Rasheed bought two kinds of candy bars, chocolate and toffee

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Source: GMAT Prep

rasheed bought two kinds of candy bars, chocolate and toffee, that came in packages of 2 bars each. He handed out 2/3 of the chocolate bars and 3/5 of the toffee bars. how many packages of chocolate bars did Rasheed buy?

1) Rasheed bought 1 fewer package of chocolate bars than toffee bars.
2) Rasheed handed out the same number of each kind of candy bar.

The OA is C

[swerve]

Let us assume
chocolate bar \(= c\); toffee bar \(= t\)
Package of chocolate bar \(= Pc\); Package of toffee bar \(= Pt\)

As per question:
\(Pc = 2c;\, Pt = 2t\)

1) \(Pc = Pt - 1\) (1 package \(=\) 2 toffee bar)
\(\Rightarrow\, 2c = 2t - 2\)
\(\Rightarrow\, c = t -1 \,\cdots \text{eq}\, 1\)

Not Sufficient since we can not find the packages of chocolate bar (\(Pc\))

2) \(\Rightarrow\, \frac{2}{3}c = \frac{3}{5}t\)
\(\Rightarrow\, 10c = 9t \,\cdots \text{eq}\, 2\)

Not Sufficient since we can not find the packages of chocolate bar (\(Pc\))

\(1 + 2\)

\(\Rightarrow\,\) two variable and two equation, we will get the value of \(c\), and \(Pc = 2c\), so sufficient; Answer \(\Rightarrow\) __C__