equation for stataement 2?

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ildude02: Master | Next Rank: 500 Posts; Posts: 320; Joined: Sun Jan 13, 2008 10:00 pm; Thanked: 10 times

by ildude02 » Fri Jul 11, 2008 1:45 pm

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

1. The bucket currently contains 9 lit of water.
2.If 3 lit 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.

I picked the answer as B by reducing it to the foll equation, but I'm not sure if that's right equation for the stataemnt 2. Can someone help me reduce the statement 2 ina equatin format.

My equation was, if x was max capticty of the bucket,

then x/2 + 3 = 4/3x; but I'm not sure if 4/3x is the correct value representing "amount of water increased by 1/3"

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Source: Beat The GMAT — Data Sufficiency | Fri Jul 11, 2008 1:45 pm

dsk: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Fri Jun 13, 2008 12:21 pm; Thanked: 1 times

by dsk » Fri Jul 11, 2008 2:16 pm

I would take the second statement as --> adding 3 liters increases the content 1/3 times what is in it which is (1/2)x where x is the total capacity..(since statement says bucket is half full)

so 3 = (1/3)*(1/2)x
x= 18

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ildude02: Master | Next Rank: 500 Posts; Posts: 320; Joined: Sun Jan 13, 2008 10:00 pm; Thanked: 10 times

by ildude02 » Fri Jul 11, 2008 6:31 pm

The OG 11 explanation has it as x + 3 = 4/3(1/2)*x
that is, x + 3 = (2/3)x; I didnt quite understand the logic.

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rey.fernandez: GMAT Instructor; Posts: 83; Joined: Sun Mar 02, 2008 9:05 pmFollowed by: 2 members; Thanked: 21 times

by rey.fernandez » Sat Jul 12, 2008 12:37 am

Statement (2):

If x is the capacity of the bucket, then x/2 is the current amount of water in the bucket.

x/2 + 3 represents adding three gallons to the current amount.

Increasing the current amount (x/2) by 1/3 is equivalent to multiplying the current amount (x/2) by 4/3, or x/2*4/3.

Equating these two, we get x/2 + 3 = x/2*4/3

In your original post, you multiplied the total capacity (x) by 4/3 instead of the current amount (x/2).

Rey Fernandez
Instructor
Manhattan GMAT

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ildude02: Master | Next Rank: 500 Posts; Posts: 320; Joined: Sun Jan 13, 2008 10:00 pm; Thanked: 10 times

by ildude02 » Sun Jul 13, 2008 7:33 am

Thanks for your response. One question in general I have is, whenever we see a fraction of an increase or a question saying fraction more, do we need to consider it as "fraction of the original".

Eg; If x is 3 more then y; Here, x = y +3;
If x is 1/3 more then y, do we say x= y +1/3y = 4/3y. Are there any exceptions for this rule?

Appreciate your response.

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