Question

Carl ate $3^5$ jelly beans and Buffy ate $5^3$ jelly beans. Who ate more jelly beans?

• A. Carl
• B. Buffy
• C. Both are the same
• D. Data insufficient

Answer 1

The correct option is A Carl

Carl ate = $3^5$ = $3\times 3\times 3\times 3\times 3$
= $9\times 9\times 3$
= $81\times 3$
= 243
Buffy ate = $5^3$ = $5\times 5\times 5$
= $25\times 5$
= $125$
It is clear that Carl ate more jelly beans than Buffy.

$\text{Note}$: If we compare $3^5$ and $5^3$, it is clear that $5^3$ has a higher base ($5>3$), but lower exponent ($3<5$). But on calculating the magnitude of the two numbers, $3^5$ > $5^3$. It is incorrect to make assumptions when both the bases and exponents are different in the given numbers.