Number Properties- divisibility

[apoorva.srivastva]

Is the positive integer n divisible by 18?

1.) n^2 is divisible by 18
2.) 2n is divisible by 18

OA is C

please explain!!

[suryapal]

my answer is C

statement 1: insufficient...
if n=6 , then n^2 = 36 which is divisible by 18 but n=6 is not divisible by 18
but if n=18 , then n^2 and n both are divisible by 18

giving both yes or no as a ans. so statement 1 is insufficient

statement 2 : insufficient
according to given condition
2n/18= x ( where x is an integer )
or n=x*18/12=x*9 so n can be 9,18,27,36,........

this situation also give both yes and no as answer ... so it is also insufficient

taking both statement together .... the answer is always yes (take few numbers which statisfy both the conditions )
so both the statement together are sufficient

[Stuart@KaplanGMAT]

Is the positive integer n divisible by 18?

1.) n^2 is divisible by 18
2.) 2n is divisible by 18

From the stem, we know that n is a positive integer. Our task: to determine if n is divisible by 18 or, in other words, if n has, among its prime factors, 2, 3 and 3.

1) n^2 is divisible by 18.

So n^2 has factors of 2, 3 and 3. Does this mean that n also has those factors? No: we know that n^2 will have pairs of primes, so n^2 has to include at least one more "2", but that doesn't mean that n has to have two "3"s.

For example, n^2 could be 2*2*3*3 = 36, which means that n=6, which isn't a multiple of 18.
Or, n^2 could be 2*2*2*2*3*3*3*3 = 36^2, which means that n=36, which is a multiple of 18.

Insufficient, eliminate A and D.

2) 2n is divisible by 18.

Well, if 2n is divisible by 18, then n must be divisible by 18/2 = 9.

We could pick n=9 to get a "no" answer or n=18 to get a "yes" answer.

Insufficient, eliminate B.

Since neither statement was sufficient alone, we need to combine.

From (1), we know that n must be even.
From (2), we know that n is a multiple of 9.

So, together, we know that n is an even multiple of 9.

Is every even multiple of 9 divisible by 18? YES - sufficient, choose C.

[eaakbari]

Is the positive integer n divisible by 18?

1.) n^2 is divisible by 18
2.) 2n is divisible by 18

Stem:
n>0
we need to know whether n is div by 18 or n has factors 3^2 and 2

Statement one
n^2 is div by 18.
or n^2 is div by 2 and 3^2.
Hence any number having factors 2 and 3 will satisfy like 6 and 6 is clearly not div by 18. Hence Insuff

Statement two
2n is div by 2 *3^2.
That implies n contains factors 3^2 , But we dont know about 2. Hence Insuff

Combining
Statement one told us that n has factors 2 and 3
Statement 2 told us it has factor 3^2
We need factors 2 *3^2
which we clearly have
Hence suff


Hence C