AMC10 2011 B

AMC10 2011 B · Q5

AMC10 2011 B · Q5. It mainly tests Divisibility & factors, Primes & prime factorization.

In multiplying two positive integers a and b, Ron reversed the digits of the two-digit number a. His erroneous product was 161. What is the correct value of the product of a and b ?

在乘两个正整数 a 和 b 时，Ron 把两位数 a 的数字颠倒了。他的错误积是 161。a 和 b 的正确积是多少？

(A) 116 116

(B) 161 161

(D) 214 214

(E) 224 224

Answer

Correct choice: (E)

正确答案：（E）

Solution

Answer (E): Because 161 = 23 · 7, the only two digit factor of 161 is 23. The correct product must have been 32 · 7 = 224.

答案 (E)：因为 161 = 23 · 7，161 的唯一两位数因子是 23。正确的积应该是 32 · 7 = 224。

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