 all the way to 180 (since N is less than 200)
The question asks "N has how many DIFFERENT positive prime factors?"
All multiples of 30 from 30 to 180 have the same number of DIFFERENT prime factors. That is, for each possible value of N, the three different prime factors are 2, 3 and 5.
In question #1, the value of N is not limited.
So, N can be ANY multiple of 30.
If N = 30, then N has 3 different prime factors: 2, 3 and 5
If N = 210, then N has 4 different prime factors: 2, 3, 5 and 7
If N = 2310, then N has 5 different prime factors: 2, 3, 5, 7 and 11
etc.
Does that help?
sir,you enlisted this one in
Link: https://gmatclub.com
Link: https://gmatclub.com/forum/stonecold-s-mock-test-217160.html#p1768023
Hi Anupom,
There are dozens of questions on that page.
I you tell me where I listed the question, I'll delete it.
sir,you enlisted this in
I have deleted that link. Don
I have deleted that link. Don't worry about those questions. There are plenty more to practice on that page.
https://gmatclub.com/forum/is
Link: https://gmatclub.com
Link: https://gmatclub.com/forum/is-integer-z-divisible-by-24-1-z-is-divisible...
Is integer z divisible by 24?
(1) z is divisible by 6.
(2) z is divisible by 4.
Statement 1: If z is divisible by 6, then the possible values of z include: 6, 12, 18, 24, 30, 36, ... etc.
If z = 6, then the answer to the target question is NO, z is not divisible by 24.
If z = 24, then the answer to the target question is YES, z IS divisible by 24.
Statement 1 is not sufficient
Statement 2: If z is divisible by 4, then the possible values of z include: 4, 8, 12, 16, 20, 24, 28, ... etc.
If z = 4, then the answer to the target question is NO, z is not divisible by 24.
If z = 24, then the answer to the target question is YES, z IS divisible by 24.
Statement 2 is not sufficient
Statements 1 and 2 combined: From the lists of possible values of z, we see that when we combine the statements, it is still possible that x = 12, in which case the answer to the target question is NO, z is not divisible by 24.
Alternatively, it could be the case that z = 24, which means the answer to the target question is YES, z IS divisible by 24.
Answer: E
actually i want to do this
Okay no problem. Here it goes
Okay no problem. Here it goes:
Is integer z divisible by 24?
(1) z is divisible by 6.
(2) z is divisible by 4.
When we prime factorize 24, we get 24 = (2)(2)(2)(3)
So we can rephrase the target question as " are there at least three 2's and one 3 hiding in the prime factorization of z?"
Statement 1: Since 6 = (2)(3), we now know that there is at least one 2 and one 3 hiding in the prime factorization of z.
This is not enough information to answer the rephrased target question with certainty.
Statement 2: Since 4 = (2)(2), we now know that there is at least two 2's hiding in the prime factorization of z.
This is not enough information to answer the rephrased target question with certainty.
Statements 1 and 2 combined: When we combine the two statements we can conclude that there are at least two 2's and one 3 hiding in the prime factorization of z.
This is not enough information to answer the rephrased target question with certainty.
Answer: E
so,the first and formost rule
Sorry, noticed your comment.
Sorry, noticed your comment.
The key takeaway in all of this is as follows:
A positive integer, N, is divisible by k and if and only if the prime factorization of k appears in the prime factorization of N.
For example, in order for N to be divisible by 18, the prime factorization 2x3x3 must appear in the prime factorization of N.