AMC8 2014

AMC8 2014 · Q4

AMC8 2014 · Q4. It mainly tests Primes & prime factorization, Parity (odd/even).

The sum of two prime numbers is $85$. What is the product of these two prime numbers?

两个质数的和是 $85$。这两个质数的乘积是多少？

(A) 85 85

(B) 91 91

(D) 133 133

(E) 166 166

Answer

Correct choice: (E)

正确答案：（E）

Solution

Since the two prime numbers sum to an odd number, one of them must be even. The only even prime number is $2$. The other prime number is $85-2=83$, and the product of these two numbers is $83\cdot2=\boxed{\textbf{(E)}~166}$.

由于两个质数的和是奇数，其中一个质数必须是偶数。唯一的偶质数是 $2$。另一个质数是 $85 - 2 = 83$，这两个数的乘积是 $83 \cdot 2 = \boxed{\textbf{(E)}~166}$。

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