VJesus12 wrote: ↑

Thu Nov 04, 2021 6:20 am

Danny bought some packets of pens, each packet at a cost of \(\$4,\) and some packets of pencils, each packet at a cost of \(\$3.\) What is the ratio of the number of packets of pens to the number of packets of pencils purchased?

(1) He paid \(\$24\) for the entire purchase.
(2) He spent equal amounts of money on pens and pencils.

Answer: D

Source: Veritas Prep

If the number of packets of pens \(=x\)
If the number of Packets of pencils \(= y\)

We need to find \(x:y\)

From 1:
Total cost is given by: \(4x + 3y = 24\)
The only integral values of \((x, y)\) that satisfy the above equation are \((3,4)\) and \((6,0)\) but since it is mentioned that he did buy some packets of pencils we have to assume that \(y > 0.\) Hence \(x:y = 3:4\) Sufficient \(\Large{\color{green}\checkmark}\)

From 2:
It's given that \(4x=3y\)
Therefore, \(x:y=3:4\) Sufficient \(\Large{\color{green}\checkmark}\)

Hence, the correct answer is D