Question: GCD of J and K

Comment on GCD of J and K

hi brent,

which lvl question is this??
gmat-admin's picture

I'd say 700-750

Cheers,
Brent

I Solved this within a minute and with this, as you said 700 level question, my confidence regained on integers. Thank God and Thank Brent.
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 also be on the 3J side?
gmat-admin's picture

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
gmat-admin's picture

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

ari.banerjee's picture

This is an excellent question. Such a simple approach to a hard qs.

You are awesome at simplifying the scary DS questions!

Thank you!!!!!!!
gmat-admin's picture

Thanks Ari!
This is, indeed, a very tricky question!

Cheers,
Brent

ari.banerjee's picture

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!
gmat-admin's picture

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.
gmat-admin's picture

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 that in some other similar questions provided in that lesson, the solutions did not take into consideration the possibility of prime numbers being repeated in the variable. So I'm confused whether to consider or not.
gmat-admin's picture

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 numbers are factors of the positive integer n ?

(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?
gmat-admin's picture

You bet!
Here's my full solution: https://gmatclub.com/forum/how-many-different-prime-numbers-are-factors-...

Cheers,
Brent

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