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

It is currently 12 Dec 2019, 19:04

Close

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
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.

Close

Request Expert Reply

Confirm Cancel

Number XYZ is the product of positive integer n and 9. Is x + y + z =

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
Joined: 11 Jul 2015
Posts: 2
Number XYZ is the product of positive integer n and 9. Is x + y + z =  [#permalink]

Show Tags

New post Updated on: 05 Sep 2015, 03:13
14
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

49% (02:00) correct 51% (02:15) wrong based on 195 sessions

HideShow timer Statistics

Number XYZ is the product of positive integer n and 9. Is x + y + z = 9?

(1) x + y + z < 15
(2) x + y + z > 8

Originally posted by allenh on 05 Sep 2015, 02:06.
Last edited by Bunuel on 05 Sep 2015, 03:13, edited 1 time in total.
Renamed the topic and edited the question.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59712
Re: Number XYZ is the product of positive integer n and 9. Is x + y + z =  [#permalink]

Show Tags

New post 05 Sep 2015, 03:22
6
2
Number XYZ is the product of positive integer n and 9. Is x + y + z = 9?

Since three-digit number XYZ is the product of positive integer n and 9, then it's divisible by 9. A number is a divisible by 9 if the sum of its digit is divisible by 9. Thus a three-digit integer to be divisible by 9 the sum of its digits must be 9 (for example 126), 18 (for example, 189) or 27 (999).

From above z + y + z is 9, 18 or 27.

(1) x + y + z < 15 --> x + y + z = 9. Sufficient.
(2) x + y + z > 8 --> x + y + z = 9, 18 or 27. Not sufficient.

Answer: A.

Hope it's clear.
_________________
General Discussion
Intern
Intern
avatar
B
Joined: 30 Mar 2017
Posts: 36
Location: United States (FL)
GMAT ToolKit User
Re: Number XYZ is the product of positive integer n and 9. Is x + y + z =  [#permalink]

Show Tags

New post 23 Jun 2017, 04:14
My gut was telling me A, however isn't that not necessarily correct?

Unless there is a rule on the GMAT that contradicts my reasoning, there is nothing that says XYZ can't the same integer (000).

If n is 0 then 9n = 0 and X + Y +Z can be equal to 0. Maybe its a stretch, but the stem could benefit from clarity by saying 3 digit number XYZ instead of just number XYZ
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4145
Location: Canada
Number XYZ is the product of positive integer n and 9. Is x + y + z =  [#permalink]

Show Tags

New post 23 Jun 2017, 06:37
Top Contributor
laxpro2001 wrote:
My gut was telling me A, however isn't that not necessarily correct?

Unless there is a rule on the GMAT that contradicts my reasoning, there is nothing that says XYZ can't the same integer (000).

If n is 0 then 9n = 0 and X + Y +Z can be equal to 0. Maybe its a stretch, but the stem could benefit from clarity by saying 3 digit number XYZ instead of just number XYZ


It's a great idea to consider the possibility that XYZ = 000, however there's one piece of given information that you forgot: XYZ is the product of positive integer n and 9
If n is a positive integer, then the product (n)(9) will be positive (which means XYZ can't equal zero)

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4145
Location: Canada
Re: Number XYZ is the product of positive integer n and 9. Is x + y + z =  [#permalink]

Show Tags

New post 23 Jun 2017, 06:52
2
Top Contributor
allenh wrote:
Number XYZ is the product of positive integer n and 9. Is x + y + z = 9?

(1) x + y + z < 15
(2) x + y + z > 8


To avoid any confusion/ambiguity, we might add some additional information that states x, y, and z are DIGITS.
Some students might think that XYZ is the product of 3 numbers.
That said, I love this question!

Target question: Is x + y + z = 9?

Given: XYZ is the product of positive integer n and 9
This is a HUGE piece of information, because it tells us that XYZ is a multiple of 9
A great feature of all positive multiples of 9 is that the sum of their digits will always be a multiple of 9.
For example, 873 is a multiple of 9, and the sum of its digits = 8 + 7 + 3 = 18, and 18 is a multiple of 9
Likewise, 113,004 is a multiple of 9, and the sum of its digits = 1 + 1 + 3 + 0 + 0 + 4 = 9, and 9 is a multiple of 9
So, we can conclude that the sum, x + y + z must equal 9 or 18 or 27
ASIDE: the greatest possible sum is 27, since there are three digits and the greatest value of each digit is 9

Statement 1: x + y + z < 15
We already know that x + y + z must equal 9 or 18 or 27
So, if x + y + z < 15, then we can be certain that x + y + z = 9
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x + y + z > 8
We already know that x + y + z must equal 9 or 18 or 27
So, if x + y + z > 8, then it COULD be the case that x + y + z = 9 OR it COULD be the case that x + y + z = 18 OR it COULD be the case that x + y + z = 27
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer:

RELATED VIDEO

_________________
Test confidently with gmatprepnow.com
Image
Senior Manager
Senior Manager
User avatar
D
Joined: 18 Jun 2018
Posts: 255
Re: Number XYZ is the product of positive integer n and 9. Is x + y + z =  [#permalink]

Show Tags

New post 01 Sep 2018, 10:18
allenh wrote:
Number XYZ is the product of positive integer n and 9. Is x + y + z = 9?

(1) x + y + z < 15
(2) x + y + z > 8


OA:A
Number XYZ is the product of positive integer n and 9.
As Number XYZ is multiple of 9, Sum of its digits should be divisible by 9.
X+Y+Z = 9 m , where m is a positive integer
Value of X+Y+Z can be 9,18,27,36,.................

Question : Is X + Y + Z = 9?

(1) X + Y + Z < 15
As per question stem,Value of X+Y+Z can be 9,18,27,36,.................
Statement 1 i.e X + Y + Z < 15 leads to only one value of X+Y+Z i.e 9.
Is X + Y + Z = 9? : Yes
Statement 1 alone is sufficient

2) X + Y + Z > 8
As per question stem,Value of X+Y+Z can be 9,18,27,36,.................
Statement 2 i.e X + Y + Z > 8 leads to multiple value of X+Y+Z .It can be 9,18,27 and so on.
Is X + Y + Z = 9? : Answer can be yes or no
Statement 2 alone is insufficient
Senior Manager
Senior Manager
User avatar
P
Joined: 07 Jul 2012
Posts: 365
Location: India
Concentration: Finance, Accounting
GPA: 3.5
Re: Number XYZ is the product of positive integer n and 9. Is x + y + z =  [#permalink]

Show Tags

New post 01 Sep 2018, 20:34
Product XYZ must be divisible by 9.

(A number is a divisible by 9 if the sum of its digit is divisible by 9.)

Value of XYZ could be: 9, 18, 27.....

(1) X+Y+Z<15. So X+Y+Z must be 9. [Suff]

(2) X+Y+Z>8. So X+Y+Z can be 9 or 18. [Insuff]

Answer: A.
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13743
Re: Number XYZ is the product of positive integer n and 9. Is x + y + z =  [#permalink]

Show Tags

New post 24 Oct 2019, 05:48
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.
_________________
GMAT Club Bot
Re: Number XYZ is the product of positive integer n and 9. Is x + y + z =   [#permalink] 24 Oct 2019, 05:48
Display posts from previous: Sort by

Number XYZ is the product of positive integer n and 9. Is x + y + z =

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne