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QOTD#29 Tasha’s favorite number can be written as 3^2.......
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13 Oct 2016, 13:42
13 Oct 2016, 13:42
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Question Stats:
60% (00:30) correct
39% (00:46) wrong based on 138 sessions
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Tasha’s favorite number can be written as \(3^2 * 17^2\).
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.
Quantity A |
Quantity B |
The number of distinct positive divisors of Tasha’s favorite number |
9 |
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.
Drill 1
Question: 14
Page: 285
Question: 14
Page: 285
Re: QOTD#29 Tasha’s favorite number can be written as 3^2.......
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13 Oct 2016, 13:46
13 Oct 2016, 13:46
1
Expert Reply
Explanation
It is easier to work with the factors of Tasha’s favorite number, rather than with the number itself. Write out the number as 3 × 3 × 17 × 17 and make a list of the divisors—or factors—in pairs. The pairs are: 1 and 3 × 3 × 17 × 17, 3 and 3 × 17 × 17, 17 and 3 × 3 × 17, 3 × 3 and 17 × 17, and 3 × 17 and 3 × 17. The final pair contains only one distinct factor, giving you a total of 9 factors.
Hence option C is the correct option.
It is easier to work with the factors of Tasha’s favorite number, rather than with the number itself. Write out the number as 3 × 3 × 17 × 17 and make a list of the divisors—or factors—in pairs. The pairs are: 1 and 3 × 3 × 17 × 17, 3 and 3 × 17 × 17, 17 and 3 × 3 × 17, 3 × 3 and 17 × 17, and 3 × 17 and 3 × 17. The final pair contains only one distinct factor, giving you a total of 9 factors.
Hence option C is the correct option.
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Re: QOTD#29 Tasha’s favorite number can be written as 3^2.......
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12 Nov 2016, 12:41
12 Nov 2016, 12:41
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sandy wrote:
Tasha’s favorite number can be written as \(3^2 * 17^2\).
Quantity A |
Quantity B |
The number of distinct positive divisors of Tasha’s favorite number |
9 |
NICE RULE: If N = (p^a)(q^b)(r^c)..., where p, q, r,...(etc.) are prime numbers, then the total number of positive divisors of N is equal to (a+1)(b+1)(c+1)...
Example: 14000 = (2^4)(5^3)(7^1)
So, the number of positive divisors of 14000 = (4+1)(3+1)(1+1) = (5)(4)(2) = 40
Here, Tasha's favorite number = (3^2)(17^2)
Notice that 3 and 17 are each prime numbers.
So, the number of positive divisors = (2+1)(2+1)
= (3)(3)
= 9
So we get....
Quantity A: 9
Quantity B: 9
Answer:
Show: ::
C
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