Grades 11-12 Video Solutions 2024-2024_11-12

Video Transcription

Video Summary

A student multiplies the number 1 by either 6 or 10 repeatedly. The results can be expressed in terms of their prime factors: \(6^A \times 10^B\), which equals \(2^{A+B} \times 3^A \times 5^B\). The requirement is that the exponent of 2 (A+B) equals the sum of the exponents of 3 and 5 (A+B). Choice B, which is 90, violates this condition because its prime factorization results do not satisfy this equation (it factors into \(2^1 \times 3^2 \times 5^1\), making the left side 1 not equal to the right side 3).

Keywords

prime factorization

multiplication

exponents

condition violation

number theory