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QOTD#15 In the equation above, x is an integer with 3
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16 Nov 2016, 13:06
16 Nov 2016, 13:06
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35% (01:19) wrong based on 31 sessions
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\(\frac{xz}{y}=420\)
In the equation above, x is an integer with 3 distinct prime factors, and y is a positive integer with no prime factors. If z is a positive, non-prime number, what is one possible value of z?
In the equation above, x is an integer with 3 distinct prime factors, and y is a positive integer with no prime factors. If z is a positive, non-prime number, what is one possible value of z?
Drill 4
Question: 6
Page: 293
Question: 6
Page: 293
Show: :: OA
4, 6, 10, and 14
Re: QOTD#15 In the equation above, x is an integer with 3
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16 Nov 2016, 13:12
16 Nov 2016, 13:12
1
Expert Reply
Explanation
Don’t forget that you can use your on-screen calculator. There’s only one positive integer with no prime factors, the number 1. Therefore, y = 1, and xz = 420. Create a prime factor tree to get the prime factors of 420: 2, 2, 3, 5, and 7. Pick 3 distinct values from that list, such as 2, 3, and 5, and multiply them to find one possible value of x. One example is 2 × 3 × 5 = 30, or one
possible value for x. If 30z = 420, then z = 14. Confirm that 14 is not prime, then enter it in the field. If you chose 2, 3, 7, then x is 42 and z is 10 and also correct, and so on.
Don’t forget that you can use your on-screen calculator. There’s only one positive integer with no prime factors, the number 1. Therefore, y = 1, and xz = 420. Create a prime factor tree to get the prime factors of 420: 2, 2, 3, 5, and 7. Pick 3 distinct values from that list, such as 2, 3, and 5, and multiply them to find one possible value of x. One example is 2 × 3 × 5 = 30, or one
possible value for x. If 30z = 420, then z = 14. Confirm that 14 is not prime, then enter it in the field. If you chose 2, 3, 7, then x is 42 and z is 10 and also correct, and so on.
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Re: QOTD#15 In the equation above, x is an integer with 3
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25 Nov 2016, 17:56
25 Nov 2016, 17:56
3
sandy wrote:
\(\frac{xz}{y}=420\)
In the equation above, x is an integer with 3 distinct prime factors, and y is a positive integer with no prime factors. If z is a positive, non-prime number, what is one possible value of z?
In the equation above, x is an integer with 3 distinct prime factors, and y is a positive integer with no prime factors. If z is a positive, non-prime number, what is one possible value of z?
Show: :: OA
4, 6, 10, and 14
y is a positive integer with no prime factors
That should strike you as an odd statement.
There's only one such number: 1
So, we already know that y = 1
So, we have (xz)/1 = 420
This means that xz = 420
When we find the prime factorization of 420, we get: 420 = (2)(2)(3)(5)(7)
In other words, xz = (2)(2)(3)(5)(7)
GIVEN: x is an integer with 3 distinct prime factors
So, for example, x could equal (2)(3)(5) [aka 30]
Or x could equal (2)(3)(7) [aka 42]
Or x could equal (3)(5)(7) [aka 105]
Or x could equal (2)(5)(7) [aka 70]
If x = 30, then z = 14
If x = 42, then z = 10
If x = 105, then z = 4
If x = 70, then z = 6
So, the possible values of z are: 4, 6, 10, and 14
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