Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

It is currently 20 Jul 2019, 17:25

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

Consider an integer x=251n9 where n represents the tens digit of x, wh

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

Hide Tags

Find Similar Topics 
Current Student
User avatar
D
Joined: 12 Aug 2015
Posts: 2609
Schools: Boston U '20 (M)
GRE 1: Q169 V154
GMAT ToolKit User
Consider an integer x=251n9 where n represents the tens digit of x, wh  [#permalink]

Show Tags

New post 04 Nov 2016, 09:35
1
4
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

69% (01:32) correct 31% (01:37) wrong based on 208 sessions

HideShow timer Statistics


CEO
CEO
User avatar
V
Joined: 12 Sep 2015
Posts: 3853
Location: Canada
Re: Consider an integer x=251n9 where n represents the tens digit of x, wh  [#permalink]

Show Tags

New post 04 Nov 2016, 11:26
Top Contributor
2
stonecold wrote:
Consider an integer x=251n9 where n represents the tens digit of x, what is the value of x?

(1) x is a multiple of 3
(2) x is a multiple of 9


Nice question, stonecold

This question tests two divisibility rules:
1) If an integer is divisible by 3 (i.e., a multiple of 3), the sum of its digits must be divisible by 3.
2) If an integer is divisible by 9 (i.e., a multiple of 9), the sum of its digits must be divisible by 9.


Target question: What is the value of x?

Given: x = 251n9 where n represents the tens digit of x

Statement 1: x is a multiple of 3
This means the sum of the digits of x must be divisible by 3
In other words, the sum 2+5+1+n+9 must be divisible by 3
Simplify: 17+n must be divisible by 3
This means there are several possible cases:
Case a: n = 1, so that 17+n = 17+1 = 18, which is divisible by 3. In this case, x = 25119
Case b: n = 4, so that 17+n = 17+4 = 21, which is divisible by 3. In this case, x = 25149
Case c: n = 7, so that 17+n = 17+7 = 24, which is divisible by 3. In this case, x = 25179
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x is a multiple of 9
This means the sum of the digits of x must be divisible by 9
In other words, the sum 2+5+1+n+9 must be divisible by 9
Simplify: 17+n must be divisible by 9
This means there is only one possible case: n = 1, so that 17+n = 17+1 = 18, which is divisible by 9.
Since no other single-digit value of n will be such that 17+n is divisible by 9, we can conclude that x = 25119
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer:

RELATED VIDEO

_________________
Test confidently with gmatprepnow.com
Image
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 11718
Re: Consider an integer x=251n9 where n represents the tens digit of x, wh  [#permalink]

Show Tags

New post 01 Sep 2018, 08:20
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: Consider an integer x=251n9 where n represents the tens digit of x, wh   [#permalink] 01 Sep 2018, 08:20
Display posts from previous: Sort by

Consider an integer x=251n9 where n represents the tens digit of x, wh

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





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