GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 21 Nov 2018, 02:07

### GMAT Club Daily Prep

#### 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

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

## Events & Promotions

###### Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### All GMAT Club Tests are Free and open on November 22nd in celebration of Thanksgiving Day!

November 22, 2018

November 22, 2018

10:00 PM PST

11:00 PM PST

Mark your calendars - All GMAT Club Tests are free and open November 22nd to celebrate Thanksgiving Day! Access will be available from 0:01 AM to 11:59 PM, Pacific Time (USA)
• ### Free lesson on number properties

November 23, 2018

November 23, 2018

10:00 PM PST

11:00 PM PST

Practice the one most important Quant section - Integer properties, and rapidly improve your skills.

# If x, y and z are integers and xyz is divisible by 8, is x e

Author Message
TAGS:

### Hide Tags

Senior Manager
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 475
Location: United Kingdom
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
If x, y and z are integers and xyz is divisible by 8, is x e  [#permalink]

### Show Tags

29 Jun 2011, 12:24
2
11
00:00

Difficulty:

85% (hard)

Question Stats:

47% (01:40) correct 53% (01:51) wrong based on 260 sessions

### HideShow timer Statistics

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.

Spoiler: :: My doubt
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.
Retired Moderator
Joined: 20 Dec 2010
Posts: 1828
Re: Divisibility (Odds & Evens)  [#permalink]

### Show Tags

29 Jun 2011, 14:47
5
1
enigma123 wrote:
Hi Fluke and everyone,

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.

Spoiler: :: My doubt
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.

Ans: "B"
_________________
##### General Discussion
Director
Joined: 01 Feb 2011
Posts: 664
Re: Divisibility (Odds & Evens)  [#permalink]

### Show Tags

29 Jun 2011, 16:39
2
1
1. Not sufficient

yz is divisible by 4 = > yz is factor of 4

x may or may not be even.

x y z
2 4 1 => x is even
3 4 2 => x is odd

2 . Sufficient

We need total of 3 2's in x,y and z. But we know each number is not divisible by 4.

=> each number has to have exactly one 2 .

Manager
Joined: 27 Jul 2011
Posts: 54
If X, Y and z are integers and xyz is divisible by 8, is x  [#permalink]

### Show Tags

Updated on: 05 Aug 2013, 23:32
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.

Originally posted by smartyman on 05 Aug 2013, 21:04.
Last edited by mau5 on 05 Aug 2013, 23:32, edited 1 time in total.
Edited the Q.
Director
Joined: 14 Dec 2012
Posts: 766
Location: India
Concentration: General Management, Operations
GMAT 1: 700 Q50 V34
GPA: 3.6
Re: Special Case of Divisibilty (odds and evens)  [#permalink]

### Show Tags

05 Aug 2013, 21:11
1
smartyman wrote:
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....

GIVE VALUE TO OFFICIAL QUESTIONS...

learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmat-analytical-writing-assessment

Senior Manager
Joined: 10 Jul 2013
Posts: 314
Re: Special Case of Divisibilty (odds and evens)  [#permalink]

### Show Tags

05 Aug 2013, 21:49
smartyman wrote:
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
_________________

Asif vai.....

Manager
Joined: 27 Jul 2011
Posts: 54
Re: If X, Y and z are integers and xyz is divisible by 8, is x  [#permalink]

### Show Tags

05 Aug 2013, 23:23
Sorry,

I misread the question; statement 2 should be
x,y, and z are all NOT divisible by 4.
then it makes sense.
Senior Manager
Joined: 10 Jul 2013
Posts: 314
Re: If X, Y and z are integers and xyz is divisible by 8, is x  [#permalink]

### Show Tags

05 Aug 2013, 23:37
smartyman wrote:
Sorry,

I misread the question; statement 2 should be
x,y, and z are all NOT divisible by 4.
then it makes sense.

thats best. sometimes it happens.
_________________

Asif vai.....

Intern
Joined: 03 May 2016
Posts: 2
Re: If x, y and z are integers and xyz is divisible by 8, is x e  [#permalink]

### Show Tags

04 Aug 2016, 07:47
enigma123 wrote:
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.

Spoiler: :: My doubt
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.

Hi,

I am a bit confused with the second statement in the question.

The statement states - x,y and z are all NOT divisible by 4. I am confused because "all" is mentioned in the statement.
Because of this I inferred that "Not all x, y,z are divisible by 4"- implying some can be divisible by 4. Hence I marked "E" as my answer.

Can anyone please clarify my doubt....

Current Student
Joined: 12 Aug 2015
Posts: 2632
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: If x, y and z are integers and xyz is divisible by 8, is x e  [#permalink]

### Show Tags

21 Aug 2016, 04:42
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: If x, y and z are integers and xyz is divisible by 8, is x e  [#permalink]

### Show Tags

11 Dec 2017, 07:37
1
enigma123 wrote:
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.

We are given that x, y, and z are integers and xyz is divisible by 8. We need to determine whether x is even, i.e., whether x is divisible by 2.

Statement One Alone:

yz is divisible by 4.

We don’t have enough information to determine whether x is even. For example, if yz = 4, then x could be 2, so that xyz = 8 is divisible by 8. However, if yz = 8, then x could be 3, so that xyz = 24 is divisible by 8. In the former case, x is even; in the latter case, x is odd. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

x, y, z are all not divisible by 4.

Notice that 4 = 2^2 and 8 = 2^3. If x, y, and z are not divisible by 4, in order for the product, xyz, to be divisible by 8, each variable has to be divisible by 2. Thus, x must be even.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: If x, y and z are integers and xyz is divisible by 8, is x e &nbs [#permalink] 11 Dec 2017, 07:37
Display posts from previous: Sort by