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n is an integers greater than or equal to 5
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05 Dec 2019, 11:16
05 Dec 2019, 11:16
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13% (00:40) wrong based on 72 sessions
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n is an integer greater than or equal to 5
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.
Kudos for the right answer and explanation
Quantity A |
Quantity B |
The number of positive factors of \(n\) |
The number of positive factors of \(n+2\) |
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.
Kudos for the right answer and explanation
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n is an integers greater than or equal to 5
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08 Dec 2019, 08:19
08 Dec 2019, 08:19
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Carcass wrote:
n is an integer greater than or equal to 5
Quantity A |
Quantity B |
The number of positive factors of \(n\) |
The number of positive factors of \(n+2\) |
Let's test some possible values of n
case i: Since \(n\geq 5\), one possible value is \(n=5\)
5 has two factors {1,5}
n + 2 = 5 + 2 = 7, and 7 has two factors: {1,7}
We get:
Quantity A: 2
Quantity B: 2
In this case, the quantities are EQUAL
case ii: Another possible value is \(n=7\)
7 has two factors: {1,7}
n + 2 = 7 + 9 = 9, and 9 has three factors: {1,3,9}
We get:
Quantity A: 2
Quantity B: 3
In this case, Quantity B is greater
Answer: D
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Re: n is an integers greater than or equal to 5
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08 Dec 2019, 19:20
08 Dec 2019, 19:20
1
This can be quickly solved by plugging in some simple values, prime numbers to be precise.
Case 1: Take n = 5. Positive factors for 5 are {1,5}. Factors for 5+2 = 7 are {1,7} (both are prime). Here A = 2, B = 2.
Case 2: Take a number such that n+2 is a prime which can be 11 {1,11}, so n=9 {1,3,9}. A = 3 and B = 2.
Hence we choose option D
Case 1: Take n = 5. Positive factors for 5 are {1,5}. Factors for 5+2 = 7 are {1,7} (both are prime). Here A = 2, B = 2.
Case 2: Take a number such that n+2 is a prime which can be 11 {1,11}, so n=9 {1,3,9}. A = 3 and B = 2.
Hence we choose option D
