Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: if x and y are integers and 2<x<y, does y =16 [#permalink]

Show Tags

09 Mar 2013, 13:09

I know that each statements are insufficient by itself. But i think Even taken together they are insufficient. We know that GCF*LCM = X*Y So X*Y = 96 Hence , when y = 24 , x =4 Similarly when y = 16 , x = 6 So i think both statements are insufficient taken together.

Re: if x and y are integers and 2<x<y, does y =16 [#permalink]

Show Tags

09 Mar 2013, 13:26

Expert's post

Archit143 wrote:

If x and y are integers and 2 < x < y, does y = 16 ?

(1) The GCF of X and Y is 2. (2) The LCM of X and Y is 48.

I know that each statements are insufficient by itself. But i think Even taken together they are insufficient. We know that GCF*LCM = X*Y So X*Y = 96 Hence , when y = 24 , x =4 Similarly when y = 16 , x = 6 So i think both statements are insufficient taken together.

Archit

Notice that the greatest factor of 24 and 4 is 4, not 2 as given in the second statement.

Re: if x and y are integers and 2<x<y, does y =16 [#permalink]

Show Tags

19 Oct 2013, 20:07

Archit143 wrote:

I know that each statements are insufficient by itself. But i think Even taken together they are insufficient. We know that GCF*LCM = X*Y So X*Y = 96 Hence , when y = 24 , x =4 Similarly when y = 16 , x = 6 So i think both statements are insufficient taken together.

Archit

If GCF is 2 and LCM is 48, than the Pair of X and Y can be: X=2,Y=48 and X=6,Y=16 and X=16, Y=6 and X=48, Y=2

Re: if x and y are integers and 2<x<y, does y =16 [#permalink]

Show Tags

20 Oct 2013, 04:36

2

This post received KUDOS

Expert's post

suk1234 wrote:

Archit143 wrote:

I know that each statements are insufficient by itself. But i think Even taken together they are insufficient. We know that GCF*LCM = X*Y So X*Y = 96 Hence , when y = 24 , x =4 Similarly when y = 16 , x = 6 So i think both statements are insufficient taken together.

Archit

If GCF is 2 and LCM is 48, than the Pair of X and Y can be: X=2,Y=48 and X=6,Y=16 and X=16, Y=6 and X=48, Y=2

Statement #1: The GCF of x and y is 2 This leave open a wide array of possibilities. All we know is that x and y are two even numbers, both bigger than 2, with no common factors other than two: they could be x = 4, y = 6 x = 6, y = 8 x = 6, y = 10 x = 6, y = 16 So, it's possible for y to equal 16 or equal something else. This statement, alone and by itself, does not give us sufficient information, so it is insufficient.

Statement #2: The LCM of x and y is 48 Without any other information, we could have x = 3, y = 16 x = 4, y = 48 So, it's possible for y to equal 16 or equal something else. This statement, alone and by itself, does not give us sufficient information, so it is insufficient.

Combined: this is where it gets interesting. The GCF of x and y is 2 The LCM of x and y is 48 This is a tricky combination. First, let's list all the factors of 48 --- in order to have a LCM of 48 with another number, each number must be a factor of 48. factors of 48 = {1, 2, 3, 4, 6, 8, 12, 16, 24, 48} Those are the possible candidates for x & y. We can eliminate 1 & 2, because x > 2, and we can eliminate 3, because that cannot have a GCF of 2 with anything else. Possibilities for x & y = {4, 6, 8, 12, 16, 24, 48} If y = 48, then every other number in the set is factor of 48, so the GCF would be the smaller number --- e.g. the GCF of 6 and 48 is 6. Therefore, we can't use 48. If y = 24, then the first four numbers are factors of 24, so they don't work, and the GCF of 16 & 24 is 8. Therefore, we can't use 24. Possibilities for x & y = {4, 6, 8, 12, 16} Suppose y = 16 x = 4, y = 16 ===> GCF = 4, doesn't work x = 6, y = 16 ===> GCF = 2 --- this is one possible pair!! x = 8, y = 16 ===> GCF = 8, doesn't work x = 12, y = 16 ===> GCF = 4, doesn't work Suppose y = 8 x = 4, y = 8 ===> GCF = 4, doesn't work x = 6, y = 8 ===> GCF = 2, but LCM = 24, doesn't work Suppose y = 6 x = 4, y = 6 ===> GCF = 2, but LCM = 12, doesn't work So, after all that, the only pair that satisfies both statements is x = 6, y = 16, so it turns out, y does in fact equal 16. We are able to give a definitive answer to the prompt question, so the combined statements are sufficient.

Statement #1: The GCF of x and y is 2 This leave open a wide array of possibilities. All we know is that x and y are two even numbers, both bigger than 2, with no common factors other than two: they could be x = 4, y = 6 x = 6, y = 8 x = 6, y = 10 x = 6, y = 16 So, it's possible for y to equal 16 or equal something else. This statement, alone and by itself, does not give us sufficient information, so it is insufficient.

Statement #2: The LCM of x and y is 48 Without any other information, we could have x = 3, y = 16 x = 4, y = 48 So, it's possible for y to equal 16 or equal something else. This statement, alone and by itself, does not give us sufficient information, so it is insufficient.

Combined: this is where it gets interesting. The GCF of x and y is 2 The LCM of x and y is 48 This is a tricky combination. First, let's list all the factors of 48 --- in order to have a LCM of 48 with another number, each number must be a factor of 48. factors of 48 = {1, 2, 3, 4, 6, 8, 12, 16, 24, 48} Those are the possible candidates for x & y. We can eliminate 1 & 2, because x > 2, and we can eliminate 3, because that cannot have a GCF of 2 with anything else. Possibilities for x & y = {4, 6, 8, 12, 16, 24, 48} If y = 48, then every other number in the set is factor of 48, so the GCF would be the smaller number --- e.g. the GCF of 6 and 48 is 6. Therefore, we can't use 48. If y = 24, then the first four numbers are factors of 24, so they don't work, and the GCF of 16 & 24 is 8. Therefore, we can't use 24. Possibilities for x & y = {4, 6, 8, 12, 16} Suppose y = 16 x = 4, y = 16 ===> GCF = 4, doesn't work x = 6, y = 16 ===> GCF = 2 --- this is one possible pair!! x = 8, y = 16 ===> GCF = 8, doesn't work x = 12, y = 16 ===> GCF = 4, doesn't work Suppose y = 8 x = 4, y = 8 ===> GCF = 4, doesn't work x = 6, y = 8 ===> GCF = 2, but LCM = 24, doesn't work Suppose y = 6 x = 4, y = 6 ===> GCF = 2, but LCM = 12, doesn't work So, after all that, the only pair that satisfies both statements is x = 6, y = 16, so it turns out, y does in fact equal 16. We are able to give a definitive answer to the prompt question, so the combined statements are sufficient.

Answer = (C)

Does all this make sense? Mike

No need to test that many cases, let's see

x,y are positive integers and 2<x<y. Is y=16?

First statement GCF (x,y) is 2

Well we could have:

x=4, y=6 answer is NO or x=6, y=16 answer is YES

Hence insufficient

Second Statement LCM (x,y) is 48 48 = 2^4 * 3

Now we can test cases here too: Either x=3 and y=2^4 when answer is YES OR x=7 y = 48 answer is NO

Both together Since GCF =2 and LCM = 48 and since 2<x<y we can only have x=6, y=16

Hence C is the correct answer Please ask if anything remains unclear Cheers J

Re: If x and y are integers and 2 < x < y, does y = 16 ? [#permalink]

Show Tags

01 Apr 2014, 20:57

1

This post received KUDOS

Expert's post

1

This post was BOOKMARKED

Archit143 wrote:

If x and y are integers and 2 < x < y, does y = 16 ?

(1) The GCF of X and Y is 2. (2) The LCM of X and Y is 48.

Given: 2 < X < Y Question: Does Y = 16?

(1) The GCF of X and Y is 2. X = 2a; Y = 2b (a and b are co prime integers) Y may or may not be 16 e.g. X = 6, Y = 16 OR X = 6, Y = 8 etc

(2) The LCM of X and Y is 48. \(48 = 2^4 * 3\) One of X and Y must have 2^4 = 16 as a factor and one must have 3 as a factor. Again, Y may or may not be 16 e.g. X = 6, Y = 16 OR X = 1, Y = 48 etc

Using both together, X = 2a, Y = 2b. Since a and b need to be co-prime and both X and Y need to be greater than 2, one of a and b must be 3 and the other must be 8 (since X and Y already have a 2 to make 16). X = 6, Y = 16 (since X is less than Y). Y must be 16.

Re: If x and y are integers and 2 < x < y, does y = 16 ? [#permalink]

Show Tags

11 Jan 2016, 17:52

Expert's post

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If x and y are integers and 2 < x < y, does y = 16 ?

(1) The GCF of X and Y is 2. (2) The LCM of X and Y is 48.

In the original condition, there are 2 variables(x,y) and 1 equation(2<x<y), which should match with the number of equations. So you need 1 more equation. For 1) 1 equation, for 2) 1equation, which is likely to make D the answer. For 1), (x,y)=(4,6) -> no, (x,y)=(6,16) -> yes, which is not sufficient. For 2), (x,y)=(3,48) -> no, (x,y)=(6,16) -> yes, which is not sufficient. When 1) & 2), (x,y)=(6,16) -> yes, which is sufficient. Therefore, the answer is C.

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E. _________________

So, my final tally is in. I applied to three b schools in total this season: INSEAD – admitted MIT Sloan – admitted Wharton – waitlisted and dinged No...

A few weeks ago, the following tweet popped up in my timeline. thanks @Uber_Mumbai for showing me what #daylightrobbery means!I know I have a choice not to use it...

“This elective will be most relevant to learn innovative methodologies in digital marketing in a place which is the origin for major marketing companies.” This was the crux...