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ds - multiple difficult

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ccassel: Master | Next Rank: 500 Posts; Posts: 118; Joined: Wed Mar 16, 2011 1:44 pmFollowed by: 2 members; Location: Canada; GMAT Score:530

by ccassel » Tue Apr 05, 2011 6:15 pm

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,

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Source: Beat The GMAT — Data Sufficiency | Tue Apr 05, 2011 6:15 pm

MAAJ: Master | Next Rank: 500 Posts; Posts: 243; Joined: Sun Jul 12, 2009 7:12 amFollowed by: 2 members; Location: Dominican Republic; Thanked: 31 times; GMAT Score:480

by MAAJ » Tue Apr 05, 2011 7:11 pm

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]

ccassel wrote: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,

Last edited by MAAJ on Tue Apr 05, 2011 7:31 pm, edited 1 time in total.

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Tue Apr 05, 2011 7:31 pm

ccassel wrote: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).

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manpsingh87: Master | Next Rank: 500 Posts; Posts: 436; Joined: Tue Feb 08, 2011 3:07 amFollowed by: 6 members; Thanked: 72 times

by manpsingh87 » Tue Apr 05, 2011 7:48 pm

ccassel wrote: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

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