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

It is currently 20 Nov 2018, 17:55

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 in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • All GMAT Club Tests are Free and open on November 22nd in celebration of Thanksgiving Day!

     November 22, 2018

     November 22, 2018

     10:00 PM PST

     11:00 PM PST

    Mark your calendars - All GMAT Club Tests are free and open November 22nd to celebrate Thanksgiving Day! Access will be available from 0:01 AM to 11:59 PM, Pacific Time (USA)
  • Free lesson on number properties

     November 23, 2018

     November 23, 2018

     10:00 PM PST

     11:00 PM PST

    Practice the one most important Quant section - Integer properties, and rapidly improve your skills.

If the positive integer x is a multiple of 4 and the

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

Hide Tags

Manager
Manager
User avatar
G
Joined: 10 Apr 2018
Posts: 181
If the positive integer x is a multiple of 4 and the  [#permalink]

Show Tags

New post Updated on: 07 Sep 2018, 15:32
Hi,

Well after doing a couple of questions in this topic i have drawn some conlusions that can come handy for this topic

1. if A is divisible by B, and B is divisible by C , then \(\frac{A}{C}= integer\) or we say A is divisible by C.
2. if A , B are natural nos then such that A is divisible by B , and B is divisible by A then A=B
3. if A is divisible by d, and B is divisible by d , then \(\frac{A+B}{d}= integer\) , \(\frac{A- B}{d}= integer\), \(\frac{ B+A}{d}= integer\),\(\frac{ B-A}{d}= integer\).
4. if A is divisible by C, and B is divisible by D , then \(\frac{AB}{CD}= integer\)
5. \(\frac{a^n}{a+1}\) leaves Remainder = a if n is odd, else 1 if n is even
6. Always \(\frac{(a+1)^n}{a}\) remainder always 1.

So in this question we use the property 4. and we can say that \(\frac{xy}{24} =integer\)

So xy must have 8, 12 as its mulitples


Probus

Originally posted by Probus on 26 Aug 2018, 22:42.
Last edited by Probus on 07 Sep 2018, 15:32, edited 1 time in total.
Manager
Manager
avatar
B
Joined: 29 May 2017
Posts: 107
Location: Pakistan
Concentration: Social Entrepreneurship, Sustainability
Re: If the positive integer x is a multiple of 4 and the  [#permalink]

Show Tags

New post 07 Sep 2018, 15:24
Bunuel wrote:
SOLUTION

If the positive integer x is a multiple of 4 and the positive integer y is a multiple of 6, then xy must be a multiple of which of the following?

I. 8
II. 12
III. 18

(A) II only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III

First of all notice that we are asked: "\(xy\) MUST be a multiple of which of the following", not COULD be a multiple.

\(x\) is a multiple of 4 --> \(x=4m\), for some positive multiple \(m\), so \(x\) could be: 4, 8, 12, ...
\(y\) is a multiple of 6 --> \(y=6n\), for some positive multiple \(n\), so \(y\) could be: 6, 12, 18, ...

So, \(xy=(4m)*(6n)=24mn\), hence \(xy\) is in any case a multiple of 24, which means it must be a multiple of 8 and 12, but not necessarily of 18. For example the least value of \(x\) is 4 and the least value of \(y\) is 6, so the least value of \(xy\) is 24, which is a multiple of both 8 and 12, but not 18.

Answer: B.

Hope it's clear.


Hi....a silly question:
"if 6 is a multiple of a number then 12 is also a multiple of that number" True or false?

x: 6n--> 6,12,18,24
since 18 is not a multiple of 12, i say false. but the book answer is true.

can you please explain?
(this question is from the O-levels math book)
GMAT Club Bot
Re: If the positive integer x is a multiple of 4 and the &nbs [#permalink] 07 Sep 2018, 15:24

Go to page   Previous    1   2   [ 22 posts ] 

Display posts from previous: Sort by

If the positive integer x is a multiple of 4 and the

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.