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Rasheed bought two kinds of candy bars, chocolate and toffee, that cam

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Rasheed bought two kinds of candy bars, chocolate and toffee, that cam [#permalink]

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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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: http://gmatclub.com/forum/rasheed-bough ... 29470.html
[Reveal] Spoiler: OA

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Re: Rasheed bought two kinds of candy bars, chocolate and toffee, that cam [#permalink]

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New post 08 Apr 2011, 10:58
Statement 1 INSUFFICIENT
Rasheed could of buy 10 packages of toffee bars and 9 packages of chocolate bars
or 25 packages of toffee bars and 24 packages of chocolate bars.

Statement 2 INSUFFICIENT
9 packages of chocolate bars, 2 bars in each package totals 18 bars. 2/3 x 18 = 12
10 packages of toffee bars , 2 bars in each package totals 20 bars 3/5 x 20 = 12
(Rasheed gives out the same number of each bar)
However, if we double the number of chocolate and toffee bars the statement remains true.

BOTH STATEMENTS : SUFFICIENT
Rasheed bought 9 packages of chocolate bars

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Re: Rasheed bought two kinds of candy bars, chocolate and toffee, that cam [#permalink]

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New post 08 Apr 2011, 11:02
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Krupa2 wrote:
Data Sufficiency

Rasheed bought 2 kinds of candy bars, chocolate and toffee, that came in packages of 2 bars each. He handed out 2/3 rd of the chocolate bars and 3/5 th 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.


Good question!!!

Let's consider Rasheed bought "C" chocolate bars' packages and "T" toffee bars' packages.

Total Chocolate bar = 2C
Total Toffee bar = 2T

Total Candy bars = 2(C+T)
Total Candy Bars Handed out = (2/3)*(2C)+(3/5)*(2T) = (4/3)C+(6/5)T

This tells us that total chocolate bars' packages were a multiple of 3 and toffee bars' packages were multiple of 5.
This also tells us that total chocolate bars were a multiple of 4 and toffee bars were multiple of 6.

Q: C = ?

1. Rasheed bought 1 fewer package of chocolate bars than toffee bars
C = T-1
C - T = -1

C can be 9, T=10
C can be 24, T=25
C can be 39, T=40

Not Sufficient.

2. Rasheed handed out the same number of each kind of candy bar.
(4/3)C = (6/5)T
20C=18T
10C=9T

C can be 9, T=10
C can be 18, T=20
C can be 27, T=30
Not Sufficient.

Combining both:
10C -10T = -10
10C -9T = 0
----------------
T=10
C=9.

Sufficient.

Ans:"C"
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Re: Rasheed bought two kinds of candy bars, chocolate and toffee, that cam [#permalink]

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New post 08 Apr 2011, 18:18
C - Chocolates Bar

T - Toffee

So C + T = ?

He gave out - 2/3 * C * 2 = 4C/3

and 3/5 * T * 2 = 6T/5


(1)
C = T - 1

which is not sufficient

(2) 4C/3 = 6T/5

=> C = 9T/10

This is also not sufficient as we'll get only a ratio

(1) and (2) together :

9T/10 + 1 = T

=> 10T = 9T + 10
=> T = 10

and C = 9

So C + T = 19

Answer - C

Of course we don't need to find the value of C + T.
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Re: Rasheed bought two kinds of candy bars, chocolate and toffee, that cam [#permalink]

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New post 08 Apr 2011, 19:32
from 2) 2/3C=3/5T
=> 10 C = 9 T
Not sufficient - above represents total number i.e 2 times x no of boxes

From 1) C/2 = T/2 -1
Not sufficient.

From above, both are sufficient to determine.
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Re: Rasheed bought two kinds of candy bars, chocolate and toffee, that cam [#permalink]

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New post 21 Feb 2012, 05:36
I had the same question in the GMAT Prep.

(1) not sufficient, as 10 to 9 solution possible as well as 25 to 24 solution
(2) not sufficient, as 9 (respective 10) hand out 12 bars each, if doubled equally again

--> only 10 respective 9 packages are possible if combined!

"C"

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Re: Rasheed bought two kinds of candy bars, chocolate and toffee, that cam [#permalink]

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New post 23 Nov 2017, 23:32
Krupa2 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 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.



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 chocolates bar did Rasheed buy?

Let C be # of packages of chocolate bars and T be # of packages of toffee bars. Rasheed handed out 2/3*2C of the chocolate bars and 3/5*2T of the toffee bars. Question: C=?

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

(2) Rasheed handed out the same number of each kind of candy bar --> 2/3*2C=3/5*2T, two variables one equation. Not sufficient.

(1)+(2) We have two distinct equations and two variables, hence we can solve for them. Sufficient.

Answer: C.

OPEN DISCUSSION OF THIS QUESTION IS HERE: http://gmatclub.com/forum/rasheed-bough ... 29470.html
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Re: Rasheed bought two kinds of candy bars, chocolate and toffee, that cam   [#permalink] 23 Nov 2017, 23:32
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