Does the positive integer n have at least 3 positive prime factors?


STATEMENT--(1) \(\frac{n}{10}\) is an integer.
this statement tells n --is a multiple of 10
n can be --10,20,30,40.....

if n = 10 =2*5--have two prime factors
---Does the positive integer n have at least 3 positive prime factors?--- the answer is --NO

if n = 30 = 2*3*5--have 3 prime factors
---Does the positive integer n have at least 3 positive prime factors?--- the answer is --YES

so, INSUFFICIENT

STATEMENT--(2) \(\frac{n}{30}\) is an integer.
This statement tells n-- is a multiple of 30

n = 30,60,90,.....210

n =30 = 2*3*5

n= 210 = 2*3*5*7

multiple of 30 will always have three prime factors 2,3 and 5
hence, the positive integer n will always have at least 3 positive prime factors

so the answer to the question--Does the positive integer n have at least 3 positive prime factors?
is YES

SUFFICIENT

B is the answer

Does the positive integer n have at least 3 positive prime factors?

(n cannot be = 0, as we are given that the number is positive.)

1) n/10 is an integer

The smallest possible number that satisfies this condition is n=10.
10 has 2 positive prime factors (2 and 5) >> so the answer will be NO
However, if n=30, then n will have 3 positive prime factors.>> in this case, the answer will be YES.
1) alone is NOT sufficient.

2) n/30 is an integer

The smallest possible number that satisfies this condition is n=30.
30 has 3 positive prime factors (2, 3, and 5) >> so the answer will be YES.
2) alone is sufficient.

Answer: B.

Question: Does n have atleast 3 prime factors?

Statement 1: n/10 is an integer
i.e n is divisible 2 and 5 for sure
but there may (if n = 30) or may not (if n = 10) be a third prime factors hence

NOT SUFFICIENT

Statement 2: n/30 is an integer
i.e. n is divisible by 2, 3 and 5 hence it is definitely divisible by atleast 3 prime factors

SUFFICIENT

Answer: Option B
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imo B ..
1: n/10 is an integer
i.e n is divisible 2 and 5
but there may (if n = 60) or may not (if n = 100) be a third prime factors .....NOT SUFFICIENT

2: n/30 is an integer
i.e. n is divisible by 2, 3 and 5 =>> definitely it will have at least 3 prime factors ===>>SUFFICIENT
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