Join us for MBA Spotlight – The Top 20 MBA Fair      Schedule of Events | Register

It is currently 04 Jun 2020, 13:21

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

A positive integer n = 345xyz has six digits. What is the maximum poss

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

Hide Tags

Find Similar Topics 
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 9022
GMAT 1: 760 Q51 V42
GPA: 3.82
A positive integer n = 345xyz has six digits. What is the maximum poss  [#permalink]

Show Tags

New post 13 Sep 2019, 07:18
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

74% (01:25) correct 26% (01:30) wrong based on 82 sessions

HideShow timer Statistics

[GMAT math practice question]

A positive integer n = 345xyz has six digits. What is the maximum possible value of n, if n is divisible by 3, 4 and 5?

A. 345960
B. 345970
C. 345980
D. 345985
E. 345990

_________________
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.
"Only $79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
CEO
CEO
User avatar
V
Joined: 03 Jun 2019
Posts: 2935
Location: India
GMAT 1: 690 Q50 V34
WE: Engineering (Transportation)
Premium Member Reviews Badge CAT Tests
Re: A positive integer n = 345xyz has six digits. What is the maximum poss  [#permalink]

Show Tags

New post 13 Sep 2019, 07:37
MathRevolution wrote:
[GMAT math practice question]

A positive integer n = 345xyz has six digits. What is the maximum possible value of n, if n is divisible by 3, 4 and 5?

A. 345960
B. 345970
C. 345980
D. 345985
E. 345990


Divisibility by 3:
A & E remaining

Divisibility by 4:
A remaining

A is divisible by 5

IMO A

Posted from my mobile device
_________________
Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 11 Sep 2015
Posts: 4887
Location: Canada
GMAT 1: 770 Q49 V46
Re: A positive integer n = 345xyz has six digits. What is the maximum poss  [#permalink]

Show Tags

New post 13 Sep 2019, 07:53
Top Contributor
MathRevolution wrote:
[GMAT math practice question]

A positive integer n = 345xyz has six digits. What is the maximum possible value of n, if n is divisible by 3, 4 and 5?

A. 345960
B. 345970
C. 345980
D. 345985
E. 345990


Key concepts:
A number is divisible by 3 if the sum of its digits is divisible by 3
A number is divisible by 4 if the number created by the last two digits is divisible by 4
A number is divisible by 5 if the units digit is 5 or 0


A quick glance tells us that all 5 numbers are divisible by 5
Now check divisibility by 4

Start with E, the biggest answer choice.
E) Since 90 (the last 2 digits) is not divisible by 4, we know that 345990 is not divisible by 4. ELIMINATE E.
D) Since 85 (the last 2 digits) is not divisible by 4, we know that 345985 is not divisible by 4. ELIMINATE D.
C) 80 (the last 2 digits) IS divisible by 4, so 345980 IS divisible by 4

Let's stay with C.
Is 345980 divisible by 3?
3+4+5+9+8+0 = 29
Since 29 is NOT divisible by 3, we know that 345980 is NOT divisible by 3
ELIMINATE C.

B. 345970
Since 70 (the last 2 digits) is not divisible by 4, we know that 345970 is not divisible by 4
ELIMINATE B.

By the process of elimination, the correct answer is A

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 18 Aug 2017
Posts: 6314
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Reviews Badge CAT Tests
Re: A positive integer n = 345xyz has six digits. What is the maximum poss  [#permalink]

Show Tags

New post 13 Sep 2019, 07:55
MathRevolution wrote:
[GMAT math practice question]

A positive integer n = 345xyz has six digits. What is the maximum possible value of n, if n is divisible by 3, 4 and 5?

A. 345960
B. 345970
C. 345980
D. 345985
E. 345990


n = 345xyz has six digits and to be divisible by 3,4,5 the no must be factor of 60 or say all three no
starting option A; 345960

for 3 ; sum of no should be divisble by3 ; i.e 27 so YES
for divisibility by 4 ; 345960 should twice divisible by 2; YES
yes for 5 since last digit is 0
IMO A ; is sufficient
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 9022
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: A positive integer n = 345xyz has six digits. What is the maximum poss  [#permalink]

Show Tags

New post 15 Sep 2019, 18:07
=>

If \(345xyz\) is divisible by \(3, 3+4+5+x+y+z\) is divisible by \(3\), and \(x+y+z\) is divisible by \(3\).
If \(345xyz\) is divisible by \(4\), the last two digits \(yz\) must form a \(2\)-digit number that is divisible by \(4\). So, \(10y+z\) is divisible by \(4.\)
If \(345xyz\) is divisible by \(5, z\) must be \(0\) or \(5.\)

In order for \(10y + z\) to be divisible by \(4\), we must have \(z = 0.\) The possible values of \(y\) are \(0, 2, 4, 6\) and \(8\).
If \(y=0\) and \(z=0\), then the maximum value of \(x\) is \(9,\) and \(345xyz\) is \(345900.\)
If \(y=2\) and \(z=0\), then the maximum value of \(x\) is \(7\), and \(345xyz\) is \(345720.\)
If \(y=4\) and \(z=0\), then the maximum value of \(x\) is \(8\), and \(345xyz\) is \(345840.\)
If \(y=6\) and \(z=0\), then the maximum value of \(x\) is \(9\), and \(345xyz\) is \(345960.\)
If \(y=8\) and \(z=0\), then the maximum value of \(x\) is \(7\), and \(345xyz\) is \(345780.\)

The maximum value of \(345xyz\) is \(345960.\)

Therefore, A is the answer.
Answer: A
_________________
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.
"Only $79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 10654
Location: United States (CA)
Re: A positive integer n = 345xyz has six digits. What is the maximum poss  [#permalink]

Show Tags

New post 01 Apr 2020, 14:06
MathRevolution wrote:
[GMAT math practice question]

A positive integer n = 345xyz has six digits. What is the maximum possible value of n, if n is divisible by 3, 4 and 5?

A. 345960
B. 345970
C. 345980
D. 345985
E. 345990


Since n is divisible by 5, the units digit must be 0 or 5. However, since n is also divisible by 4, it must be even, and thus the units digit must be 0. That is, z = 0. Finally, since n is divisible by 3, the sum of the digits of n must be a multiple of 3. Since 3 + 4 + 5 + 0 = 9, which is already a multiple of 3, we need the sum of x and y to be a multiple of 3 also. The largest such number (in our given choices) for n is 345990. However, recall that if a number is divisible by 4, the last two digits of the number has to be divisible by 4 also. So n can’t be 345990 since 90 is not divisible by 4. The next number that fits the criteria (i.e., the last digit of the number is 0 and the sum of the digits is a multiple of 3) is 345960. Since 60 is divisible by 4, we see that the maximum possible value of n is 345960.

Answer: A
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
202 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Intern
Intern
avatar
B
Joined: 06 Feb 2020
Posts: 26
CAT Tests
Re: A positive integer n = 345xyz has six digits. What is the maximum poss  [#permalink]

Show Tags

New post 02 Apr 2020, 03:56
Divisibility by 3 : sum of digits is divided by 3
Divisibility by 4 : last two digits are divided by 4
Divisibility by 5 : last digit is either 0 or 5

n = 345xyz

z = either 0 or 5 but odd number can't be divisible by 4, so z = 0.

possible combinations of yz = 00, 20, 40, 60, 80.

Now sum of digits 3+4+5+0 = 12 which is divisible by 3. Hence x+y should be divisible by 3.

Now going through the answer choices, choices B,D,E can be eliminated as last two digits are not divisible by 4. In choice C, x+y = 17 (not divisible by 3). In A, x+y = 15. Hence choice A.
GMAT Club Bot
Re: A positive integer n = 345xyz has six digits. What is the maximum poss   [#permalink] 02 Apr 2020, 03:56

A positive integer n = 345xyz has six digits. What is the maximum poss

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





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