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 n2
• 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?

### Answers

 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.

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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.