Question

Shishir is trying to express every cube as the sum of consecutive odd numbers. He is struggling to express $7^3$ in this way. Can you find the odd numbers whose sum leads to $7^3$?

• A. 39, 45, 47, 49, 51, 53, 59
• B. 43, 45, 41, 49, 57, 53, 55
• C. 43, 45, 47, 49, 51, 53, 55
• D. 39, 45, 47, 49, 51, 43, 59

Answer 1

The correct options are
C

43, 45, 47, 49, 51, 53, 55

The sum of 7 consecutive odd numbers gives $7^3$. To find the odd numbers whose sum is $7^3$, we first divide $7^3$ by 7.
$\Rightarrow \frac{7^3}{7}=7^2=49$
Since 49 is an odd number, it is the middle number of the series. The other odd numbers are the 3 odd ones before and after 49.
So the odd numbers whose sum gives $7^3$ are 43, 45, 47, 49, 51, 53, 55.