How many different prime numbers are factors of the positive integer n?

1) Four different prime numbers are factors of 2n

2) Four different prime numbers are factors of n^{2}

- a)Exactly one of the statements can answer the question
- b)Both statements are required to answer the question
- c)Each statement can answer the question individually
- d)More information is required as the information provided is insufficient to answer the question

Correct answer is option 'A'. Can you explain this answer?

Souro Mukherjee
May 04, 2019 |

1) Four different prime numbers are factors of 2n implies that one of the four prime numbers is 2 but 2 may be a factor of n, and if that is so then the total number of prime factors will not change.

If n = 2 * 3 * 5 * 7 (here n has 4 prime factors), then 2n = 2 * 2 * 3 * 5 * 7. Here 2n has 4 prime factors.

If n = 3 * 5 * 7 (here n has 3 prime factors), then 2n = 2 * 3 * 5 * 7. Here 2n has 4 prime factors.

From the above examples, it can be seen that number of different prime numbers may vary; NOT sufficient.

(2) Four different prime numbers are factors of n� implies four different prime numbers are factors of n as well; SUFFICIENT.

The correct answer is B.

1) Four different prime numbers are factors of 2n implies that one of the four prime numbers is 2 but 2 may be a factor of n, and if that is so then the total number of prime factors will not change.If n = 2 * 3 * 5 * 7 (here n has 4 prime factors), then 2n = 2 * 2 * 3 * 5 * 7. Here 2n has 4 prime factors.If n = 3 * 5 * 7 (here n has 3 prime factors), then 2n = 2 * 3 * 5 * 7. Here 2n has 4 prime factors.From the above examples, it can be seen that number of different prime numbers may vary; NOT sufficient.(2) Four different prime numbers are factors of n� implies four different prime numbers are factors of n as well; SUFFICIENT.The correct answer is B.