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30 Jul 2024, 10:23
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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A student made a conjecture that for any integer n, the integer 4n + 3 is a prime number. Which of the following values of n could be used to disprove the student’s conjecture?
Indicate all such values.
A. 1
B. 3
C. 4
D. 6
E. 7
Indicate all such values.
A. 1
B. 3
C. 4
D. 6
E. 7
13 Nov 2024, 10:42
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OE
Recall that a prime number is an integer greater than 1 that has no positive divisors other than 1 and itself.
The answer choices for this question are integer values of n. Any of the answer choices for which the integer 4n + 3 is not a prime number could be used to disprove the conjecture that for any integer n, the integer 4n + 3 is a prime number.
To answer this question, you must determine for each of the answer choices whether the integer 4n + 3 is a prime number. The evaluations are as follows:
Choice A: For n = 1, the integer 4n + 3 is 4(1) + 3, or 7, which is a prime number.
Choice B: For n = 3, the integer 4n + 3 is 4(3) + 3, or 15, which is not a prime number.
Choice C: For n = 4, the integer 4n + 3 is 4(4) + 3, or 19, which is a prime number.
Choice D: For n = 6, the integer 4n + 3 is 4(6) + 3, or 27, which is not a prime number.
Choice E: For n = 7, the integer 4n + 3 is 4(7) + 3, or 31, which is a prime number.
Therefore, of the answer choices, only Choices B and D, that is, n = 3 and n = 6, result in integers 4n + 3 that are not prime numbers. Thus, the correct answer consists of Choices B and D.
Recall that a prime number is an integer greater than 1 that has no positive divisors other than 1 and itself.
The answer choices for this question are integer values of n. Any of the answer choices for which the integer 4n + 3 is not a prime number could be used to disprove the conjecture that for any integer n, the integer 4n + 3 is a prime number.
To answer this question, you must determine for each of the answer choices whether the integer 4n + 3 is a prime number. The evaluations are as follows:
Choice A: For n = 1, the integer 4n + 3 is 4(1) + 3, or 7, which is a prime number.
Choice B: For n = 3, the integer 4n + 3 is 4(3) + 3, or 15, which is not a prime number.
Choice C: For n = 4, the integer 4n + 3 is 4(4) + 3, or 19, which is a prime number.
Choice D: For n = 6, the integer 4n + 3 is 4(6) + 3, or 27, which is not a prime number.
Choice E: For n = 7, the integer 4n + 3 is 4(7) + 3, or 31, which is a prime number.
Therefore, of the answer choices, only Choices B and D, that is, n = 3 and n = 6, result in integers 4n + 3 that are not prime numbers. Thus, the correct answer consists of Choices B and D.
