Divisible by 15 -- Please help

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rjanardhanan: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Sun Dec 21, 2008 7:19 pm

by rjanardhanan » Tue Feb 14, 2012 5:58 am

Is X divisible by 15?

1. When X is divided by 10, the result is an integer.
2. X^2 is a multiple of 30.

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Source: Beat The GMAT — Data Sufficiency | Tue Feb 14, 2012 5:58 am

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by Jim@StratusPrep » Tue Feb 14, 2012 6:17 am

Six ally, does x have a factor of 5 and 3?

1). Has a factor of 2 and 5. Insufficient

2). Has a factor of 2,3, and 5. (if x^2 has these factors so does x). Sufficient

B

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mankey: Legendary Member; Posts: 627; Joined: Thu Jun 23, 2011 9:12 amFollowed by: 1 member; Thanked: 4 times

by mankey » Thu Feb 16, 2012 10:17 am

IMO: C. Please check.

Regards.

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amanne: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Tue Feb 14, 2012 1:48 am

by amanne » Thu Feb 16, 2012 9:52 pm

Inorder for X to be divisible by 15, X must have 5 and 3 as factors.

1) X has only 2 and 5 as factors. Insufficient

2) X^2 has only 2,3 and 5 as factors. But X^2 should have at least 2 three's and 2 five's for X to be divisible by 15. Insufficient

Both statements combined are still insufficient.

Answer E.

Can anyone confirm this explanation.

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[email protected]: Legendary Member; Posts: 934; Joined: Tue Nov 09, 2010 5:16 amFollowed by: 14 members; Location: AAMCHI MUMBAI LOCAL; Thanked: 63 times

by [email protected] » Thu Feb 16, 2012 11:23 pm

Is X divisible by 15?

1. When X is divided by 10, the result is an integer.
2. X^2 is a multiple of 30.

Exactly the answer is turning out to be C. Not B.

There are many numbers whose square must be the multiple of 30 but remember their squares are the multiple of 30 X itself...

When both the statements are combined, the answer turns out to be good...

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Fri Feb 17, 2012 12:27 am

rjanardhanan wrote:Is X divisible by 15?

1. When X is divided by 10, the result is an integer.
2. X^2 is a multiple of 30.

I. This means that X is divisible by 10, hence not necessarily divisible by 15. Insufficient

II. Once X^2 is a multiple of 30, X is a multiple of 30, and hence a multiple of 15 as well. Sufficient

[spoiler]Take B[/spoiler]

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knight247: Legendary Member; Posts: 504; Joined: Tue Apr 19, 2011 1:40 pmFollowed by: 11 members; Thanked: 114 times

by knight247 » Fri Feb 17, 2012 12:31 am

Hey Amit,
The answer IS B not C.

Is x divisible by 15?
(1)When x is divided by 10, the result is an integer. Ok, so x could be 20,30,40,50,50 ETC all of which meet the requirement of giving an integer result when divided by 10. But x could be 30 which is divisible 15 or it could be 20 which isn't divisible by 15. Conflicting answers so INSUFFICIENT.
(2)xÂ²= some multiple of 30
xÂ²=2*3*5....
Prime factors of perfect squares will obviously come in pairs. So we could rewrite xÂ² as
xÂ²=2Â²*3Â²*5Â²..... And taking square root on both sides
x=2*3*5... Which is divisible by 15. SUFFICIENT.

Hence B

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Fri Feb 17, 2012 12:32 am

[email protected] wrote:Is X divisible by 15?

1. When X is divided by 10, the result is an integer.
2. X^2 is a multiple of 30.

Exactly the answer is turning out to be C. Not B.

There are many numbers whose square must be the multiple of 30 but remember their squares are the multiple of 30 X itself...

When both the statements are combined, the answer turns out to be good...

Can you please give me a square integer divisible by 30?

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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[email protected]: Legendary Member; Posts: 934; Joined: Tue Nov 09, 2010 5:16 amFollowed by: 14 members; Location: AAMCHI MUMBAI LOCAL; Thanked: 63 times

by [email protected] » Fri Feb 17, 2012 1:20 am

Just got stuck a bit here...

Square integer of a multiple of 30 is 900...

And knight247

x^2 = 30, how do u know that it has to be a perfect square... please help me understand this...

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[email protected]: Legendary Member; Posts: 934; Joined: Tue Nov 09, 2010 5:16 amFollowed by: 14 members; Location: AAMCHI MUMBAI LOCAL; Thanked: 63 times

by [email protected] » Fri Feb 17, 2012 1:24 am

X^2 is a multiple of 30.

this can be: x^2 = 30 X 1 = 30
x^2 = 30 X 2 = 60
etc.......

and also x^2 = 30 X 30 this goes , hence insufficient...

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Fri Feb 17, 2012 1:59 am

[email protected] wrote:X^2 is a multiple of 30.

this can be: x^2 = 30 X 1 = 30
x^2 = 30 X 2 = 60
etc.......

and also x^2 = 30 X 30 this goes , hence insufficient...

If you take X^2 = 30, then X would no more be an integer, and this would contradict the stem which reads the term 'divisible'. Remember, whenever GMAT uses the terms like divisible, a factor of, or a multiple of, they customarily mean integers, preferably non-negative ones.

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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by [email protected] » Fri Feb 17, 2012 2:18 am

Ok sanju09! thank you for your support...

I got my mistake...

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shekhar.kataria: Master | Next Rank: 500 Posts; Posts: 268; Joined: Mon Mar 15, 2010 12:10 am; Thanked: 13 times

by shekhar.kataria » Fri Feb 17, 2012 4:45 am

Hi Sanju

II. Once X^2 is a multiple of 30, X is a multiple of 30, and hence a multiple of 15 as well. Sufficient

How can you prove the above quoted. Just a case which goes opposite to what you said.

6^2 is a multiple of 4, but 6 is not a multiple of 4.

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Jim@StratusPrep: MBA Admissions Consultant; Posts: 2279; Joined: Fri Nov 11, 2011 7:51 amFollowed by: 266 members; Location: New York; Thanked: 660 times; GMAT Score:770

by Jim@StratusPrep » Fri Feb 17, 2012 9:38 am

shekhar.kataria wrote:Hi Sanju

II. Once X^2 is a multiple of 30, X is a multiple of 30, and hence a multiple of 15 as well. Sufficient
How can you prove the above quoted. Just a case which goes opposite to what you said.

6^2 is a multiple of 4, but 6 is not a multiple of 4.

Please see my original post. This has to do with prime factors. If a number is squared, it has "pairs" for each of the prime factors (see below) - 2 and 3 in the case of 6. To be a multiple of 4 there would have to be 4 factors of 2 in the x^2.

2^2 = 2^2
3^2 = 3^3
4^2 = 2^2 * 2^2
5^2 = 5^2
6^2 = 2^2 * 3^2
7^2 = 7^2
8^2 = 2^2 * 2^2 * 2^2
9^2 = 3^2 * 3^2

Basically, all squared numbers have an even number of prime factors. So if x^2 is a multiple of 30, then x^2 has pairs of prime factors for 2,3 and 5. Thus , so does X.

Hope this clarifies things.

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ArunangsuSahu: Master | Next Rank: 500 Posts; Posts: 382; Joined: Thu Mar 31, 2011 5:47 pm; Thanked: 15 times

by ArunangsuSahu » Fri Feb 17, 2012 11:10 am

X^2=30*K

K=1
x^2=30
x=30^1/2 or -30^1/2

Any thought about this?

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