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What is the greatest integer factor of x if both x and y are integers?

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What is the greatest integer factor of x if both x and y are integers?  [#permalink]

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New post 31 Jul 2018, 21:02
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

57% (01:31) correct 43% (01:31) wrong based on 128 sessions

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What is the greatest integer factor of x if both x and y are integers?

(1) The least common multiple of x and y is 12

(2) The greatest common factor of x and y is 6

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Re: What is the greatest integer factor of x if both x and y are integers?  [#permalink]

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New post 31 Jul 2018, 21:38
2
1
What is the greatest integer factor of x if both x and y are integers?

Whenever x and y are interchangeable, specific values of x and y in most cases cannot be found
What will be greatest integer factor of x? - it will be x itself.
so we are looking for value of x

(1) The least common multiple of x and y is 12
so x and y can be 3 and 4, so greatest factor of x is 3
x and y can be 4 and 3, so greatest factor of x is 4
they can also be (12,1) or (4,6) or (3 and 12) and so on
insuff

(2) The greatest common factor of x and y is 6
again various values possible
x=12, y = 6........factor 12
x=6,y=12....factor 6
insuff

combined..
x=12 and y = 6
and x=6 and y =12
insuff

E
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: What is the greatest integer factor of x if both x and y are integers?  [#permalink]

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New post 31 Jul 2018, 22:36
chetan2u wrote:
What is the greatest integer factor of x if both x and y are integers?

Whenever x and y are interchangeable, specific values of x and y in most cases cannot be found
What will be greatest integer factor of x? - it will be x itself.
so we are looking for value of x

(1) The least common multiple of x and y is 12
so x and y can be 3 and 4, so greatest factor of x is 3
x and y can be 4 and 3, so greatest factor of x is 4
they can also be (12,1) or (4,6) or (3 and 12) and so on
insuff

(2) The greatest common factor of x and y is 6
again various values possible
x=12, y = 6........factor 12
x=6,y=12....factor 6
insuff

combined..
x=12 and y = 6
and x=6 and y =12
insuff

E


Sir,
Can you elaborate your below statement abit more wrt to the question
"Whenever x and y are interchangeable, specific values of x and y in most cases cannot be found"
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Re: What is the greatest integer factor of x if both x and y are integers?  [#permalink]

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New post 02 Aug 2018, 10:14
Veritas official Solution
In this question, you are asked for the greatest integer factor of x
- the greatest integer that will divide evenly into x
- given that x
and y
are integers.

Statement (1) gives you that the least common multiple of x
and y
is 12. Remember that you can find the least common multiple one of two ways - either by listing out multiples of both numbers until you find a match or by combining the prime factorizations of both numbers. Since you don't have any values for x
or y
, listing out multiples is going to be impractical, so your next step should be to find the prime factorization of 12.

12 can be rewritten as (4)(3)
, or (22)(3)
.

However, notice that x
could be almost any combination of these numbers based on what you know so far -- it could be 12, 3, 2, or 4 -- and because of that it could have multiple greatest integer factors. Statement (1) is not sufficient. Eliminate (A) and (D).

Statement (2) gives you that the greatest common factor of x
and y
is 6. Remember that the greatest common factor is going to be the largest number that divides into both x
and y
respectively. However, that means that - as long as x
is a multiple of 6, that x
could be anything. Again, by itself statement (2) is insufficient. Eliminate (B).

Taken together, you know that x
must be a multiple of 6 between 6 and 12. However, since x
could be 12, there is no way of determining the value of x
- and therefore no way of determining the largest factor of x
. The statements are therefore insufficient even when taken together and answer choice (E) is correct.
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Re: What is the greatest integer factor of x if both x and y are integers?  [#permalink]

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New post 16 Nov 2018, 04:25
I don't understand the answers with this one.

It says he least common multiple of x and y is 12. Therefore potential values for X and Y are;
1+12
12+1
6+2
2+6
4+3
3+4

The greatest common factor of x and y is 6
6+12
12+6

Am I missing something here? The pairing of y and x being 6 and 12 is the only possibility for the 2nd statement but this is not an option in the first statement.
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Re: What is the greatest integer factor of x if both x and y are integers? &nbs [#permalink] 16 Nov 2018, 04:25
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