VJesus12 wrote: ↑

Sat Jun 26, 2021 5:54 am

Alice bought a certain number of 30 cent stamps, 35 cent stamps, and 40 cent stamps. She spent a total of $4.20 in buying these stamps. Did she buy more than 5 stamps of any of the three values?

(1) The number of 35 cent stamps and 40 cent stamps that Alice bought are equal.

(2) The number of 30 cent stamps and 40 cent stamps that Alice bought are equal. The number of 35 cent stamps that she bought was not more than the number of 40 cent stamps that she bought.

Answer: B

Source: Princeton Review

The number of \(30\) cent stamp \(= a\)
The number of \(35\) cent stamp \(= b\)
The number of \(40\) cent stamp \(= c\)
\(\Longrightarrow 30a +35b +40c = 420\)

1) \(b=c\)
If \(b=c=1,\) then \(a>5\, \color{green}\checkmark\)
If \(b=c=4,\) then \(a=4 \leq 5 \, \color{red}\chi\)
Not Sufficient \(\Large{\color{red}\chi}\)

2) \(a=c. b \leq a\) or \(c\)
If \(a=c=4,\) then \(b=4\, \color{green}\checkmark\)
If \(a=c=5,\) then \(b=2 \, \color{green}\checkmark\)
If \(a=c=6,\) then \(b=0,\) BUT \(b\) must be at least \(1\, \color{green}\checkmark\)
Sufficient \(\Large{\color{green}\checkmark}\)

Therefore, B