BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Integer or not

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 16
Joined: Sun Jan 24, 2010 9:36 am

Integer or not

by mchaubey » Wed Apr 14, 2010 3:14 pm
If the integers v and w are both positive, is v/w an integer?

(1) For every factor n of w, n is also a factor of v.

(2) For every prime factor p of w, p is also a prime factor of v.


Here I came to conclusion that both the statements are suff. D

My friend said neither are because we dont know weather v>w. E

The solution stated only statement (1) is suff. A

Can some one help me out with this one.
Top
Source: — Data Sufficiency |
Legendary Member
Posts: 576
Joined: Sat Mar 13, 2010 8:31 pm
Thanked: 97 times
Followed by:1 members

by liferocks » Wed Apr 14, 2010 5:44 pm
from condition 1 For every factor n of w, n is also a factor of v
now every number is one of its own factor.hence condition 1 clearly states that V is divisible by W-->sufficient

from condition 2 For every prime factor p of w, p is also a prime factor of v.
now there cab be possibility that V and W share same prime factors but foes not share the composite factors
ex V=6 and W=12..both are divisible by either 2 or 3 but 6 is not divisible by 12 because 4 is a factor of 12 but not of 6 hence this is insufficient.
[spoiler]Ans is A [/spoiler]
please put the answer in spoiler.It helps us solving the question independently.
Top
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 Apr 15, 2010 12:42 am
mchaubey wrote:If the integers v and w are both positive, is v/w an integer?

(1) For every factor n of w, n is also a factor of v.

(2) For every prime factor p of w, p is also a prime factor of v.


Here I came to conclusion that both the statements are suff. D

My friend said neither are because we dont know weather v>w. E

The solution stated only statement (1) is suff. A

Can some one help me out with this one.
Statement (1) talks about all factors identical, hence the two positive integers are the same positive integer, and their ratio is 1, an integer. Sufficient

Statement (2) talks about all prime factors identical, hence the two positive integers may or may not be the same positive integer or the numerator integer could be less or more than the denominator integer to spoil the party. Insufficient
[spoiler]
A[/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
Top
Legendary Member
Posts: 576
Joined: Sat Mar 13, 2010 8:31 pm
Thanked: 97 times
Followed by:1 members

by liferocks » Thu Apr 15, 2010 1:43 am
sanju09 wrote:Statement (1) talks about all factors identical, hence the two positive integers are the same positive integer, and their ratio is 1, an integer. Sufficient
the two positive integers not necessarily has to be same but one will be multiple of another i.e v is a multiple of W or
v=nw where n is any integer ,if it is 1 then they are identical else not
Ex v=12 and w=6
Top
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 Apr 15, 2010 3:52 am
liferocks wrote:
sanju09 wrote:Statement (1) talks about all factors identical, hence the two positive integers are the same positive integer, and their ratio is 1, an integer. Sufficient
the two positive integers not necessarily has to be same but one will be multiple of another i.e v is a multiple of W or
v=nw where n is any integer ,if it is 1 then they are identical else not
Ex v=12 and w=6
Please read this statement one more time
(1) For every factor n of w, n is also a factor of v.


Doesn't it mean that all factors of w are factors of v as well? Oh yes! This way, w is a certain multiple or factor of v. Now, v/w an integer or not, remains mystery.

[spoiler]who was screaming Eeeeeeeeeeeee...?[/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
Top
Legendary Member
Posts: 576
Joined: Sat Mar 13, 2010 8:31 pm
Thanked: 97 times
Followed by:1 members

by liferocks » Thu Apr 15, 2010 9:25 am
sanju09 wrote:
liferocks wrote:
sanju09 wrote:Statement (1) talks about all factors identical, hence the two positive integers are the same positive integer, and their ratio is 1, an integer. Sufficient
the two positive integers not necessarily has to be same but one will be multiple of another i.e v is a multiple of W or
v=nw where n is any integer ,if it is 1 then they are identical else not
Ex v=12 and w=6
Please read this statement one more time
(1) For every factor n of w, n is also a factor of v.


Doesn't it mean that all factors of w are factors of v as well? Oh yes! This way, w is a certain multiple or factor of v. Now, v/w an integer or not, remains mystery.

[spoiler]who was screaming Eeeeeeeeeeeee...?[/spoiler]
Please read the statement carefully..it says 'every factor n of w, n is also a factor of v' so v is a multiple of w or w is a factor of v,not 'w is a certain multiple'..so v/w definitely integer.
Top
Legendary Member
Posts: 2326
Joined: Mon Jul 28, 2008 3:54 am
Thanked: 173 times
Followed by:2 members
GMAT Score:710

by gmatmachoman » Fri Apr 16, 2010 12:29 am
liferocks wrote:
sanju09 wrote:Statement (1) talks about all factors identical, hence the two positive integers are the same positive integer, and their ratio is 1, an integer. Sufficient
the two positive integers not necessarily has to be same but one will be multiple of another i.e v is a multiple of W or
v=nw where n is any integer ,if it is 1 then they are identical else not
Ex v=12 and w=6
Bro ,

coming to u r case ,

what if V =6 & w = 12??

V/W wont be a integer.. So as per Sanju bhai Gyan...both v & w are the same and the ratio of V:W = 1

Kya Sanju Bhai Sahi na?? Sanju u owe me a thx now!!
Top
Legendary Member
Posts: 576
Joined: Sat Mar 13, 2010 8:31 pm
Thanked: 97 times
Followed by:1 members

by liferocks » Fri Apr 16, 2010 12:51 am
gmatmachoman wrote:what if V =6 & w = 12??
if this is the case then the condition 'For every factor n of w, n is also a factor of v.' will not hold true .because
factors of V 1,2,3,6
factors of W 1,2,3,4,,12

so for n=4 or 12 the condition does not hold good

so it has to be the other way round i.e v=12 and w=6
Top
Legendary Member
Posts: 2326
Joined: Mon Jul 28, 2008 3:54 am
Thanked: 173 times
Followed by:2 members
GMAT Score:710

by gmatmachoman » Fri Apr 16, 2010 1:25 am
liferocks wrote:
gmatmachoman wrote:what if V =6 & w = 12??
if this is the case then the condition 'For every factor n of w, n is also a factor of v.' will not hold true .because
factors of V 1,2,3,6
factors of W 1,2,3,4,,12

so for n=4 or 12 the condition does not hold good

so it has to be the other way round i.e v=12 and w=6
Now Sanju, u have to convince him!!

@Lrocks!!

So only we said V & W are one and the same!!!
Top
User avatar
Legendary Member
Posts: 526
Joined: Sat Feb 21, 2009 11:47 pm
Location: India
Thanked: 68 times
GMAT Score:680

by harshavardhanc » Fri Apr 16, 2010 1:27 am
liferocks wrote:
gmatmachoman wrote:what if V =6 & w = 12??
if this is the case then the condition 'For every factor n of w, n is also a factor of v.' will not hold true .because
factors of V 1,2,3,6
factors of W 1,2,3,4,,12

so for n=4 or 12 the condition does not hold good

so it has to be the other way round i.e v=12 and w=6

Precisely. I'm with liferocks here. Statement 1 just says that every factor of W is a factor of V. It doesn't mean that the number of factors is same.

Look at this way :

set of factors of W is a subset of set of factors of V. Having equal number of elments in both is just one of the possibility.

Either way, V/W will be an integer.

Statement2 :

It just tells us that the prime factors are same : i.e if W has 2,3, and 5 as the prime factors, V also has 2,3, and 5.

But we don't know the exact power of each prime factor. Hence, it is insufficient.

Therefore, the answer is A.
Regards,
Harsha
Top
Legendary Member
Posts: 2326
Joined: Mon Jul 28, 2008 3:54 am
Thanked: 173 times
Followed by:2 members
GMAT Score:710

by gmatmachoman » Fri Apr 16, 2010 1:46 am
mchaubey wrote:If the integers v and w are both positive, is v/w an integer?

(1) For every factor n of w, n is also a factor of v.



.
Let us split the stem given :

Let W =12
factors : 1, 2,3, 4,6,12

Let V =??( could be 24/36..any mulitple of W)

Factors : 1, 2, 3, 4,6, 12 , X, Y ........N

Now it means V >=W .

Harsha, u are also correct. Its not that V has to be equal to W, It can also be greater than W provided V is a multiple of W!!

Agreed???
Top
Legendary Member
Posts: 576
Joined: Sat Mar 13, 2010 8:31 pm
Thanked: 97 times
Followed by:1 members

by liferocks » Fri Apr 16, 2010 1:57 am
gmatmachoman wrote:
mchaubey wrote:If the integers v and w are both positive, is v/w an integer?

(1) For every factor n of w, n is also a factor of v.



.
Let us split the stem given :

Let W =12
factors : 1, 2,3, 4,6,12

Let V =??( could be 24/36..any mulitple of W)

Factors : 1, 2, 3, 4,6, 12 , X, Y ........N

Now it means V >=W .

Harsha, u are also correct. Its not that V has to be equal to W, It can also be greater than W provided V is a multiple of W!!

Agreed???
finally we all are in the same page bro..this it what i am saying ,V is a multiple of W ,,they can be equal if multiplicity factor is 1 but its not necessary that they are equal :)
Top
Legendary Member
Posts: 2326
Joined: Mon Jul 28, 2008 3:54 am
Thanked: 173 times
Followed by:2 members
GMAT Score:710

by gmatmachoman » Fri Apr 16, 2010 2:02 am
liferocks wrote:
gmatmachoman wrote:
mchaubey wrote:If the integers v and w are both positive, is v/w an integer?

(1) For every factor n of w, n is also a factor of v.



.
Let us split the stem given :

Let W =12
factors : 1, 2,3, 4,6,12

Let V =??( could be 24/36..any mulitple of W)

Factors : 1, 2, 3, 4,6, 12 , X, Y ........N

Now it means V >=W .

Harsha, u are also correct. Its not that V has to be equal to W, It can also be greater than W provided V is a multiple of W!!

Agreed???
finally we all are in the same page bro..this it what i am saying ,V is a multiple of W ,,they can be equal if multiplicity factor is 1 but its not necessary that they are equal :)
Agreed Mr Rocks!!
Top
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 » Fri Apr 16, 2010 4:03 am
If every factor of w is a factor of v, then v/w is an integer. But, is this what the statement (1) exactly saying?

You always deserve my thanks, Govind Moshai, specially when you are on the wrongside of road all in order to follow me
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
Top
Legendary Member
Posts: 2326
Joined: Mon Jul 28, 2008 3:54 am
Thanked: 173 times
Followed by:2 members
GMAT Score:710

by gmatmachoman » Sun Apr 18, 2010 9:01 pm
sanju09 wrote:If every factor of w is a factor of v, then v/w is an integer. But, is this what the statement (1) exactly saying?

You always deserve my thanks, Govind Moshai, specially when you are on the wrongside of road all in order to follow me
hehehehe

Sanju.. thx fo tat Thx buttoning!!LOL! Actually we were bit hasty in deciphering the statement 1!!
Top
Post new topic Post Reply
• Page 1 of 1