It is currently 17 Feb 2018, 11:10

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

In the 6-digit integer 543, 2xy, x and y are chosen from the digits 0

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

Hide Tags

Expert Post
Math Revolution GMAT Instructor
User avatar
D
Joined: 16 Aug 2015
Posts: 4862
GPA: 3.82
In the 6-digit integer 543, 2xy, x and y are chosen from the digits 0 [#permalink]

Show Tags

New post 14 Jan 2018, 23:30
Expert's post
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

49% (01:37) correct 51% (01:40) wrong based on 37 sessions

HideShow timer Statistics

[GMAT math practice question]

In the 6-digit integer \(543, 2xy, x\) and \(y\) are chosen from the digits \(0, 2, 4, 6\) and \(8\). What is the probability that \(543, 2xy\) is divisible by \(8\)?

\(A. \frac{1}{5}\)
\(B. \frac{6}{25}\)
\(C. \frac{7}{25}\)
\(D. \frac{8}{25}\)
\(E. \frac{9}{25}\)
[Reveal] Spoiler: OA

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself
See our Youtube demo

BSchool Forum Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 2033
Location: India
GPA: 3.12
Premium Member CAT Tests
In the 6-digit integer 543, 2xy, x and y are chosen from the digits 0 [#permalink]

Show Tags

New post 15 Jan 2018, 00:53
MathRevolution wrote:
[GMAT math practice question]

In the 6-digit integer \(543, 2xy, x\) and \(y\) are chosen from the digits \(0, 2, 4, 6\) and \(8\). What is the probability that \(543, 2xy\) is divisible by \(8\)?

\(A. \frac{1}{5}\)
\(B. \frac{6}{25}\)
\(C. \frac{7}{25}\)
\(D. \frac{8}{25}\)
\(E. \frac{9}{25}\)



In order to solve the question, we must know the rule for divisibility of 8.
The rule is as follows: If the last 3 digits are divisible by 8, the number is divisible by 8.

Since the last 3 digits are 2xy we need to find out how many of the combinations are divisible by 8.

They are 200,208,224,240,248,264,280,288(8 options)
The denominator must be the total options possible: 5*5 = 25

Therefore, the probability that \(543, 2xy\) is divisible by \(8\) is \(\frac{8}{25}\)(Option D)
_________________

Stay hungry, Stay foolish

2017-2018 MBA Deadlines

Class of 2020: Rotman Thread | Schulich Thread
Class of 2019: Sauder Thread

1 KUDOS received
Manager
Manager
User avatar
S
Joined: 20 Feb 2017
Posts: 91
Location: United States
Premium Member CAT Tests
Re: In the 6-digit integer 543, 2xy, x and y are chosen from the digits 0 [#permalink]

Show Tags

New post 15 Jan 2018, 10:07
1
This post received
KUDOS
MathRevolution wrote:
[GMAT math practice question]

In the 6-digit integer \(543, 2xy, x\) and \(y\) are chosen from the digits \(0, 2, 4, 6\) and \(8\). What is the probability that \(543, 2xy\) is divisible by \(8\)?

\(A. \frac{1}{5}\)
\(B. \frac{6}{25}\)
\(C. \frac{7}{25}\)
\(D. \frac{8}{25}\)
\(E. \frac{9}{25}\)


Total possible number - xy -> 5X5 = 25

In given question, we have 2xy as 200 is divisible by 8, we just need to worry about xy. (2xy = 200 + xy)

So combination with 0,2,4,6,8 divisible by 8 -> 00,08,24,40,48,64,80,88
_________________

*****************************************************************
Kudos are always welcome.

Expert Post
Math Revolution GMAT Instructor
User avatar
D
Joined: 16 Aug 2015
Posts: 4862
GPA: 3.82
Re: In the 6-digit integer 543, 2xy, x and y are chosen from the digits 0 [#permalink]

Show Tags

New post 17 Jan 2018, 00:05
=>

An integer with three or more digits is divisible by 8 if and only if its last three digits from a number that is divisible by \(8\).

The values of \(2xy\) that are divisible by \(8\) are \(200, 208, 224, 240, 248, 264, 280\), and \(288\).
The total number of 6-digit integers of the form \(543,2xy\) is equal to the number of ways of choosing two digits from \(0, 2, 4, 6\) and \(8\), which is \(5*5 = 25.\)
Thus, the probability that \(543,2xy\)is divisible by \(8\) is \(\frac{8}{25}\)

Therefore, the answer is D.
Answer: D
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself
See our Youtube demo

Re: In the 6-digit integer 543, 2xy, x and y are chosen from the digits 0   [#permalink] 17 Jan 2018, 00:05
Display posts from previous: Sort by

In the 6-digit integer 543, 2xy, x and y are chosen from the digits 0

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


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.