January 26, 2019 January 26, 2019 07:00 AM PST 09:00 AM PST Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions. January 27, 2019 January 27, 2019 07:00 AM PST 09:00 AM PST Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 25 Nov 2011
Posts: 179
Location: India
Concentration: Technology, General Management
GPA: 3.95
WE: Information Technology (Computer Software)

The “connection” between any two positive integers a and b
[#permalink]
Show Tags
29 Feb 2012, 08:24
Question Stats:
65% (02:48) correct 35% (02:48) wrong based on 433 sessions
HideShow timer Statistics
The “connection” between any two positive integers a and b is the ratio of the smallest common multiple of a and b to the product of a and b. For instance, the smallest common multiple of 8 and 12 is 24, and the product of 8 and 12 is 96, so the connection between 8 and 12 is 24/96 = 1/4 The positive integer y is less than 20 and the connection between y and 6 is equal to 1/1. How many possible values of y are there? A. 7 B. 8 C. 9 D. 10 E. 11
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
 Aravind Chembeti




Math Expert
Joined: 02 Sep 2009
Posts: 52431

Re: Problem related to LCM
[#permalink]
Show Tags
29 Feb 2012, 09:12
Chembeti wrote: The “connection” between any two positive integers a and b is the ratio of the smallest common multiple of a and b to the product of a and b. For instance, the smallest common multiple of 8 and 12 is 24, and the product of 8 and 12 is 96, so the connection between 8 and 12 is 24/96 = 1/4
The positive integer y is less than 20 and the connection between y and 6 is equal to 1/1. How many possible values of y are there?
A. 7 B. 8 C. 9 D. 10 E. 11 Since “connection” between y and 6 is 1/1 then LCM(6, y)=6y, which means that 6 and y are coprime (they do not share any common factor but 1), because if the had any common factor but 1 then LCM(6, y) would be less than 6y. So, we should check how many integers less than 20 are coprime with 6, which can be rephrased as how many integers less than 20 are not divisible by 2 or 3 (6=2*3). There are (182)/2+1=9 multiples of 2 in the range from 0 to 20, not inclusive; There are (183)/3+1=6 multiples of 3 in the range from 0 to 20, not inclusive; There are 3 multiples of 6 in the range from 0 to 20, not inclusive (6, 12, 18)  overlap of the above two sets; Total multiples of 2 or 6 in the range from 0 to 20, not inclusive is 9+63=12; Total integers in the range from 0 to 20, not inclusive is 19; Hence, there are total of 1912=7 numbers which have no common factor with 6 other than 1: 1, 5, 7, 11, 13, 17 and 19. Answer: A.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Intern
Joined: 09 Sep 2012
Posts: 28
Location: United States

Re: The “connection” between any two positive integers a and b
[#permalink]
Show Tags
21 Sep 2012, 09:54
Hi, Can you please explain what method have you used below:
There are (182)/2+1=9 multiples of 2 in the range from 0 to 20, not inclusive; There are (183)/3+1=6 multiples of 3 in the range from 0 to 20, not inclusive;
Thanks



Senior Manager
Joined: 06 Aug 2011
Posts: 336

Re: The “connection” between any two positive integers a and b
[#permalink]
Show Tags
22 Sep 2012, 02:10
I took apprx 3 to 3.5 min to solve this question.. i tried every posibility from 1 to 7 then i get at that point , what bunuel saying ...num should not b multiple of 2 and 3... 1,5,7,11,13,17,19... all primes less than 20 except 2 and 3.
_________________
Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !



Senior Manager
Joined: 15 Sep 2011
Posts: 323
Location: United States
WE: Corporate Finance (Manufacturing)

Re: The “connection” between any two positive integers a and b
[#permalink]
Show Tags
27 Jun 2015, 09:22
Bunuel wrote: Chembeti wrote: The “connection” between any two positive integers a and b is the ratio of the smallest common multiple of a and b to the product of a and b. For instance, the smallest common multiple of 8 and 12 is 24, and the product of 8 and 12 is 96, so the connection between 8 and 12 is 24/96 = 1/4
The positive integer y is less than 20 and the connection between y and 6 is equal to 1/1. How many possible values of y are there?
A. 7 B. 8 C. 9 D. 10 E. 11 Since “connection” between y and 6 is 1/1 then LCM(6, y)=6y, which means that 6 and y are coprime (they do not share any common factor but 1), because if the had any common factor but 1 then LCM(6, y) would be less than 6y. So, we should check how many integers less than 20 are coprime with 6, which can be rephrased as how many integers less than 20 are not divisible by 2 or 3 (6=2*3). There are (182)/2+1=9 multiples of 2 in the range from 0 to 20, not inclusive; There are (183)/3+1=6 multiples of 3 in the range from 0 to 20, not inclusive; There are 3 multiples of 6 in the range from 0 to 20, not inclusive (6, 12, 18)  overlap of the above two sets; Total multiples of 2 or 6 in the range from 0 to 20, not inclusive is 9+63=12; Total integers in the range from 0 to 20, not inclusive is 19; Hence, there are total of 1912=7 numbers which have no common factor with 6 other than 1: 1, 5, 7, 11, 13, 17 and 19. Answer: A. Hello, Could you or someone else elaborate what the value of counting noninclusive numbers is? After all, it seems if the you know that (6,y) are coprime, counting the number of primes excluding 2 or 3 would lead to the answer quicker.



Retired Moderator
Joined: 18 Sep 2014
Posts: 1112
Location: India

Re: The “connection” between any two positive integers a and b
[#permalink]
Show Tags
22 Dec 2015, 11:25
The “connection” between any two positive integers a and b is the ratio of
 the smallest common multiple of a and b ...........i.e., LCM(least common multiple)
 the product of a and b.
For instance, the smallest common multiple of 8 and 12 is 24, and the product of 8 and 12 is 96, so the connection between 8 and 12 is 24/96 = 1/4
The positive integer y is less than 20 and the connection between y and 6 is equal to 1/1. How many possible values of y are there?
the ratio is 1:1 i.,e., LCM and product are equal.
this can happen only when there is no common factor(other than 1) between y and 6.
since 6 has two factors 2 and 3.
y can have values as all those numbers which are not multiples of 2 and 3 and less than 20.
y={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19}
y={1,5,7,11,13,17,19}
so total 7 values are possible for y..................A is the answer.



Board of Directors
Joined: 17 Jul 2014
Posts: 2598
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

Re: The “connection” between any two positive integers a and b
[#permalink]
Show Tags
05 Feb 2016, 18:10
it can be 1/1 only if y is a prime number or 1, otherwise, it will be messed up. 3 won't work here, because LCM of 3 and 6 is 6, and 6/3*6 is not 1/1. thus, we are left with 1, 5, 7, 11, 13, 17, and 19. 7 options.



Current Student
Joined: 12 Aug 2015
Posts: 2626

Re: The “connection” between any two positive integers a and b
[#permalink]
Show Tags
14 Apr 2016, 01:53
Hey chetan2u can you look at my solution for this one=> Here connection = LCM / product = 1/HCF now Connection between Y and ^=1/1 so the HCF must be 1 so the values possible are => 1,5,7,11,13,17,19 So 7 values Hence A Am i missing something here ?
_________________
MBA Financing: INDIAN PUBLIC BANKS vs PRODIGY FINANCE! Getting into HOLLYWOOD with an MBA! The MOST AFFORDABLE MBA programs!STONECOLD's BRUTAL Mock Tests for GMATQuant(700+)AVERAGE GRE Scores At The Top Business Schools!



Math Expert
Joined: 02 Aug 2009
Posts: 7213

Re: The “connection” between any two positive integers a and b
[#permalink]
Show Tags
14 Apr 2016, 02:45
stonecold wrote: Hey chetan2u can you look at my solution for this one=> Here connection = LCM / product = 1/HCF now Connection between Y and ^=1/1 so the HCF must be 1 so the values possible are => 1,5,7,11,13,17,19 So 7 values Hence A Am i missing something here ? Hi, you are absolutely correct with the logic and concept behind this Q.. HCF * LCM = product of two numbers.. so IF 'connection' is 1, LCM/(LCM*HCF) is 1 or HCF = 1, as correctly pointed by you..so Actually we are looking for COPRIMES to 6.. factors of 6 are 2 and 3.. in first 19 digits 19/2 or 9 are multiples of 2.. 19/3 or 6 are multiple of 3, out of which 19/6 or 3 are already catered for in multiples of 2 above .. SO total = 1996+3 = 7
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



Intern
Joined: 21 Oct 2015
Posts: 46

Re: The “connection” between any two positive integers a and b
[#permalink]
Show Tags
14 Apr 2016, 04:34
Do you guys think that 6 would make a good trap answer here?
I just started this problem by factoring 6 = 2*3. With additional clue that Y should not have these two factors I went on to evaluate subsequent numbers <20 and ended up with 6 numbers. And then, I realized that I didn't count 1.



Current Student
Joined: 12 Aug 2015
Posts: 2626

Re: The “connection” between any two positive integers a and b
[#permalink]
Show Tags
14 Apr 2016, 06:59
HarisinghKhedar wrote: Do you guys think that 6 would make a good trap answer here?
I just started this problem by factoring 6 = 2*3. With additional clue that Y should not have these two factors I went on to evaluate subsequent numbers <20 and ended up with 6 numbers. And then, I realized that I didn't count 1. Maybe .. P.S => Never ever forget zero or 1 they are core to the gmat.. regards Stone Cold
_________________
MBA Financing: INDIAN PUBLIC BANKS vs PRODIGY FINANCE! Getting into HOLLYWOOD with an MBA! The MOST AFFORDABLE MBA programs!STONECOLD's BRUTAL Mock Tests for GMATQuant(700+)AVERAGE GRE Scores At The Top Business Schools!



Manager
Joined: 03 May 2014
Posts: 160
Location: India
WE: Sales (Mutual Funds and Brokerage)

Re: The “connection” between any two positive integers a and b
[#permalink]
Show Tags
07 Aug 2017, 21:36
Can you please elaborate on this concept and thanks in advance so Actually we are looking for COPRIMES to 6.. factors of 6 are 2 and 3.. in first 19 digits 19/2 or 9 are multiples of 2.. 19/3 or 6 are multiple of 3, out of which 19/6 or 3 are already catered for in multiples of 2 above .. SO total = 1996+3 = 7[/quote chetan2u wrote: stonecold wrote: Hey chetan2u can you look at my solution for this one=> Here connection = LCM / product = 1/HCF now Connection between Y and ^=1/1 so the HCF must be 1 so the values possible are => 1,5,7,11,13,17,19 So 7 values Hence A Am i missing something here ? Hi, you are absolutely correct with the logic and concept behind this Q.. HCF * LCM = product of two numbers.. so IF 'connection' is 1, LCM/(LCM*HCF) is 1 or HCF = 1, as correctly pointed by you..so Actually we are looking for COPRIMES to 6.. factors of 6 are 2 and 3.. in first 19 digits 19/2 or 9 are multiples of 2.. 19/3 or 6 are multiple of 3, out of which 19/6 or 3 are already catered for in multiples of 2 above .. SO total = 1996+3 = 7



Senior Manager
Status: love the club...
Joined: 24 Mar 2015
Posts: 273

The “connection” between any two positive integers a and b
[#permalink]
Show Tags
15 Mar 2018, 18:02
Chembeti wrote: The “connection” between any two positive integers a and b is the ratio of the smallest common multiple of a and b to the product of a and b. For instance, the smallest common multiple of 8 and 12 is 24, and the product of 8 and 12 is 96, so the connection between 8 and 12 is 24/96 = 1/4
The positive integer y is less than 20 and the connection between y and 6 is equal to 1/1. How many possible values of y are there?
A. 7 B. 8 C. 9 D. 10 E. 11 there are a total of 8 primes (2, 3 ,5 ,7, 11, 13, 17, 19) between 1 and 20 inclusive, and out of these 8 primes, y can take on 6 values, because y cannot be 2 or 3 so there exist 6 values plus 1 = 7 possible values of y thanks




The “connection” between any two positive integers a and b &nbs
[#permalink]
15 Mar 2018, 18:02






