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chocolate and toffee candy bars

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chocolate and toffee candy bars

by lukaswelker » Tue Apr 01, 2014 12:54 am
Might sounds delicious, but the headache is far from pretty :)

Here comes the question;

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.

I can't see how both of the data combined are sufficient. Let me know if you can
Many thanks
Lukas
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Source: — Data Sufficiency |
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by GMATGuruNY » Tue Apr 01, 2014 2:29 am
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 bars.
If we know the number of chocolate BARS that were purchased, we can determine the number of chocolate bar PACKAGES that were purchased, since each package contains 2 bars.
Let c = the number of chocolate bars purchased and t = the number of toffee bars purchased.
Question rephrased: What is the value of c?

Statement 1: Rasheed bought 1 fewer package of chocolate bars than toffee bars.
Since each package contains 2 bars, the number of chocolate bars purchased is 2 less than the number of toffee bars purchased.
c = t - 2.
No way to solve for c.
INSUFFICIENT.

Statement 2: Rasheed handed out the same number of each kind of candy bar.
Thus, the 2/3 of the chocolate bars handed out are equal to the 3/5 of the toffee bars handed out:
(2/3)c = (3/5)t.
10c = 9t.
No way to solve for c.
INSUFFICIENT.

Statements combined:
Since we have 2 variables (c and t) and 2 distinct linear equations (c = t-2 and 10c = 9t), we can solve for each variable and thus determine the value of c.
SUFFICIENT.

The correct answer is C.

One way to solve:
c = t-2
9c = 9t - 18
9c + 18 = 9t.

Since 9c + 18 = 9t and 9t = 10c, we get:
9c + 18 = 10c
c = 18.

Since 18 chocolate bars are handed out, and each package contains 2 bars, the number of packages of chocolate bars = 9.
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