Data Sufficiency

23) Is N a factor of 24?
(1) 48 is a factor of 3n
(2) 60 is a factor of 5n

My Solution :

Rephrase : do factors contain 2*2*2*3
(1) Gives 2*2*2*2 hence insuff
(2) Gives 2*2*3 hence insuff


I feel the answer is C but it's given as B? What are your views?

varunkh85 wrote:23) Is N a factor of 24?
(1) 48 is a factor of 3n
(2) 60 is a factor of 5n

My Solution :

Rephrase : do factors contain 2*2*2*3
(1) Gives 2*2*2*2 hence insuff
(2) Gives 2*2*3 hence insuff


I feel the answer is C but it's given as B? What are your views?

A --> 48 is a factor of 3n => 16 is a factor of n. So n can be 1, 2, 4, 8 and 16. Now all these values are factors of 24 except 16 so Insuff.
B --> 60 is a factor of 5n => 12 is a factor of n. So n can be 1, 2, 3, 4, 6 and 12. All of these are factors of 24 so this is sufficient to say that N is a factor of 24. Hence B is the answer

okay,

(1) 48 is a factor of 3n

that means that the least value of 3n would be 48.
you know, 3n/48 = 48/48 = 1.

if that is so then solving 3n = 48 gives me: n= 16.

but 16 is not a factor of 24,

so go to (2):

if 60 is a factor of 5n, then the least value of 5n would be 60.
again, 5n/60 = 60/60 = 1 if 5n = 60

solving for n gives us n = 12,

so yep, 12 is a factor of 24.

However, if in (2) we take 5n = 180, then 60 is a factor of 5n. but then n becomes 180/5 = 36, but 36 is NOT a factor of 24!!!

y'know, for n to be a factor of 24, it must have a maximum value of 24. i can give you n = 24 if i take 5n = 120

so with (2) only 2 values of n will suit us - 12 and 24. but like is showed, there are other possible values of n as well.

combining (1) & (2) is not helping me either. so, i'll go with 'E'

please correct me if my approach is wrong.

riteshbindal wrote:

varunkh85 wrote:23) Is N a factor of 24?
(1) 48 is a factor of 3n
(2) 60 is a factor of 5n

My Solution :

Rephrase : do factors contain 2*2*2*3
(1) Gives 2*2*2*2 hence insuff
(2) Gives 2*2*3 hence insuff


I feel the answer is C but it's given as B? What are your views?

A --> 48 is a factor of 3n => 16 is a factor of n. So n can be 1, 2, 4, 8 and 16. Now all these values are factors of 24 except 16 so Insuff.
B --> 60 is a factor of 5n => 12 is a factor of n. So n can be 1, 2, 3, 4, 6 and 12. All of these are factors of 24 so this is sufficient to say that N is a factor of 24. Hence B is the answer

i'm just curious:

if we look at (2) which says 60 is a factor of n,
and then you said n = 1,2,3,4,5,6,12;

if, say n = 1, then 5n = 5.
then how will (2) hold that says 60 is a factor of 5n.

it become that 60 is a factor of 5?

i didn't quite get it.

varunkh85 wrote:23) Is N a factor of 24?
(1) 48 is a factor of 3n
(2) 60 is a factor of 5n

My Solution :

Rephrase : do factors contain 2*2*2*3
(1) Gives 2*2*2*2 hence insuff
(2) Gives 2*2*3 hence insuff


I feel the answer is C but it's given as B? What are your views?

i feel C should be answer.

from each statement nothing can be told but both statements together say that n is multiple of 48. hence not a factor of 24

Question rephrase:Is N of the form 2^3*3k

1. 48 is a factor of 3N => 2^4*3 is a factor of 3N.Hence N is of the form 2^4*k1

2. 60 is a factor of 5N hence N is of the form 2^2*3.

From 1 and 2 N is def of the form 2^4*3.Hence suff.

C is the answer.

varunkh85 wrote:23) Is N a factor of 24?
(1) 48 is a factor of 3n
(2) 60 is a factor of 5n

My Solution :

Rephrase : do factors contain 2*2*2*3
(1) Gives 2*2*2*2 hence insuff
(2) Gives 2*2*3 hence insuff


I feel the answer is C but it's given as B? What are your views?

guys,

I am lost here..plz help and correct me, because this is fundamental issue I am not getting.

question asks if n is a factor of 24?

The restate: is N equal to 1, 2, 3, 4, 6, 8, 12, or 24?
So we are looking to see if based on statements if N equals these possibilities. This is a yes/no data sufficiency problem. Therefore if I can definitively answer NO or YES based on the statements given, the data is sufficient.

Statement 1)

48 is a factor of 3n translates to 16 is a factor of n. This means at the very least n is 2^4 or 16. 16 is not one of the possibilities in the restate. Moreso, if N comprises of an additional prime(on top of 2^4) we don't know about such as 3 , 5, 7 etc. N would definitely not be a factor of 24. We definitively know N is not a factor of 24, so isn't this sufficient??

Statement 2)

60 is a factor of 5n translates to 12 is a factor of n. This means at the very least n is 2^2 x 3 or 12. Now there is a 12 in the possibilities of factors for N. However, if N comprises of an additional prime(on top of 2^2 x 3) we don't know about such as , 5, 7 etc. N would not be a factor of 24 if it was 2^2 x 3 x 7 or 84. So insufficient, N could be a factor of 24 or not.

Why not A?

Thanks.

Factors of 60 are 12, 6,4,3,2,1

To find out if n is one among them

St 1 - (1) 48 is a factor of 3n...in this case n could be 1,2 or 4 insufficient as rest of factors are not divisors of 48.

(2) 60 is a factor of 5n...again n could be 1,2,4 or 6..insuficient

Combining both......still insufficient.

I would go with E.

GID09

answer should be C

From 1 we get N/16 is an integer - insufficient
From 2 we get N/12 is an integer - insufficient

From 1 and 2 we get that N/12 and N/16 are integers. therefore N has to be minimum of 48 i.e. LCM of 12 and 16 to be integer.

Hence C.

IMO A

1)48K=3N
N=16K
N=16,32,..
Definitely not a factor of 24.

SUFF

2)60K=5N
N=12K
N=12,24,36..not suff

or am i missing something here??

whats the source? A makes sense

3N is a multiple of 48

=> 3N could be 48, 96, 144, 192 ...
=> N could be 16, 32, 48, etc.

Hence 24 cannot be a multiple of N. In other words, N cannot be a factor of 24.

Hence A.

varunkh85 wrote:23) Is N a factor of 24?
(1) 48 is a factor of 3n
(2) 60 is a factor of 5n

My Solution :

Rephrase : do factors contain 2*2*2*3
(1) Gives 2*2*2*2 hence insuff
(2) Gives 2*2*3 hence insuff


I feel the answer is C but it's given as B? What are your views?

Hi, people, this is my opinion:

From (1) We can say this: 3n=48xK (k is a positive integer) =>
n=16xK

For N, to be a factor of 24, it's because 24=16xK, and that it is not possible: K is a positive integer!

From (2) We can say this: 5n=60xK1( K1 is a positive integer) =>
n=12xK1.

For N, to be a factor of 24, it's because 24=12xK1, and that it's possible: K1=2 (positive integer)

In that way, only from (2) we can say that N is a factor of 24. And, finally, we have to choose :
(B) if statement (2) by itself is sufficient to answer the question, but statement (1) by itself is not;

I hope this can help!

Cheers!