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
A
a.) 7
b.) 8
c.) 9
d.) 10
e.) 11
A
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solution plz..
Source: Beat The GMAT — Problem Solving |
The only way I can come up with 7 is if you take the number of even integers from 6-19 (since Y is less than 20), but I have never seen a word problem use the word connection, so I have no clue what that means.
if that's the case how does Y not equal 6, and that would mean there is only one possible value for Y.brick2009 wrote:that was a kaplan CD test...
i figured..connection = relation of y/6 = 1/1
The connection was explained and then there were two subsequent questions. It stated:
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.
If someone can please now further explain the original problem in this post now that the connection is clear, I would really appreciate it!
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.
If someone can please now further explain the original problem in this post now that the connection is clear, I would really appreciate it!
-
stephen@knewton
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- Posts: 22
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I haven't seen the original source on this one, but it sounds a lot like an "invented symbol function" problem, which is that often-confusing question type where the GMAT will give you something like the following:
if A
B = some function, what is 5 3 ?
You guys have probably seen these. They can be intimidating, without doubt. But just be methodical:
So for this problem, A B = LCM {A, B} / AB, and we are told that Y 6 = 1. In other words, the LCM and product of Y and 6 are the same value! THIS realization is the key to the problem, and leads us to a very important property of multiples, which is that Y and 6 do not share any prime factors! In other words, the only factor that they DO have in common is 1 (which is, of course, not prime).
As an aside, if any two integers DO share prime factors, their LCM is always going to be smaller than their product ... the LCM will be "sharing" at least one prime factor, and thus will not need to use all of the primes that are "contained" in both. Hope that makes sense.
The prime factors of 6 are 2 and 3, so Y must be less than 20, and not have 2 as a factor (in other words, it's odd) and not have 3 as a factor. It turns out that our possible values for Y are: 1, 5, 7, 11, 13, 17 and 19. Thus, the answer is A! Notice that we've had to remember that 1, although it's not a prime factor, is still a possible value for Y (the LCM and product of 1 and 6 are both 6). It turns out, because of the numbers we're working with, that our possible values are all primes greater than 3 and less than 20 ... but we can attack any "invented function" problem the same way.
Hope this helps!
if A
B = some function, what is 5 3 ?You guys have probably seen these. They can be intimidating, without doubt. But just be methodical:
So for this problem, A
B = LCM {A, B} / AB, and we are told that Y 6 = 1. In other words, the LCM and product of Y and 6 are the same value! THIS realization is the key to the problem, and leads us to a very important property of multiples, which is that Y and 6 do not share any prime factors! In other words, the only factor that they DO have in common is 1 (which is, of course, not prime).As an aside, if any two integers DO share prime factors, their LCM is always going to be smaller than their product ... the LCM will be "sharing" at least one prime factor, and thus will not need to use all of the primes that are "contained" in both. Hope that makes sense.
The prime factors of 6 are 2 and 3, so Y must be less than 20, and not have 2 as a factor (in other words, it's odd) and not have 3 as a factor. It turns out that our possible values for Y are: 1, 5, 7, 11, 13, 17 and 19. Thus, the answer is A! Notice that we've had to remember that 1, although it's not a prime factor, is still a possible value for Y (the LCM and product of 1 and 6 are both 6). It turns out, because of the numbers we're working with, that our possible values are all primes greater than 3 and less than 20 ... but we can attack any "invented function" problem the same way.
Hope this helps!
Stephen
GMAT Instructor
Knewton Inc.
GMAT Instructor
Knewton Inc.
