Comparing Sums

Algebra Level pending

$A$ is the set of prime numbers $m$ where $100 < m^2 < 600$ .

$B$ is the set of prime numbers $n$ where $5000 < n^3 < 25,000$ .

Which one is greater:

Sum of the numbers in set $A$ .
Sum of the numbers in set $B$ .

2 1 They are equal. Relationship can not be determined from the information given

1 solution

Hana Wehbi
Jun 23, 2017

For the first set, since $100<m^2<600$ , then $10<m<25$ .

Since $25^2= 625$ and $24^2= 576$ , the prime numbers between $10$ and $25$ are $A=$ { $11, 13, 17, 19, 23$ } and the sum of these numbers is $83$ .

Now, testing cubes, we find that $19^3= 6859$ and $23^3= 12167$ and $29^3= 24389$ , then set $B=$ { $19, 23, 29$ } and the sum of these numbers is $71$ , thus, the first quantity is greater.

How did you get these numbers? It's better to explain how these figures came about...

Pi Han Goh - 3 years, 11 months ago

Ok, l will

Hana Wehbi - 3 years, 11 months ago

Comparing Sums

1 solution

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