Rasheed bought two kinds of candy bars, chocolate and toffee

[BTGmoderatorDC]

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 2/5 of the toffee bars. How many pachages of chocolate bars did Rasheed buy?

(1) Rasheed bought 2 fewer packages of chocolate bars than toffee bars.

(2) Rasheed handed out the same number of each kind of candy bar.

OA C

Source: GMAT Prep

[Jay@ManhattanReview]

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 2/5 of the toffee bars. How many pachages of chocolate bars did Rasheed buy?

(1) Rasheed bought 2 fewer packages of chocolate bars than toffee bars.

(2) Rasheed handed out the same number of each kind of candy bar.

OA C

Source: GMAT Prep

Say Rasheed bought x numbers of packages of chocolate bars and x numbers of packages of toffee bars.

He handed out 2/3 *2x numbers of chocolate bars and 2/5 * 2y numbers of toffee bars.

We need the value of x.

(1) Rasheed bought 2 fewer packages of chocolate bars than toffee bars.

x = y - 1. Insufficient.

(2) Rasheed handed out the same number of each kind of candy bar.

=> 2/3 *2x = 2/5 * 2y

x/3 = y/5. Insufficient.

(1) and (2) together

From x/3 = y/5 and x = y - 1, we get

(y - 1)/3 = y/5

y = 5, thus x = 4 Sufficient.

The correct answer: C

Hope this helps!

-Jay
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[GMATGuruNY]

I believe that the problem has been transcribed incorrectly.
Statement 1 should indicate that Rasheed bought not 2 fewer packages but only 1 fewer package, as shown in the following screen shot:



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.