A number theory problem by Odin Wang

Number Theory Level 2

there are $x$ people at a party and $y$ cans of drinks.

Given that $1 < x < 10$ and $10 < y \leq30$ and that $\frac{y}{x}$ is an integer, how many combinations for number of adults and drinks are there?

2 solutions

Joshua Lowrance
Sep 4, 2020

$y$	factors $1<x<10$
$11$	$0$

In total, there are $\boxed{37}$ possible scenarios.

I apologize for the weird gap in the table. The table wouldn't load properly when I tried to fix the gap :(

Joshua Lowrance - 9 months, 1 week ago

Odin Wang
Aug 13, 2020

possible factors for 2: 10

possible factors for 3: 7

possible factors for 4: 5

possible factors for 5: 4

possible factors for 6: 4

possible factors for 7: 3

possible factors for 8 and 9: 2 for each

10 + 7 + 5 + 4+ 4 + 3 + 2 + 2 = $\boxed{37}$

I think you phrased incorrectly the question, it should say integer, not rational

Matteo Bianchi - 10 months ago

ah yes of course

Odin Wang - 10 months ago

There are only four multiples of 5: 15, 20, 25, and 30. This makes the answer 37.

Jon Haussmann - 10 months ago

sry miscounted

Odin Wang - 10 months ago

The answer should be 37

A Former Brilliant Member - 9 months, 3 weeks ago

I KNOW THAT

Odin Wang - 9 months, 3 weeks ago