Can someone explain how to approach these types of problems

[bjd83]

I understand the explanations for each, but I guess I'm more interested in learning the general approach to answering these questions when you have to determine what the variables could equal to make the answer choice correct.

If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y?
5
5(x - y)
20x
20y
35x

If k and x are positive integers and x is divisible by 6, which of the following CANNOT be the value of sqrt (288kx)?

A) 24k sqrt(3)
B) 24 sqrt(k)
C) 24 sqrt(3k)
D) 24 sqrt(6k)
E) 72 sqrt(k)

[freelance21]

Is Ans for 1: E (35x) ??

35x -> 5, 7, x

20y -> 2, 5, y

Also, Can you please complete Question 2

[bjd83]

Is Ans for 1: E (35x) ??

35x -> 5, 7, x

20y -> 2, 5, y

Also, Can you please complete Question 2

Sorry about that, I copied and pasted it from the CAT and the square root is an image. The answer to the first question is 20x.

If you divide 20y/20x you get 1 an integer when y=x, but if you divide 35x/20x you get 35/20 which can never be an integer. Thanks for the reply.

[sanyalpritish]

For the Second q Imo B , well takes me time to do these questions for sure but you can factorize the questions and answer them

[RonPurewal]

I understand the explanations for each, but I guess I'm more interested in learning the general approach to answering these questions when you have to determine what the variables could equal to make the answer choice correct.

If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y?
5
5(x - y)
20x
20y
35x

If k and x are positive integers and x is divisible by 6, which of the following CANNOT be the value of sqrt (288kx)?

A) 24k sqrt(3)
B) 24 sqrt(k)
C) 24 sqrt(3k)
D) 24 sqrt(6k)
E) 72 sqrt(k)

well, if you're looking for ONE perfectly general approach to these questions, you are going to be sorely disappointed - there isn't one.
"divisibility/primes" is one of the most astoundingly diverse topics of everything on the gmat. pretty much the only unifying thread running through all these problems is prime factorization - i.e., most of them have something to do with the prime factorizations of the numbers involved, although the connections are different in each case.

in any case, i'm not sure whether you're aware of the sweepingly general nature of your question. it's a lot like asking, "what's the general approach for an algebra equation, when they ask you to solve for x?"
just as in that case, there's definitely no single answer - it depends on the problem.

--

ON THE OTHER HAND:

if the problem starts out with
"which of the following..."
then you have a much-better-than-normal chance of being able to PLUG IN THE ANSWER CHOICES, run them through the problem (however you can), and see whether they work.

[lj6871849]

I understand the explanations for each, but I guess I'm more interested in learning the general approach to answering these questions when you have to determine what the variables could equal to make the answer choice correct.

If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y?
5
5(x - y)
20x
20y
35x

If k and x are positive integers and x is divisible by 6, which of the following CANNOT be the value of sqrt (288kx)?

A) 24k sqrt(3)
B) 24 sqrt(k)
C) 24 sqrt(3k)
D) 24 sqrt(6k)
E) 72 sqrt(k)

well, if you're looking for ONE perfectly general approach to these questions, you are going to be sorely disappointed - there isn't one.
"divisibility/primes" is one of the most astoundingly diverse topics of everything on the gmat. pretty much the only unifying thread running through all these problems is prime factorization - i.e., most of them have something to do with the prime factorizations of the numbers involved, although the connections are different in each case.

in any case, i'm not sure whether you're aware of the sweepingly general nature of your question. it's a lot like asking, "what's the general approach for an algebra equation, when they ask you to solve for x?"
just as in that case, there's definitely no single answer - it depends on the problem.

--

ON THE OTHER HAND:

if the problem starts out with
"which of the following..."
then you have a much-better-than-normal chance of being able to PLUG IN THE ANSWER CHOICES, run them through the problem (however you can), and see whether they work.

Hello Ron - I used the general idea that GCF of A and B is X then each nos is divisible by X (the other factors of X are also factors of the 2 nos )

option C - 35 / 20 is not divisible all other options we have variable to make it divisible hence the correct answer is C.....

Regards

[lj6871849]

Also in the below reasoning correct for the 2nd problem posted in the 1st thread..

x is divisible by 6 --> x = 6i, for some positive integer i.

= sqrt(288kx)
= sqrt{(2x2x2x2x2x3x3)(k)(x)}
= sqrt{(2^5 x 3^2)(k)(6i)}
= sqrt{(2^6 x 3^3)(ki)}
= (2^3 x 3) sqrt(3ki)
= 24 sqrt(3ki)

Now, for any values of positive integers K and I 24 sqrt(3ki) is always more than (B) 24 sqrt(k)

Answer: B.

[tim]

looks good to me. nice job..

[rkafc81]

hi all,

I really don't understand MGMAT's answer for answer choice (A) of the first question in this post. Specifically, the part in bold below -->

i.e.
(A) CAN be the greatest common divisor. First, 35x / 5 = 7x, which is an integer for every possible value of x. Second, 20y / 5 = 4y, which is an integer for every possible value of y. Therefore, 5 is a common divisor. It will be the greatest common divisor when 7x and 4y share no other factors. To illustrate, if x = 1 and y = 1, then 35x = 35 and 20y = 20, and their greatest common divisor is 5.

can someone please explain this a bit more? I've tried generating examples to try and understand this but i just can't get my head around it

thanks

[RonPurewal]

hi all,

I really don't understand MGMAT's answer for answer choice (A) of the first question in this post. Specifically, the part in bold below -->

i.e.
(A) CAN be the greatest common divisor. First, 35x / 5 = 7x, which is an integer for every possible value of x. Second, 20y / 5 = 4y, which is an integer for every possible value of y. Therefore, 5 is a common divisor. It will be the greatest common divisor when 7x and 4y share no other factors. To illustrate, if x = 1 and y = 1, then 35x = 35 and 20y = 20, and their greatest common divisor is 5.

can someone please explain this a bit more? I've tried generating examples to try and understand this but i just can't get my head around it

thanks

hmm.
it's interesting that this is even in the solution, considering that it's wholly unnecessary to solving the problem.
i.e., all you have to do is establish that 5 can be the greatest common divisor; there's no need to establish the exact conditions under which that will happen.

nevertheless, since you asked... it's like this:
* clearly, 5 goes into 35x, and 5 goes into 20y.
* if you divide the 5 out of those numbers, then you have 7x and 4y left over.
* if those numbers don't have any more common factors (besides 1), then 5 is the only common factor you have, and so the GCF is 5.
* if those numbers do have further common factors, then the GCF is going to be the product of 5 and those factors ... so, basically, not just 5 anymore.

for instance, let's say x = 3 and y = 6. in this case x and y have the factor 3 in common, so 7x and 4y will also have that factor in common. ... so, we would expect the GCF of 35x and 20y to be 3 x 5, not just 5.
if you work those numbers out, you get 35x = 105 and 20y = 120, in which case the GCF is indeed 15 and not 5.