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by fangtray » Sun May 13, 2012 2:53 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 bar
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Source: — Data Sufficiency |
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by sam2304 » Sun May 13, 2012 5:59 am
fangtray wrote: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
X chocolate, y = toffee

X = Y-1. Two unknowns and one eqn. INSUFF
2. Rasheed handed out the same number of each kind of candy bar
2/3*2*x = 3/5*2*y [multiply 2 on both sides - one package = 2 bars]
x/y = 9/10. We know the ratio alone but without any additional data we cannot find the individual values. INSUFF.

Using both we can solve for the values.

IMO C. Is it right ?
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by Mohitbhatia880 » Sun May 13, 2012 6:12 am
1. 1 fewer packages so first equation should be x/2 = y/2 - 1
2. (2/3)x = (3/5)y

Plug value of x from second equation to first equation and find y. Do not consider any outside information.
from 2: x = 9/10 y
after plug in, from 1: 9/10 *y/2 = y/2 - 1 .... solve it.

So C is suffice.
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by GmatKiss » Mon May 14, 2012 3:51 am
IMO: C, good one!
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by Anurag@Gurome » Mon May 14, 2012 4:01 am
fangtray wrote: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
Let the number of packages of chocolate bars = C
Number of packages of toffee bars = T
Rasheed handed out (2/3) * 2C of the chocolate bars and (3/5) * 2T of the toffee bars.

We have to find C.

(1) Rasheed bought 1 fewer package of chocolate bars than toffee bars implies C = T - 1, two variables one equation; NOT sufficient.

(2) Rasheed handed out the same number of each kind of candy bar implies (2/3) * 2C = (3/5) * 2T, there are two variables but one equation; NOT sufficient.

Combining (1) and (2), we have two equations and two variables, which can be solved for C; SUFFICIENT.

The correct answer is C.
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