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For any positive integer n, π(n) represents the number of fa
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04 Apr 2018, 12:33
04 Apr 2018, 12:33
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53% (00:49) correct
46% (00:59) wrong based on 102 sessions
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For any positive integer n, \(\pi(n)\) represents the number of factors of n, inclusive of 1 and itself. a and b are prime numbers
Quantity A |
Quantity B |
\(\pi(a) + \pi(b)\) |
\(\pi(a * b)\) |
A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Re: For any positive integer n, π(n) represents the number of fa
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04 Apr 2018, 15:43
04 Apr 2018, 15:43
1
Answer: C (DOUBTS)
A: P(a) + P(b)
The only factors of a prime number are 1 and the number itself.
So P(a) + P(b) always equals 2+2 = 4
B: P(a*b)
The factors of a*b are 1, a, b, a*b. Why not more than 4? Because no new divider is produced with multiplying a to b. If there were any it was a factor of a or b (a factor other than a and b themselves and a) and thus a or b couldn’t be prime. So factors of a*b are 4 numbers.
For example if a = 3 and b = 11 then P(a*b) = P(33) = 4 (1, 3, 11, 33)
A and B are both 4 and equal. The answer is C.
A: P(a) + P(b)
The only factors of a prime number are 1 and the number itself.
So P(a) + P(b) always equals 2+2 = 4
B: P(a*b)
The factors of a*b are 1, a, b, a*b. Why not more than 4? Because no new divider is produced with multiplying a to b. If there were any it was a factor of a or b (a factor other than a and b themselves and a) and thus a or b couldn’t be prime. So factors of a*b are 4 numbers.
For example if a = 3 and b = 11 then P(a*b) = P(33) = 4 (1, 3, 11, 33)
A and B are both 4 and equal. The answer is C.
Re: For any positive integer n, π(n) represents the number of fa
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06 May 2018, 18:29
06 May 2018, 18:29
2
I have reservation on the ans
because it could be a case of \(a = b\)
and hence qty B can have 3 factors
because it could be a case of \(a = b\)
and hence qty B can have 3 factors
