ds - multiple difficult

[ccassel]

Hi,

How would you explain the answer to this question?

If positive integer x is a multiple of 6 and positive integer y is a multiple of 14, is xy a multiple of 105?

(1) x is a multiple of 9
(2) y is a multiple of 25

Cheers,

[MAAJ]

If positive integer x is a multiple of 6 and positive integer y is a multiple of 14, is xy a multiple of 105?

105 -> 3,5,7

x -> 2,3...?
y -> 2,7...?
SO xy -> 2,2,3,7...?

x or y has 5 in its prime factors?

(1) x is a multiple of 9
If x -> 2,3...? and x -> 3,3...?
THEN x -> 2,3,3...?
Not sufficient

(2) y is a multiple of 25
y -> 2,7...? and y -> 5,5...?
THEN y -> 2,5,5,7...?

If we combine x -> 2,3...? with y -> 2,5,5,7...?
We get xy -> 2,2,3,5,5,7...? which contains 3,5,7...? So xy is divisible by 105

IMHO [spoiler](B)[/spoiler]

Hi,

How would you explain the answer to this question?

If positive integer x is a multiple of 6 and positive integer y is a multiple of 14, is xy a multiple of 105?

(1) x is a multiple of 9
(2) y is a multiple of 25

Cheers,

[Anurag@Gurome]

Hi,

How would you explain the answer to this question?

If positive integer x is a multiple of 6 and positive integer y is a multiple of 14, is xy a multiple of 105?

(1) x is a multiple of 9
(2) y is a multiple of 25

Cheers,

Solution:
Let us first consider (1) alone.
Take some examples.
Let x = 18 and y = 70.
So, x is a multiple of 6,9 and y is a multiple of 14.
Now, xy = 1260 = 105 * 12 which is a multiple of 105.
Next let x = 18 and y = 28.
So, x is a multiple of 6,9 and y is a multiple of 14.
But xy = 18 * 28 = 504 is not a multiple of 105.
So, we cannot say anything definite from (1) alone.
Or, (1) alone is not sufficient to answer the question.
Next consider (2) alone.
So, what we have is that x is a multiple of 6 and y is a multiple of 14,25.
So xy is a multiple of 3, 5 and 7.
Since 3, 5 and 7 have no factor in common apart from 1, we can safely assume that
xy is a multiple of 3*5*7 = 105.
Or, (2) alone is sufficient to answer the question.

The correct answer is (B).

[manpsingh87]

Hi,

How would you explain the answer to this question?

If positive integer x is a multiple of 6 and positive integer y is a multiple of 14, is xy a multiple of 105?

(1) x is a multiple of 9
(2) y is a multiple of 25

Cheers,

x=6k; also y=14m; (k and m are integers)
105=3*5*7;
xy=84k*m;
now for xy to become multiple of 105 we must have either x or y as a multiple of 5.
1)not sufficient because x will be of the type 18t(i.e. multiple of both 6 and t);
therefore xy=18t*14m; here t and m are integers..!!
xy=252p here p is an intger.. now if p=1, then xy=252, if p=5 xy=1260; which is a multiple of 5 as here different answer are possible for different values of p, hence 1 is not sufficient to answer the question.

2)as y is also a multiple of 25 therefore y will be of the type 350t; and xy will be of the type 1050m, where m is an intger...!!!
now xy now is a multiple of 105, hence 2 alone is sufficient to answer the question..!!!!

hence B