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x is an integer greater than 3.
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11 Dec 2017, 10:01
11 Dec 2017, 10:01
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x is an integer greater than 3.
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal
D. The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
The number of even factors of 2x |
The number of odd factors of 3x |
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal
D. The relationship cannot be determined from the information given.
Re: x is an integer greater than 3.
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10 Jan 2018, 21:08
10 Jan 2018, 21:08
1
If we want to find a number of factors of any number we have to follow next steps:
1. We need to make prime factorization and identify their powers
2. And then this formula can help us (x+1)(y+1)(z+1), x,y,z are prime’s powers
Example, 5^2*3^1* 2^1=150, so (2+1)(1+1)(1+1)
Total number of factors of 150 including 1 and 150 itself is (2+1)(1+1)(1+1)=3*2*2 = 12 factors
About our questions, I think we can test some numbers,
if x=4 then the numbers of even factors of 2x is 4 and the number of odd factors of 3x is 2, in this scenario quantity A is bigger than B
if x=5 then the numbers of even factors 2x is 2 and the number of odd factors of 3x is 4, in this scenario quantity B is bigger than A
1. We need to make prime factorization and identify their powers
2. And then this formula can help us (x+1)(y+1)(z+1), x,y,z are prime’s powers
Example, 5^2*3^1* 2^1=150, so (2+1)(1+1)(1+1)
Total number of factors of 150 including 1 and 150 itself is (2+1)(1+1)(1+1)=3*2*2 = 12 factors
About our questions, I think we can test some numbers,
if x=4 then the numbers of even factors of 2x is 4 and the number of odd factors of 3x is 2, in this scenario quantity A is bigger than B
if x=5 then the numbers of even factors 2x is 2 and the number of odd factors of 3x is 4, in this scenario quantity B is bigger than A
Re: x is an integer greater than 3.
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27 May 2024, 16:33
27 May 2024, 16:33
1
yell2012prime wrote:
If we want to find a number of factors of any number we have to follow next steps:
1. We need to make prime factorization and identify their powers
2. And then this formula can help us (x+1)(y+1)(z+1), x,y,z are prime’s powers
Example, 5^2*3^1* 2^1=150, so (2+1)(1+1)(1+1)
Total number of factors of 150 including 1 and 150 itself is (2+1)(1+1)(1+1)=3*2*2 = 12 factors
About our questions, I think we can test some numbers,
if x=4 then the numbers of even factors of 2x is 4 and the number of odd factors of 3x is 2, in this scenario quantity A is bigger than B
if x=5 then the numbers of even factors 2x is 2 and the number of odd factors of 3x is 4, in this scenario quantity B is bigger than A
1. We need to make prime factorization and identify their powers
2. And then this formula can help us (x+1)(y+1)(z+1), x,y,z are prime’s powers
Example, 5^2*3^1* 2^1=150, so (2+1)(1+1)(1+1)
Total number of factors of 150 including 1 and 150 itself is (2+1)(1+1)(1+1)=3*2*2 = 12 factors
About our questions, I think we can test some numbers,
if x=4 then the numbers of even factors of 2x is 4 and the number of odd factors of 3x is 2, in this scenario quantity A is bigger than B
if x=5 then the numbers of even factors 2x is 2 and the number of odd factors of 3x is 4, in this scenario quantity B is bigger than A
if x = 4, the numbers of even factors of 2x is 3. Since the set of all factors of 2x is {1, 2, 4, 8}, besides, only 2, 4, 8 are even elements in the set.
