y^3 divisible by 9

This topic has expert replies
Junior | Next Rank: 30 Posts
Posts: 14
Joined: Thu Oct 08, 2009 12:34 am

y^3 divisible by 9

by GhassanMBA » Thu Feb 04, 2010 2:56 am
If y is an integer, is y^3 divisible by 9?

1) y is divisible by 4
2) y is divisible by 6


The OA is B

The explanation in the book is too confusing, and I would appreciate if someone can clarify why B is the answer. I've generally been having difficulties with this kind of questions.
Thanks
Source: — Data Sufficiency |

Senior | Next Rank: 100 Posts
Posts: 31
Joined: Sat Jan 02, 2010 9:21 am
Location: mumbai
Thanked: 3 times
GMAT Score:540

by ramsharma » Thu Feb 04, 2010 3:33 am
Here is the solution to show why B is correct

Statement 2 says y is divisible by 6. so Y will be multiple of 6.
Hence Y can be written as ;Y=k*6=k*2*3(where K is constant)
If take cube of Y ,So y^3=k^3*2^3*3^3=k^3*2^3*3*9

You can see y^3 has 9 as factor, so it is divisible by 9
RAM SHARMA

User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 am
Location: India
Thanked: 267 times
Followed by:80 members
GMAT Score:760

by sanju09 » Thu Feb 04, 2010 3:34 am
GhassanMBA wrote:If y is an integer, is y^3 divisible by 9?

1) y is divisible by 4
2) y is divisible by 6


The OA is B

The explanation in the book is too confusing, and I would appreciate if someone can clarify why B is the answer. I've generally been having difficulties with this kind of questions.
Thanks
If y is an integer then y^3 is a cube integer which will be divisible by 9 once y is divisible by 3, otherwise NOT.

(1) A number divisible by 4 may or may not be divisible by 3 or is NOT necessarily divisible by 3. Insufficient

(2) A number divisible by 6 is necessarily divisible by 3. Sufficient

So, [spoiler]B[/spoiler]
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

User avatar
Legendary Member
Posts: 1132
Joined: Mon Jul 20, 2009 3:38 am
Location: India
Thanked: 64 times
Followed by:6 members
GMAT Score:760

by harsh.champ » Thu Feb 04, 2010 4:57 am
sanju09 wrote:
GhassanMBA wrote:If y is an integer, is y^3 divisible by 9?

1) y is divisible by 4
2) y is divisible by 6


The OA is B

The explanation in the book is too confusing, and I would appreciate if someone can clarify why B is the answer. I've generally been having difficulties with this kind of questions.
Thanks
If y is an integer then y^3 is a cube integer which will be divisible by 9 once y is divisible by 3, otherwise NOT.

(1) A number divisible by 4 may or may not be divisible by 3 or is NOT necessarily divisible by 3. Insufficient

(2) A number divisible by 6 is necessarily divisible by 3. Sufficient

So, [spoiler]B[/spoiler]
_______________________
Hey sanju09,
I see that you have pointed out 2 divisibility rules.
My question is that :Isn't it better to solve the question using the long approach as given by ramsharma.
I personally don't gain any confidence until I solve the questions involving both the "power" and the "divisibility rules".

Going by the long approach atleast I can be sure of my answer or should I try to save some time on these question types by just remembering the rules and applying shortcut techniques.

Seeking advice??

User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 am
Location: India
Thanked: 267 times
Followed by:80 members
GMAT Score:760

by sanju09 » Thu Feb 04, 2010 5:27 am
harsh.champ wrote:
Hey sanju09,
I see that you have pointed out 2 divisibility rules.
My question is that :Isn't it better to solve the question using the long approach as given by ramsharma.
I personally don't gain any confidence until I solve the questions involving both the "power" and the "divisibility rules".

Going by the long approach atleast I can be sure of my answer or should I try to save some time on these question types by just remembering the rules and applying shortcut techniques.

Seeking advice??
Ramsharma's approach is to show why statement (2) by itself is sufficient and he did justice with that. While dealing with small positive integer numbers and powers simultaneously, his approach is quite handy. This question could be answered well within 2 minutes with his approach, no doubt. But that never means that a GMAT aspirant can deal with its quantitative section effectively without learning and practicing the most required strategies and short cuts that have been tried and tested so many times on the test so far. Divisibility rules of very a few positive integers, like 2, 3, 4, 5, 6, 8, 9, and 11 are very important to ponder and practice before writing the main test.

It's true that going by the long approach at least they can be sure of their answer but that won't work for them throughout the section. You'll start getting faith in strategies and short cuts too, once you give it few chances, and that would, in fact, turn out to be really productive for you on real test.

ATB
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

Senior | Next Rank: 100 Posts
Posts: 65
Joined: Wed Nov 25, 2009 6:33 pm
Thanked: 3 times

by dxgamez » Wed Mar 24, 2010 7:38 am
Hi sanju,

where can I get information on divisibility of numbers that you mentioned?

Thanks.

User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 am
Location: India
Thanked: 267 times
Followed by:80 members
GMAT Score:760

by sanju09 » Thu Mar 25, 2010 1:13 am
dxgamez wrote:Hi sanju,

where can I get information on divisibility of numbers that you mentioned?

Thanks.
see if this page could be of any help...


https://en.wikipedia.org/wiki/Divisibility_rule


ATB
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

User avatar
Senior | Next Rank: 100 Posts
Posts: 36
Joined: Mon Nov 18, 2013 2:03 pm
Followed by:1 members

by ozlemmetje » Mon May 05, 2014 9:00 am
Hello,

here is the explanation in the book:

1) Some multiples of 4 are divisible by 3, such as 12(y=12 is divisible by 3 hence y^3=12^3 is divisible by 27, and so y^3 = 12^3 is divisible by 9), and some multiples of 4 are not divisible by 3(y=8 is not divisible by 3, hence y^3 = 8^3 is not divisible by 3, and so y^3=8^3 certainly cannot be divisible by 9); NOT SUFFICIENT

Now my question is; how can one understand whether a power of a number is divisible by some other number or not without doing a long calculation each time. For example, I know that 12 is divisible by 3 so I take 12 but how do I know if 12^3 is divisible by 9 without doing the calculation as 12x12x12/9? What is the short way to know this??

Thanks

User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 am
Location: India
Thanked: 267 times
Followed by:80 members
GMAT Score:760

by sanju09 » Tue May 06, 2014 12:11 am
ozlemmetje wrote:Hello,

here is the explanation in the book:

1) Some multiples of 4 are divisible by 3, such as 12(y=12 is divisible by 3 hence y^3=12^3 is divisible by 27, and so y^3 = 12^3 is divisible by 9), and some multiples of 4 are not divisible by 3(y=8 is not divisible by 3, hence y^3 = 8^3 is not divisible by 3, and so y^3=8^3 certainly cannot be divisible by 9); NOT SUFFICIENT

Now my question is; how can one understand whether a power of a number is divisible by some other number or not without doing a long calculation each time. For example, I know that 12 is divisible by 3 so I take 12 but how do I know if 12^3 is divisible by 9 without doing the calculation as 12x12x12/9? What is the short way to know this??

Thanks
Hi ozlemmetje,

Once you know that 3 is a factor of 12, you are in every position to accept that (3)(3) is a factor of (12)(12). Hence we can say that 9 is a factor of (12)^2 and the greater positive integer exponents of 12 beyond 2, such as, YES, 9 is a factor of (12)^3 as well.
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