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Suppose you have access to a large vat of distilled water, several gal

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Bunuel
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Suppose you have access to a large vat of distilled water, several gal [#permalink] New post   11 Mar 2015, 04:39
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Suppose you have access to a large vat of distilled water, several gallons large. You have two precise measuring pipettes, one to measure exactly 1/3 of an ounce and one to measure exactly 1/4 of an ounce. You can pour precisely measured amounts into a beaker, which initially is empty. You can use either pipette to remove distilled water from the vat or from the beaker and use either pipette to dispense water into either of those receptacles, but you cannot use either pipette to take any quantity of distilled water other than the amount for which it is designed. Which of the following represents, in ounces, a precise amount of distilled water you can transfer from the vat to the beaker?

I. 1/6
II. 1/7
III. 1/12

A. I only
B. III only
C. I and III only
D. II and III only
E. I, II, and III

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C
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Re: Suppose you have access to a large vat of distilled water, several gal [#permalink] New post   11 Mar 2015, 08:26
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Basically you can have two measures 1/4 and 1/3. Now you can get combinations of 1/3 an 1/4 so if you take 1/3 and then take 1/4 of that you get 1/3-1/4 = 1/12
if you do that two times you get 1/6 however 7 being prime we cannot get that 1/7 ratio . Hence answer is C.
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Re: Suppose you have access to a large vat of distilled water, several gal [#permalink] New post   11 Mar 2015, 11:21
Hi

what i did here is a check for feasible denominators for the transferred solution to empty jar as after that solution
can be taken out to make the numerator 1. This approach seems easy to me.

Let's say 1/3 + 1/3 + 1/4 =7/12 >> So iii is in.

Now add 1/3 + 1/4 + 1/4 = 5/6 >> so i is in

dr's no way you are getting a 7 in the denominator . So answer is C

Now You'll be confused how to get rid of the numerator, It is not necessary to answer the question but still lets consider the following scenarios

For 5/6
to make it 1/6 we have to subtract something

Let's say 5/6 - X = 1/6 >> X = 2/3

2/3 = 1/3 +1/3 >> take out 1/3 two times
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Re: Suppose you have access to a large vat of distilled water, several gal [#permalink] New post   11 Mar 2015, 16:26
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Bunuel wrote:
Suppose you have access to a large vat of distilled water, several gallons large. You have two precise measuring pipettes, one to measure exactly 1/3 of an ounce and one to measure exactly 1/4 of an ounce. You can pour precisely measured amounts into a beaker, which initially is empty. You can use either pipette to remove distilled water from the vat or from the beaker and use either pipette to dispense water into either of those receptacles, but you cannot use either pipette to take any quantity of distilled water other than the amount for which it is designed. Which of the following represents, in ounces, a precise amount of distilled water you can transfer from the vat to the beaker?

I. 1/6
II. 1/7
III. 1/12

A. I only
B. III only
C. I and III only
D. II and III only
E. I, II, and III

Kudos for a correct solution.


Looking at the potential answer choices, 1/7 is immediately out as 7 is a prime that cannot be created from either 4 or 3.
1/3-1/4=1/12 Choice III works
1/12+1/12=2/12 Choice I works

Answer: C
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Re: Suppose you have access to a large vat of distilled water, several gal [#permalink] New post   11 Mar 2015, 18:41
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the answer is C .

we can get 1/6 from 1/3-1/4=4/12-4/12 = 1/12 ok

if we repeat this same procedure so we will transfer another 1/12 and we will get 2/12=1/6
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Re: Suppose you have access to a large vat of distilled water, several gal [#permalink] New post   15 Mar 2015, 21:25
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Bunuel wrote:
Suppose you have access to a large vat of distilled water, several gallons large. You have two precise measuring pipettes, one to measure exactly 1/3 of an ounce and one to measure exactly 1/4 of an ounce. You can pour precisely measured amounts into a beaker, which initially is empty. You can use either pipette to remove distilled water from the vat or from the beaker and use either pipette to dispense water into either of those receptacles, but you cannot use either pipette to take any quantity of distilled water other than the amount for which it is designed. Which of the following represents, in ounces, a precise amount of distilled water you can transfer from the vat to the beaker?

I. 1/6
II. 1/7
III. 1/12

A. I only
B. III only
C. I and III only
D. II and III only
E. I, II, and III

Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:

If you fill the 1/3 oz pipette and put this into the beaker. Then use the other pipette to remove 1/4 oz from the beaker. This 1/4 oz can be put back in the vat.
1/3 - 1/4 = 1/12.

Thus, there would be 1/12 oz left in the beaker: that’s the amount that would have been transferred from the vat to the beaker.

If we repeat this same procedure, we will transfer another 1/12 oz from the vat to the beaker, and 2/12 = 1/6. Therefore, we could transfer either 1/12 or 1/6 from the vat to the beaker.

There is no way to transfer 1/7 to the beaker. No combination of arithmetic involving 1/3 and 1/4 will produce 1/7.

Answer = (C).
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Re: Suppose you have access to a large vat of distilled water, several gal [#permalink] New post   02 Apr 2016, 19:31
Bunuel wrote:
Suppose you have access to a large vat of distilled water, several gallons large. You have two precise measuring pipettes, one to measure exactly 1/3 of an ounce and one to measure exactly 1/4 of an ounce. You can pour precisely measured amounts into a beaker, which initially is empty. You can use either pipette to remove distilled water from the vat or from the beaker and use either pipette to dispense water into either of those receptacles, but you cannot use either pipette to take any quantity of distilled water other than the amount for which it is designed. Which of the following represents, in ounces, a precise amount of distilled water you can transfer from the vat to the beaker?

I. 1/6
II. 1/7
III. 1/12

A. I only
B. III only
C. I and III only
D. II and III only
E. I, II, and III

Kudos for a correct solution.



The question is a nightmare..takes a lot of time to just simply read the question stem..even more is needed to comprehend it..
we can take 1/3 and pour from 1/3 to 1/4, and we are left with 1/3-1/4 = 1/12
so III is definitely true. A is out.
now..
we can pour this 1/12 into the beaker, and repeat the process. we get with another 1/12
we pour it again into the beaker
now, from the beaker we can take 2/12 or 1/6. so I is an answer. B and D are out.

1/7 - we can't get in any way, as 7 is not a multiple of 3 and 4 nor a factor of LCM of 3 and 4, so C is the answer.
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Re: Suppose you have access to a large vat of distilled water, several gal [#permalink] New post   14 Jan 2024, 04:02
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Re: Suppose you have access to a large vat of distilled water, several gal [#permalink]
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