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:

If x, y and z are positive integers, such that x is a factor of y, and x is a multiple of z, which of the following is not necessarily an integer?

x+z/z y+z/x x+y/z xy/z yz/x

Given: \(z\) goes into \(x\) and \(x\) goes into \(y\). Note that it's not necessarily means that \(z<x<y\), it means that \(z\leq{x}\leq{y}\) (for example all three can be equal x=y=z=1);

Now, in all options but B we can factor out the denominator from the nominator and reduce it. For example in A: \(\frac{x+z}{z}\) as \(z\) goes into \(x\) we can factor out it and reduce to get an integer result (or algebraically as \(x=zk\) for some positive integer \(k\) then \(\frac{x+z}{z}=\frac{zk+z}{z}=\frac{z(k+1)}{z}=k+1=integer\)).

But in B. \(\frac{y+z}{x}\) we can not be sure that we'll be able factor out \(x\) from \(z\) thus this option might not be an integer (for example x=y=4 and z=2).

Answer: B.

Alternately you could juts plug some smart numbers and the first option which would give a non-integer result would be the correct choice. _________________

From the statement; z <= x <= y; such that; x is a multiple of z and y is a multiple of x. \(\therefore\) y is a multiple of z.

1. (x+z)/z = x/z+1 x is a multiple of z; so x/z= integer; integer+1 = integer. ALWAYS INTEGER.

2. (z+y)/x = z/x + y/x y/x is always an integer because y is a multiple of x. z/x is not necessarily an interger. NOT ALWAYS AN INTEGER.

3. (x+y)/z = x/z+y/z x/z - always an integer. x is a multiple of z y/z - always an integer. y is a multiple of z integer+integer=integer. ALWAYS INTEGER.

4. xy/z = y*(x/z) x/z - integer - x is a multiple of z y* integer = integer. Integer multiplied by integer is always integer. ALWAYS INTEGER

5. yz/x = z *(y/x) y/x - integer - y is a multiple of x z* integer = integer. Integer multiplied by integer is always integer. ALWAYS INTEGER

Ans: B

One may also substitute and see; Perhaps faster. z=2 x=4 y=8 _________________

If x,y, and z are positive integers such that x is a factor of y, and x is a multiple of z, which of the following is NOT necessarily an integer?

A. x+z/z B. y+z/x C. x+y/z D. xy/z E. yz/x

i did as: x=9 y=18 z=3 all options except B are integer so B is the answer. Is there any other good approach?

x is factor of y so \(y = x*A\) where A is another positive integer x is a multiple of z, so \(x = B*z\) where B is another positive integer and \(y=A*B*z\)

Now \((x+z)/z = x/z + 1 = B+1\) so integer \((y+z)/x = (A*B*z+z)/(B*z) = A + 1/B\) which will not be an integer if B is an integer greater than 1, so Answer B

We can quickly see that C reduces to \(B + A*B\), so integer, D is \(A*B^2\), so integer and E is \(A*z\), so integer again.

It looks elaborate but can be done in less than 90 seconds with pen and paper and would always give right answer, whereas trying to plug numbers may or may not work.

modifying my approach a little bit here and using algebra instead of picking numbers. Given y/x = integer x/z = integer This implies - y/z = integer

Now B stands out. y+z/x y/x + z/x z/x is the inverse of the x/z. The reversal of the relationship may not be TRUE always. Hence z/x may NOT be an integer !

Baten80 wrote:

If x,y, and z are positive integers such that x is a factor of y, and x is a multiple of z, which of the following is NOT necessarily an integer?

A. x+z/z B. y+z/x C. x+y/z D. xy/z E. yz/x

i did as: x=9 y=18 z=3 all options except B are integer so B is the answer. Is there any other good approach?

Re: If x, y and z are positive integers such that x is a factor [#permalink]

Show Tags

27 Apr 2015, 11:00

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Re: If x, y and z are positive integers such that x is a factor [#permalink]

Show Tags

27 May 2016, 03:43

Lolaergasheva wrote:

If x, y and z are positive integers such that x is a factor of y, and x is a multiple of z, which of the following is not necessarily an integer?

A. (x+y)/z B. (y+z)/x C. (x+y)/z D. (xy)/z E. (yz)/x

Dear Moderators, Answer choice A and C are same. This is a question from OG. I believe answer option A must be (x+z)/z. Could you please rectify this? Thank you, Nalin

Given: 1) x is a factor of y, and 2) x is a multiple of z. In other words, z is a factor of x This implies that z is also a factor of y.

A. (x+z)/z z is a factor of x. Hence, this will always be an integer B. (y+z)/x x is a factor of y but we don't know whether x is a factor of z or not. Hence, this could be or could not be an integer C. (x+y)/z z is a factor of both x and y. Hence, this will always be an integer D. (xy)/z z is a factor of both x and y. Hence, this will always be an integer E. (yz)/xx is a factor of y. Hence, this will always be an integer

The correct answer is B.

gmatclubot

Re: If x, y and z are positive integers such that x is a factor
[#permalink]
27 May 2016, 03:43

Excellent posts dLo saw your blog too..!! Man .. you have got some writing skills. And Just to make an argument = You had such an amazing resume ; i am glad...

So Much $$$ Business school costs a lot. This is obvious, whether you are a full-ride scholarship student or are paying fully out-of-pocket. Aside from the (constantly rising)...

They say you get better at doing something by doing it. then doing it again ... and again ... and again, and you keep doing it until one day you look...