Paired products

Algebra Level 2

I have 3 positive integers. The product of any 2 of these integers is 12, 15, or 20.

What is the product of all 3 of these numbers?


The answer is 60.

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Pi Han Goh by Pi Han Goh , 30, Malaysia

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1 solution

Rahil Sehgal
Mar 21, 2017

2 Helpful 0 Interesting 0 Brilliant 0 Confused

@Pi Han Goh What if x = y = z = 12 x = y = z = \sqrt{ 12 } ? Or x = y = 12 x = y = \sqrt{12} and z = 15 12 z = \frac{ 15 } { \sqrt{12} } ?

Problem phrasing needs to be clarified. We seem to be assuming uniqueness here, but that's not necessarily the case.

Calvin Lin Staff - 4 years, 2 months ago

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Well, I did mention that they are integers in then second part of the first sentence, maybe I should just replace "numbers" with "integers" directly...

Pi Han Goh - 4 years, 2 months ago

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Ah true. I didn't see the word integers.

Well, you need integers. If you change to "real numbers", then you need the products to be distinct, or at least that the 3 numbers are distinct.

Calvin Lin Staff - 4 years, 2 months ago

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