Question

Martina has a jewelry box with necklaces and bracelets. The number of necklaces and bracelets with her is in the ratio of $4:3$. Which of the following CANNOT be the total number of pieces of jewelry Martina can have in the box?

• A. $12$
• B. $28$
• C. $84$
• D. $112$
• E. $140$

Answer 1

The correct option is A $12$

Let $4x$ be the number of necklaces that Martina had in her jewellery box and let $3x$ be the number of bracelets that Martina had in her jewellery box.

If we add the number of necklaces and bracelets we get $7x$.

Let us assume that $x=2$ and substitute in $7x$, we get $7x=7\left(2\right)=14$.

Since $28$, $84$, $112$, and $140$ are divisible by $14$, therefore, option A that is $12$ cannot be the total number of pieces of jewellery Martina can have in the box.