Higer Difficulty, PS on Number Properties

[bretania]

I don't really understand this problem. I'm not sure if there is a missing info on the question but here it is. If you guys know how to do this, please enlighten the rest of us:

The "connection" between any two positive integers x and y is the ratio of the smallest common multiple of x and y. The positive integer w is less than 20 and the connection between w and 6 is equal to 1/1. How many possible values of w are there ?


A.7
B.8
C.9
D.10
E.11

[clock60]

Originally Posted by bretania

I don't really understand this problem. I'm not sure if there is a missing info on the question but here it is. If you guys know how to do this, please enlighten the rest of us:

The "connection" between any two positive integers x and y is the ratio of the smallest common multiple of x and y. The positive integer w is less than 20 and the connection between w and 6 is equal to 1/1. How many possible values of w are there ?


A.7
B.8
C.9
D.10
E.11

it seems that the question is missing something. ratio is commonly two numbers but here i see smallest common multiple of x and y (one number) and what?
p.s may be i am wrong can you check the condition

[bretania]

Clock60, I also think that their is sommetinig amiss in this problem.
But that's all the info I have. Plus, the answer given here is 11. The solution went along the line saying that since the ratio between W and 6 is 1/1, it follows that we should look for values of W less than 20 that will not have a common factor with 6. Hence the possible values for w are: 1, 5, 7, 11, 13, 17, 19. Hence, according to the solution, the correct choice is E (7).

I think cocept-wise, if we understand that this is about LCM and GCF, I'm hoping that the actual GMAT question will be much clearer.

[clock60]

it seems to me that i understand the missing part of the problem. It should be written that connection between two numbers is the ratio between product of its numbers (that is missing in the problem) and LCM with that we can solve upper problem
connection between w and 6 is 1 it means that 6*w/LCM=1/1 and it follows that 6*w=LCM of (6,w)
when the product of two numbers equals its LCM it means that they have no
common factors except 1. immagine for example 6 and 7 . 6=1*2*3. 7=1*7.
LCM (6,7) is 42 and the product of 6*7=42 . connection =1
in above problem 6=2*3 and w <20 we must find numbers less than 20 that have no 2 and 3.
let us count 19 ,17, 13, 11,7,5,and1. any other number have common factors with 6. let it be 15 for example 6*15=90 but LCM of (6,15) is 30 divide 90/30=3 but according to the problem it must 1 so 15 does not fit
I hope this helps

[bretania]

Jeez... thanks! Again, this is a very lucid explanation.
I tried searching the net for "connection" but didn't find one right away so I gave up. Now this definition of connection exactly comports well with the problem. Thanks again!

[clock60]

do not seach what does it mean connection. it does not exist exept in the problem. There is no math term like that. I saw the problem like that it seems to me that in kaplan

[sonikamadala]

yes that correct queston is

The "connection" between any two positive integers x and y is the ratio of the smallest common multiple of x and y to the product of x and y . The positive integer w is less than 20 and the connection between w and 6 is equal to 1/1. How many possible values of w are there ?

and the IMO answer is A. That is 7.

If w is even number, then the LCm will be definitely < the product of 6 and w. So t will not yields 1/1 ratio. so we can conlude that definitely W is an odd number.

there are ten odd number < 20. out of that 3,9 and 15 are either factor or multiple of 6. Again the LCM will be definitely < the product of 6 and w. So t will not yields 1/1 ratio.

remaining numbers are 1,5,7,11,13,17,19

[rb999]

what is this question asking?

[rb999]

should it be factor, not multiple...