If n and m are integers, is n/3 an integer?

Question

(1) 54n=6m
(2) 32n=12m

chetan2u · Answer

Hi,
lets se ethe statements

(1) 54n=6m 
or 9n = m..
we cannot say anything about n but m is a multiple of 9..
Insuff

(2) 32n=12m 
or 8n=3m..
n is surely a multiple of 3 ..
so n/3 will be an integer
Suff

B

chandan276 · Answer

Hi Chetan,

For statement 1, can we not write n = m/9 that means n is a number, which is divisible by 9. So, it will be divisible by 3?

Kurtosis · Answer

Hi,

m = 9n
If you take n = m/9 then m has to be a multiple of 9 for n to be an integer. n can take many values.

If you look at St2, we have 8n = 3m. This means that n must contain atleast one 3 as factor and m must contain atleast one 8 as factor to ensure the expression 8n = 3m is satisfied.

DrAB · Answer

If n & m are integers, is n/3 a integer?

1) 54n=6m
2) 32n=12m

Bunuel · Answer

Merging topics. Please refer to the discussion above. Also, please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Thank you.

adiagr · Answer

Statement 1

54n = 6m

This means n = (m/9), m is a multiple of 9 because n is an integer. We have no info about n.

m=9n, 
n= 1 then m is an integer; n is not divisible by 3
n = 3, even then m is an integer. n is divisible by 3.

Not sufficient.
 
 Statement 2 
32n = 12m

m = (32/12)*n = (8/3)n.

Since m is an integer,  n has to be a multiple of 3  --> Sufficient.

B is the answer.

bumpbot · Answer

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If n and m are integers, is n/3 an integer?

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