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Marcia's bucket can hold a maximum of how many liters of wat

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Marcia's bucket can hold a maximum of how many liters of wat

by BTGmoderatorDC » Sat Dec 29, 2018 4:37 pm

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Marcia's bucket can hold a maximum of how many liters of water?

(1) The bucket currently contains 9 liters of water.
(2) If 3 liters of water are added to the bucket when it is half full of water, the amount of water in the bucket will increase by 1/3.

OA B

Source: Official Guide
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Source: — Data Sufficiency |
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by Manasa3190 » Sat Dec 29, 2018 7:34 pm

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1) Bucket can hold at least 9 liters of water, but doesn't give any info regarding the capacity of the bucket
Insufficient

2)Let x be the capacity of the Bucket
Given that Bucket contains x/2 liters
When 3 liters is added water content increased by 1/3
(x/2) + 3 = (x/2)*(1/3)
x/6 = 3
x = 18
Sufficient

So, B alone is sufficient
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by fskilnik@GMATH » Sun Dec 30, 2018 11:02 am

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BTGmoderatorDC wrote:Marcia's bucket can hold a maximum of how many liters of water?

(1) The bucket currently contains 9 liters of water.
(2) If 3 liters of water are added to the bucket when it is half full of water, the amount of water in the bucket will increase by 1/3.
Source: Official Guide
$$? = C\,\,\,\,\left[ {{\rm{capacity}}\,\,{\rm{in}}\,\,{\rm{liters}}\,\,{\rm{of}}\,\,{\rm{water}}} \right]$$
$$\left( 1 \right)\,\,9\,\,{\rm{liters}}\,\,\,\left\{ \matrix{
\,\,{\rm{full}}\,\,\, \Rightarrow \,\,\,{\rm{?}}\,\,{\rm{ = }}\,\,{\rm{9}}\,\, \hfill \cr
\,\,{\rm{not}}\,\,{\rm{full}}\,\,\, \Rightarrow \,\,\,{\rm{?}}\,\,{\rm{ > }}\,\,{\rm{9}}\,\, \hfill \cr} \right.\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{INSUFF}}.$$
$$\left( 2 \right)\,\,\,{C \over 2} + 3\,\, = \,\,\left( {1 + {1 \over 3}} \right){C \over 2}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,{C \over 2}\,\,{\rm{unique}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{SUFF}}{\rm{.}}$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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by Brent@GMATPrepNow » Sun Dec 30, 2018 11:04 am

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BTGmoderatorDC wrote:Marcia's bucket can hold a maximum of how many liters of water?

(1) The bucket currently contains 9 liters of water.
(2) If 3 liters of water are added to the bucket when it is half full of water, the amount of water in the bucket will increase by 1/3.

OA B

Source: Official Guide
Target question: Marcia's bucket can hold a maximum of how many liters of water?
In other words, what is the TOTAL CAPACITY of Marcia's bucket?

Statement 1: The bucket currently contains 9 liters of water.
Not enough info to determine the TOTAL CAPACITY of Marcia's bucket.
Since we cannot answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: If 3 liters of water are added to the bucket when it is half full of water, the amount of water in the bucket will increase by 1/3.
Let C = total capacity of bucket.
If the bucket is half full, then the volume of water = (1/2)C
We're told that adding 3 liters of water increases volume of water by 1/3
In other words, the 3 extra liters is equal to 1/3 of (1/2)C
We can write: 3 = (1/3)(1/2)C
Simplify: 3 = (1/6)C
So, C = 18
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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