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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
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65% (01:43) correct
34% (01:17) wrong based on 29 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?
Re: QOTD#15 In the equation above, x is an integer with 3
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16 Nov 2016, 13:12
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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.
Re: QOTD#15 In the equation above, x is an integer with 3
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25 Nov 2016, 17:56
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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?
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
Re: QOTD#15 In the equation above, x is an integer with 3
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13 Feb 2021, 05:56
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?
Re: QOTD#15 In the equation above, x is an integer with 3
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15 Aug 2023, 23:57
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