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If a prime number, p, is squared and the result is added to the next p

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If a prime number, p, is squared and the result is added to the next p [#permalink] New post   18 May 2023, 10:41
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If a prime number, p, is squared and the result is added to the next prime number greater than p, which of the following integers could be the resulting sum?

Indicate all such integers.

A. 3
B. 4
C. 7
D. 14
E. 58
F. 60
G. 65
H. 69


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C,D,F
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Re: If a prime number, p, is squared and the result is added to the next p [#permalink] New post   28 May 2023, 01:57
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To solve this problem, try writing out the possibilities. The least prime number is 2. (2 × 2) + 3 = 7; so (C) is correct. The next prime number is 3: (3 × 3) + 5 = 14, so (D) is correct. The next prime number is 5: (5 × 5) + 7 = 32, which is not an answer choice. The next prime number is 7: (7 × 7) + 11 = 60, so (F) is correct. The next prime number is 11: (11 × 11) + 13 = 134, which is a greater value than the answer choice possibilities. The correct answer is (C), (D), and (F).
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Re: If a prime number, p, is squared and the result is added to the next p [#permalink]
28 May 2023, 01:57
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