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:

I am struggling to understand this question. The approach that I am trying to use is :

Statemenen 1 alone: INSUFFICIENT. Why? Because it doesn't say anything about x. x could be 1 and yz could be 4. x could be 8 and yz could e 4. So x can be ODD and EVEN both. Therefore, not sufficient. Is my understanding and concept correct for declining Statement 1?

Statement 2: If x,y and z are not divisible by 4, but they are divisible by 8 i.e they are divisible by at least 2^3. I am stuck after that. Can someone please help to tell me how to approach this mathematically?

The correct answer is B i.e statement 2 alone is sufficient.

I am struggling to understand this question. The approach that I am trying to use is :

Statemenen 1 alone: INSUFFICIENT. Why? Because it doesn't say anything about x. x could be 1 and yz could be 4. x could be 8 and yz could e 4. So x can be ODD and EVEN both. Therefore, not sufficient. Is my understanding and concept correct for declining Statement 1?

Statement 2: If x,y and z are not divisible by 4, but they are divisible by 8 i.e they are divisible by at least 2^3. I am stuck after that. Can someone please help to tell me how to approach this mathematically?

The correct answer is B i.e statement 2 alone is sufficient.

Just think in terms of prime factors;

xyz is divisible by 8. means; x*y*z must have at least 3 2's, doesn't matter from where those 2 come; the 3 2's are there.

Then think what possible ways can I get those three 2's. x=8, y=1,z=1 We got 3 2's; this time from x.

x=1,y=8,z=1 I got 3 2's; this time from y.

x=1,y=1,z=8 I got 3 2's; this time from z.

There are many such combinations. x=2,y=2,z=2 x=4,y=2,z=1 x=1,y=2,z=4

Q: Is x=even?

1. yz is divisible by 4. This means that yz must have at least two 2's because 4 has two 2's. Now, if y=2, z=2; yz=4; But from the stem we know xyz contains three 2's Thus, the one additional 2 must come from x AND x becomes even. If "x" contains one 2, it becomes even.

But, we don't know whether y=2, z=2; y may be 4 or 8 or 16 Then the odd/even for x or z doesn't make a difference. Because, y alone took care of both statements.

If y=8; y has 3 2's Now even if x=1; z=1; xyz will be divisible by 8 AND yz will be divisible by 4. Thus, we saw two different scenario where x may be an even or an odd. Not sufficient.

2. x,y and z are all NOT divisible by 4. This statement tells us that neither of x, y or z is divisible by 4. What does it mean?

It means; x does not contain two 2's. It may contain 0 2's or 1 2's. y does not contain two 2's. It may contain 0 2's or 1 2's. z does not contain two 2's. It may contain 0 2's or 1 2's.

However, we already know that xyz contain 3 2's. Combining both the stem condition and statement 2, we can conclude that each variable has one AND only one 2 in its factors.

x=2 y=2 z=2

OR

x=2*3*7*11*13*13*13 y=2*5*43 z=2

The point is x will contain exactly one 2 in its factor. And if x contains one 2 in its factors, it must be even. Sufficient.

If X, Y and z are integers and xyz is divisible by 8, is x [#permalink]

Show Tags

05 Aug 2013, 22:04

Please help explain: If x,y, and z are integers and xyz is divisible by 8, is x even? 1. yz is divisible by 4. 2. x,y, and z are all NOT divisible by 4.

I could not comprehend the explanation given by MGMAT for the second part of the statement. Please further explain. Thanks. Please ignore the difficulty tag.

Last edited by mau5 on 06 Aug 2013, 00:32, edited 1 time in total.

Re: Special Case of Divisibilty (odds and evens) [#permalink]

Show Tags

05 Aug 2013, 22:11

smartyman wrote:

Please help explain: If x,y, and z are integers and xyz is divisible by 8, is x even? 1. yz is divisible by 4. 2. x,y, and z are all NOT divisible by 8.

I could not comprehend the explanation given by MGMAT for the second part of the statement. Please further explain. Thanks. Please ignore the difficulty tag.

there is a typo in second statement. question is as follows:

If X, Y and z are integers and xyz is divisible by 8, isx even?

(1) yz is divisible by 4 (2) X, Y, and z are all NOTdivisible by 4

solution:

(1) yz is divisible by 4 If the value of yz = 4, then x should be even If the value of yz = 8, then x can be odd or even Insufficient!

Quote: (2) X, Y, and z are all NOT divisible by 4 If x , y , z are multiples of 2, then xyz is divisible by 8 and x is even. This is the only condition which satisfies the conditions xyz divisible by 8 and x,y,z are all not divisible by 4 Sufficient!

hence B _________________

When you want to succeed as bad as you want to breathe ...then you will be successfull....

Re: Special Case of Divisibilty (odds and evens) [#permalink]

Show Tags

05 Aug 2013, 22:49

smartyman wrote:

Please help explain: If x,y, and z are integers and xyz is divisible by 8, is x even? 1. yz is divisible by 4. 2. x,y, and z are all NOT divisible by 8.

I could not comprehend the explanation given by MGMAT for the second part of the statement. Please further explain. Thanks. Please ignore the difficulty tag.

In which book of Manhattans' did you find this problem can you tell me? did you write the question correctly? check it once more..plz _________________

Re: If x, y and z are integers and xyz is divisible by 8, is x e [#permalink]

Show Tags

23 Jul 2015, 12:38

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. _________________

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...