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Comment on GCD of J and K
hi brent,
which lvl question is this??
I'd say 700-750
I'd say 700-750
Cheers,
Brent
I Solved this within a minute
I solved like this.
1. 3J and 2K is 2 ---> means J and 2K is 2.. We dont know originally k is having any 2 or because of 2k, its having 2 in GCD. So 1 is Not sufficient.
2. 5J and K is 10. So, J is originally having 2, but we dont know whether it is having originally 5 or is it due to now 5J. So Not sufficient.
Combining, yeah J is having only 2. K is having both 5 & 2. So GCD is 2.
Excellent video explanation!
For 1) Can the optional 2
We COULD have more optional 2
We COULD have more optional 2's on the 3J side, but that wouldn't change anything about the question.
Hey, I have a doubt here
In statement 2, when we divide both sides by 5, if there are any optional 5's it will be divided right?
And also, it may be the case that K has optional 2's in its prime factorization! In that case, Statement 2 is sufficient as it gives only 2 as a common factor between J & K. Please explain
It's probably easiest to use
It's probably easiest to use numbers to show that statement 2 is insufficient.
case a: If J = 4 and K = 30, then 5J = 20. Here the GCD of 5J (20) and K (30) is 10, which satisfies statement 2. In this case the GCD of J (4) and K (30) is 2. In other words, the answer to the target question is 2.
case b: If J = 10 and K = 30, then 5J = 50. Here the GCD of 5J (50) and K (30) is 10, which satisfies statement 2. In this case the GCD of J (10) and K (30) is 10. In other words, the answer to the target question is 10.
Since cases a and b yield different answers to the target question, statement 2 is insufficient.
Does that help?
Cheers,
Brent
This is an excellent question
You are awesome at simplifying the scary DS questions!
Thank you!!!!!!!
Thanks Ari!
Thanks Ari!
This is, indeed, a very tricky question!
Cheers,
Brent
Hi Brent,
Can you help me understand this qs?
If x and y are integers, what is the least possible positive value of 21x+35y?
A. 1
B. 3
C. 5
D. 7
E. 9
Shouldnt the question read x and y are positive integers?
I mean what if both x and y are negative? The least value wont be 7? right? But the choices are all positive.
So is that assumed that x and y are positive? Can we expect such ambiguity in the GMAT exam?
Thank you!
You missed an important word
You missed an important word in the question:
If x and y are integers, what is the least possible POSITIVE value of 21x+35y?
Here are 2 of my solutions:
- https://gmatclub.com/forum/if-x-and-y-are-integers-what-is-the-least-pos...
- https://gmatclub.com/forum/if-x-and-y-are-integers-what-is-the-least-pos...
Cheers,
Brent
Hey Brent,
Why are we taking optional numbers into consideration? All the previous questions, we have always divided it as the question asks only for J not 5J. Then the answer will be B, common divisor 2.
Sorry, I'm not sure what you
Sorry, I'm not sure what you mean by "we have always divided it as the question asks only for J not 5J"
That said, we must consider the possibility of other primes (like 2 and 5) existing in the prime factorizations, since those optional values don't change the fact that the GCD in each case remains the same.
That came out wrong. I meant
Were those other questions
Were those other questions regarding Greatest Common Divisor (GCD)?
If we actually know the values that we want to find the GCD of, then we need not consider optional values in the prime factorizations. However, if we don't know the actual values, we must take into account the possibility of optional values.
For example, if I say that the GCD of x and y is 15, we know that the prime factorizations of x and y share a 3 and a 5 only.
That is:
x = (3)(5)(?)(?)(?)(?)
y = (3)(5)(?)(?)(?)(?)
We don't know what unknown values in the prime factorizations are.
So, for example, if we had a Data Sufficiency question that asked whether x is divisible by 2, we must take optional values into consideration.
For example, it COULD be the case that we have:
x = (3)(5)(2) = 60
y = (3)(5)(7) = 105
In this case, we can see that x IS divisible by 2.
Alternatively, it also COULD be the case that we have:
x = (3)(5)(5) = 75
y = (3)(5)(7) = 105
In this case, we can see that x is NOT divisible by 2.
Does that help?
Cheers,
Brent
How many different prime
(1) Four different prime numbers are factors of 2n
(2) Four different prime numbers are factors of n²
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient
Can you help me out with this?
You bet!
You bet!
Here's my full solution: https://gmatclub.com/forum/how-many-different-prime-numbers-are-factors-...
Cheers,
Brent
Hi Brent,
Along the same topic as above, would you be able to explain how you would solve the following question?
Thank you.
M and N are integers such that 6 < M < N. What is the value of N ?
(1) The greatest common divisor of M and N is 6.
(2) The least common multiple of M and N is 36.
I used the GCD * LCM = M*N rule, meaning M*N=36*6, but was not sure how to continue from there.
Good question.
Good question.
My full solution shows two different approaches to analyzing the combined statements: https://gmatclub.com/forum/m-and-n-are-integers-such-that-6-m-n-what-is-...
Cheers,
Brent
This question is so complex
This is a super difficult
This is a super difficult question. Keep in the mind that getting difficult questions wrong on the GMAT does not significantly reduce your score, whereas getting easy questions wrong will definitely hurt your score.
For more on this, read the following: https://www.gmatprepnow.com/articles/gmat-scoring-algorithm