NEW HERE? LEARN MORE
closeclose
Last visit was: 07 May 2024, 22:14 It is currently 07 May 2024, 22:14
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

If the number x3458623y is divisible by 88, what is the

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
avatar
sarb
Intern
Intern
Joined: 12 May 2012
Posts: 15
Own Kudos [?]: 1194 [13]
Given Kudos: 19
Location: United States
Concentration: Technology, Human Resources
Send PM
If the number x3458623y is divisible by 88, what is the [#permalink] New post   Updated on: 22 Jul 2014, 05:01
3
Kudos
10
Bookmarks
00:00
A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

60% (02:01) correct 40% (02:02) wrong based on 300 sessions
Hide Show timer Statistics
If the number x3458623y is divisible by 88, what is the value of x?

A. 1
B. 2
C. 3
D. 4
E. 5
ShowHide Answer
Official Answer
A

Originally posted by sarb on 08 Jun 2012, 09:21.
Last edited by Bunuel on 22 Jul 2014, 05:01, edited 2 times in total.
Edited the question and added the OA.
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93081
Own Kudos [?]: 622037 [12]
Given Kudos: 81798
Send PM
CAT Tests Forum Quiz Mode
Re: If the number x3458623y is divisible by 88, what is the [#permalink] New post   08 Jun 2012, 09:47
12
Bookmarks
Expert Reply
sarb wrote:
If the number x3458623y is divisible by 88, what is the value of x?

A. 1
B. 2
C. 3
D. 4
E. 5


Since x34,586,23y is divisible by 88=8*11 then it's divisible by both 8 and 11.

Now, in order a number to be divisible by 8 its last three digits must be divisible by 8, so 23y must be divisible by 8. That's only possibly if y=2 --> 232/8=29. So, our number is x34,586,232.

Next, in order a number to be divisible by 11 the difference between the sum of the odd numbered digits (1st, 3rd, 5th...) and the sum of the even numbered digits (2nd, 4th...) must be divisible by 11. So, (x+4+8+2+2)-(3+5+6+3)=x-1 must be divisible by 11, which means that x can only be 1.

Answer: A.

For more on divisibility check Number Theory chapter of Meth Book: math-number-theory-88376.html

Hope it helps.
General Discussion
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93081
Own Kudos [?]: 622037 [0]
Given Kudos: 81798
Send PM
CAT Tests Forum Quiz Mode
Re: If the number x3458623y is divisible by 88, what is the [#permalink] New post   26 Jun 2013, 02:25
Expert Reply
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

All DS Divisibility/Multiples/Factors questions to practice: search.php?search_id=tag&tag_id=354
All PS Divisibility/Multiples/Factors questions to practice: search.php?search_id=tag&tag_id=185
avatar
kpali
Intern
Intern
Joined: 22 May 2013
Posts: 35
Own Kudos [?]: 34 [2]
Given Kudos: 10
Concentration: General Management, Technology
Schools: Tippie '16 Sloan '16 Tepper '16 Duke '16
GPA: 3.9
WE:Information Technology (Computer Software)
Send PM
GMAT ToolKit User
Re: If the number x3458623y is divisible by 88, what is the [#permalink] New post   26 Jun 2013, 20:47
2
Kudos
sarb wrote:
If the number x3458623y is divisible by 88, what is the value of x?

A. 1
B. 2
C. 3
D. 4
E. 5


x3458623y is divisible by 88 so, it should be divisible by 8 and 11

x+14+y -17 = n * 11
x+y-3 = n*11
n cant be 2, as in that case RHS will become 22, and on LHS the max we can get is 9+9-3 = 15

so n=0 or 1

now it should be divisible by 8 also, so 23y should be divisible by 8
240 is perfectly divisible by 8, so the no less then that will be 232

thus, y=2

now, x+2-3 =n*11
x-1=n*11

now n=1 is also not possible as lhs max can only be 9-1 =8

thus, n=0
hence, x=1

Ans: A
User avatar
cumulonimbus
Manager
Manager
Joined: 14 Nov 2011
Posts: 100
Own Kudos [?]: 57 [0]
Given Kudos: 103
Location: United States
Concentration: General Management, Entrepreneurship
GPA: 3.61
WE:Consulting (Manufacturing)
Send PM
GMAT ToolKit User
Re: If the number x3458623y is divisible by 88, what is the [#permalink] New post   12 Jul 2013, 01:23
sarb wrote:
If the number x3458623y is divisible by 88, what is the value of x?

A. 1
B. 2
C. 3
D. 4
E. 5



to be divisible by 11:

3+5+6+3=2+y+8+4+x
3=x+y

x y
3 0 - not correct (not divisible by 4)
0 3 - not correct (not divisible by 2)
2 1 - not correct (not divisible by 2)
1 2 - correct (divisible by 4) - (...232) - is divisible by 4
avatar
PareshGmat
SVP
SVP
Joined: 27 Dec 2012
Status:The Best Or Nothing
Posts: 1560
Own Kudos [?]: 7222 [0]
Given Kudos: 193
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Send PM
Re: If the number x3458623y is divisible by 88, what is the [#permalink] New post   04 Mar 2014, 01:31
cumulonimbus wrote:
sarb wrote:
If the number x3458623y is divisible by 88, what is the value of x?

A. 1
B. 2
C. 3
D. 4
E. 5



to be divisible by 11:

3+5+6+3=2+y+8+4+x
3=x+y

x y
3 0 - not correct (not divisible by 4)
0 3 - not correct (not divisible by 2)
2 1 - not correct (not divisible by 2)
1 2 - correct (divisible by 4) - (...232) - is divisible by 4



Did in the same way, however considered last three digits 23y for divisibility check with 8
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32830
Own Kudos [?]: 827 [0]
Given Kudos: 0
Send PM
Re: If the number x3458623y is divisible by 88, what is the [#permalink] New post   13 Feb 2023, 06:46
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
gmatclubot
Re: If the number x3458623y is divisible by 88, what is the [#permalink]
13 Feb 2023, 06:46
Moderators:
Bunuel
Math Expert
93081 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions