A and B are two partially filled buckets of water. If 5

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

A and B are two partially filled buckets of water. If 5

by BTGmoderatorDC » Fri Jul 20, 2018 9:57 pm

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A and B are two partially filled buckets of water. If 5 liters are transferred from A to B, then A would contain one-third of the amount of water in B. Alternatively, if 5 liters are transferred from B to A, B would contain one-half of the amount of water in A. Bucket A contains how many liters of water?

A. 11
B. 13
C. 17
D. 21
E. 23

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Source: Beat The GMAT — Problem Solving | Fri Jul 20, 2018 9:57 pm

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by [email protected] » Sat Jul 21, 2018 12:00 pm

Hi All,

We're told that A and B are two partially filled buckets of water; if 5 liters are transferred from A to B, then A would contain one-third of the amount of water in B, but if 5 liters are transferred from B to A, then B would contain one-half of the amount of water in A. We're asked for the number of liters of water in Bucket A. This question can be solved in a couple of different ways, including by TESTing THE ANSWERS.

Let's TEST Answer B: 13 liters
IF.... Bucket A currently holds 13 liters of water...
then transferring 5 liters from A to B would leave 13-5 = 8 liters in Bucket A
and A would contain 1/3 of the amount in B, so B would equal 24 liters.
Thus, A STARTED with 13 liters and B STARTED with 24 - 5 = 19 liters
Transferring 5 liters from B to A would give us...
19 - 5 = 14 liters in Bucket B
13 + 5 = 18 liters in Bucket A
The amount in B is NOT exactly 1/2 of what is in Bucket A, so this is NOT the correct answer. There are two ways to 'fix' this issue: either decrease the starting amount in Bucket B or increase the starting amount in Bucket A. Increasing the amount in Bucket A would lead to a significant increase in the starting amount in Bucket B though (after transferring 5 liters from A to B, Bucket A ends up having 1/3 of the amount in Bucket B), so it's likely that we need to DECREASE the starting amount in Bucket A...

Let's TEST Answer A: 11 liters
IF.... Bucket A currently holds 11 liters of water...
then transferring 5 liters from A to B would leave 11-5 = 6 liters in Bucket A
and A would contain 1/3 of the amount in B, so B would equal 18 liters.
Thus, A STARTED with 11 liters and B STARTED with 18 - 5 = 13 liters
Transferring 5 liters from B to A would give us...
13 - 5 = 8 liters in Bucket B
11 + 5 = 16 liters in Bucket A
Bucket B now holds EXACTLY 1/2 of what is in Bucket A. This is an exact match for what we were told, so this MUST be the answer!

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8085; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

hi

by Scott@TargetTestPrep » Tue Apr 23, 2019 6:39 pm

BTGmoderatorDC wrote:A and B are two partially filled buckets of water. If 5 liters are transferred from A to B, then A would contain one-third of the amount of water in B. Alternatively, if 5 liters are transferred from B to A, B would contain one-half of the amount of water in A. Bucket A contains how many liters of water?

A. 11
B. 13
C. 17
D. 21
E. 23

We can let a = the amount of water, in liters, in bucket A and b = the amount of water, in liters, in bucket B. We can create the equations:

a - 5 = (1/3)(b + 5)

and

b - 5 = Â½(a + 5)

Multiplying the first equation by 3 and the second by 2, we have:

3a - 15 = b + 5

and

2b - 10 = a + 5

Isolating b in the first equation, we have b = 3a - 20. Substituting this into the second equation, we have:

2(3a - 20) - 10 = a + 5

6a - 40 - 10 = a + 5

5a = 55

a = 11

Answer: A

Scott Woodbury-Stewart
Founder and CEO
[email protected]