Question

Syd chooses two different primes, both of which are greater than $10,$ and multiplies them. The resulting product is less than $350.$ How many different products could Syd have ended up with?

Answer 1

10

Explanation:

There are 7 primes between 10 and 35: 11, 13, 17, 19, 23, 29, 31.

The product of 11 and any of the others will be less than 350, 6 products.

The product of 13 and any below 26 will be less than 350, 3 more products.

The product of 17 and any below 20 will be less than 350, 1 more product.

There are a total of 10 different products below 350 possible.

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11·13, 11·17, 11·19, 11·23, 11·29, 11·31, 13·17, 13·19, 13·23, 17·19