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Grades 11-12 Video Solutions 2012
2012_11-12_03
2012_11-12_03
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Video Transcription
In a list of 5 numbers, the first number is 2 and the last number is 12. The product of the first 3 numbers is 30, the product of the 3 numbers in the middle is 90, and the product of the last 3 numbers is 360. Which number is in the center of the list? So if we look at the first 3 numbers, these guys multiply to 30, and we already have a 2, so that means these 2 numbers right here have to multiply to a 15. But now if we look at the middle 3 numbers, which multiply to 90, the first 2 contribute a 15, and so that means this number has to be 6, so that they multiply to 90. But now if we look at the last 3 numbers, we know that they multiply to 360, we already have 6 times 12, and so the remaining number must be a 5, and so the answer is 5.
Video Summary
The problem involves a list of five numbers with specific multiplication conditions. The sequence has 2 as the first number and 12 as the last. The first three numbers multiply to 30, requiring the second and third numbers to multiply to 15. For the middle three numbers multiplying to 90, with the first two contributing a product of 15, the third number must be 6. Finally, the last three numbers multiply to 360. Since 6 and 12 are known, the fifth number must be 5. Thus, the center number in the list is 5.
Keywords
number sequence
multiplication conditions
list problem
mathematical puzzle
sequence analysis
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