The "connection" between any two positive integers

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 am; Followed by:2 members

The "connection" between any two positive integers

by Gmat_mission » Sat Mar 24, 2018 4:10 am

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). What is the connection between 12 and 21?

a) 1/9
b) 1/7
c) 1/3
d) 4/7
e) 1/1

[spoiler]OA=C[/spoiler].

I'm really confused here. Experts, could you help me, please? Thanks in advanced.

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Source: Beat The GMAT — Problem Solving | Sat Mar 24, 2018 4:10 am

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » Sat Mar 24, 2018 10:29 am

Hi Gmat_mission,

We're told that 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). We're asked for the connection between 12 and 21. This is an example of a "Symbolism" question - you're told what a 'symbol' means, then you're asked to perform a calculation using it.

Here, we have to find the least common multiple of 12 and 21 and then find the product of 12 and 21...

To find the least common multiple, you can either list out 'multiples' of both values until you find the least common multiple OR you can use the prime factors of the two numbers....
12 = (2)(2)(3)
21 = (3)(7)
The least common multiple has to account for all of the prime factors in those two numbers (with any 'shared' factor counted just once). Here, the '3' shows up in both 12 and 21, so we need just one 3...
LCM of 12 and 21 = (2)(2)(3)(7) = 84

Based on the answers, we know that we're going to end up with a fraction that has been 'reduced.' Instead of multiplying 12 and 21 at this point, we can 'simplify' the final ratio...

(84)/(12)(21) =
(4)/(12) =
1/3

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Fri May 24, 2019 3:04 pm

Gmat_mission 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). What is the connection between 12 and 21?

a) 1/9
b) 1/7
c) 1/3
d) 4/7
e) 1/1

[spoiler]OA=C[/spoiler].

The smallest common multiple of 12 and 21 is 3 x 4 x 7 = 84. The product of 12 and 21 is 12 x 21 = 252. Therefore, the connection between 12 and 21 is 84/252 = 1/3.

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]