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

It is currently 21 Jul 2019, 20:43

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

Which of the following is the greatest possible common divisor of two

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56307
Which of the following is the greatest possible common divisor of two  [#permalink]

Show Tags

New post 12 Jul 2016, 04:37
2
7
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

71% (01:19) correct 29% (01:30) wrong based on 145 sessions

HideShow timer Statistics


Retired Moderator
avatar
G
Joined: 26 Nov 2012
Posts: 586
Which of the following is the greatest possible common divisor of two  [#permalink]

Show Tags

New post 12 Jul 2016, 05:48
Bunuel wrote:
Which of the following is the greatest possible common divisor of two different positive integers, both smaller than 124?

A. 123.
B. 122.
C. 63.
D. 62.
E. 61.




Given to find the greatest possible common divisor for two different positive number.

Let X be GCD and A and B are two different number.

We need to see the XA and XB has to be less than 124.

Now from options,

if we consider 62 * 2 = 124, which is equal to 124, we need to consider some number lesser than 124.

Consider 61 * 2 = 122 and 61 * 1 = 61 ( Both these numbers are lesser than 124 as requested ).

So GCD will be 61.

IMO E is correct option.

For clarity purpose let's check all the options.

A. 123 = ( 123 * 1 ) ( 123 * 0) can't be this. ( value = GCD * some number) . Apart from 0 and 1 , we'll get more result which is > 124 ( for ex 123 * 2 = 246 )
B. 122 = ( 122 * 1 ) ( 122 * 0 )
C. 63 = ( 63 * 1 ) ( 63 * 0 )

OA please...will correct if I missed anything.
Intern
Intern
avatar
Joined: 05 Sep 2015
Posts: 43
Re: Which of the following is the greatest possible common divisor of two  [#permalink]

Show Tags

New post 12 Jul 2016, 06:06
e.
61,122 because rest all are greater than 124 for their second multiple only.
Current Student
User avatar
D
Joined: 12 Aug 2015
Posts: 2609
Schools: Boston U '20 (M)
GRE 1: Q169 V154
GMAT ToolKit User
Re: Which of the following is the greatest possible common divisor of two  [#permalink]

Show Tags

New post 29 Apr 2017, 05:46
Retired Moderator
avatar
P
Joined: 22 Aug 2013
Posts: 1435
Location: India
Re: Which of the following is the greatest possible common divisor of two  [#permalink]

Show Tags

New post 20 May 2017, 12:00
1
1
GCD of two different integers is a factor of both of them, first of all. So whatever two integers we choose less than 124 - both have to be multiples of that GCD.
Lets go by options here.

A) 123.. but next multiple of 123 will be >124. So not possible
B) 122. same as above. not possible
C) 63. Again same. next multiple of 63 is 126
D) 62. Again next multiple of 62 is 124. But both numbers must be less than 124

This leaves only option E, 61 as the correct answer
(61 and 122 have a GCD of 61)
Intern
Intern
avatar
B
Joined: 30 Dec 2018
Posts: 4
Re: Which of the following is the greatest possible common divisor of two  [#permalink]

Show Tags

New post 05 Feb 2019, 11:01
chetan2u: i am unable to understand the reasoning behing it. Why it can't be 123?
Could you please help me here?

Regards.
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7763
Re: Which of the following is the greatest possible common divisor of two  [#permalink]

Show Tags

New post 05 Feb 2019, 11:28
1
kaulmeankit08 wrote:
chetan2u: i am unable to understand the reasoning behing it. Why it can't be 123?
Could you please help me here?

Regards.



Our answer has to be greatest possible common divisor of TWO numbers less than 124.
Now if it is 123, then WHICH are the two numbers which can be divisible by 123. It us just 1, that is 123.
Similarly for 122..

So 122 and 61 are divisible by 61as 122 is 61*2..
_________________
Intern
Intern
avatar
B
Joined: 30 Dec 2018
Posts: 4
Re: Which of the following is the greatest possible common divisor of two  [#permalink]

Show Tags

New post 06 Feb 2019, 01:08
chetan2u wrote:
kaulmeankit08 wrote:
chetan2u: i am unable to understand the reasoning behing it. Why it can't be 123?
Could you please help me here?

Regards.



Our answer has to be greatest possible common divisor of TWO numbers less than 124.
Now if it is 123, then WHICH are the two numbers which can be divisible by 123. It us just 1, that is 123.
Similarly for 122..

So 122 and 61 are divisible by 61as 122 is 61*2..



Now I got it. thank you for putting it in simple terms :)
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6967
Location: United States (CA)
Re: Which of the following is the greatest possible common divisor of two  [#permalink]

Show Tags

New post 06 Feb 2019, 19:42
Bunuel wrote:
Which of the following is the greatest possible common divisor of two different positive integers, both smaller than 124?

A. 123.
B. 122.
C. 63.
D. 62.
E. 61.


Let x be the greatest possible common divisor of two distinct positive integers, each less than 124. To keep x as large as possible, we need to have the factors of the two integers besides x to be as small as possible. Thus, we need to take the two integers to be x and 2x. Now, since 2x is the greater of these two integers, we should let 2x to be the greatest even number less than 124, which is 122. Then, 2x = 122 and therefore, x = 61.

Answer: E
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 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.

GMAT Club Bot
Re: Which of the following is the greatest possible common divisor of two   [#permalink] 06 Feb 2019, 19:42
Display posts from previous: Sort by

Which of the following is the greatest possible common divisor of two

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





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