Question: 3 Flasks

Comment on 3 Flasks

I did find the solution in another way. I multiplied 1/6 from flask one by 1/2 and 1/8 from flask two by half. Then I summed up the both fractions 1/12 from flask one and 1/16 from flask two to get 1/6. Is this a correct way of doing it?
greenlight-admin's picture

Unfortunately, that approach is incorrect; it just happened to work with the numbers given in the question.
If we were to change the question so that one flask was 1/6 full, one flask was 1/7 full, and one flask was 1/12, the correct answer would still be 1/6. However, your approach would yield an incorrect answer.

you mentioned in other video that
bigger denominator = small value(as whole)and vice versa then here how did you take 1/6 and 1/8 as a smallest flasks and 1/12 as largest? 1/6 = 0.167, 1/8 = 0.125,
1/12 = 0.8333 doesn't that make 1/6 largest and 1/6 and 1/8 smallest?
greenlight-admin's picture

Those examples (from https://www.greenlighttestprep.com/module/gre-arithmetic/video/1067) is different from this question.

In that other video lesson, I say that 113/400 is greater than 113/401, because the denominator 400 is less than the other denominator (401).

When we compare the 3 flasks (which are 1/12 full, 1/8 full and 1/6 full), we aren't comparing fractions. We are trying to determine which flask has the greatest capacity.

Think of it this way: If I pour a can of soda into a large glass, the glass becomes 1/2 full. If I pour a can of soda into an empty swimming pool, the pool becomes 1/100,000 full. Which has a greater CAPACITY? The glass or the pool.

Here's a mathematical way to look at it:

Keep in mind that the 3 flasks each contain an equal volume of water. So, let's just focus on two flasks and let:
A = the capacity of the flask that is 1/12 full
B = the capacity of the flask that is 1/8 full

Since both flasks contain an equal volume of water, we can write: 1/12 of A = 1/8 of B
In other words: (1/12)A = (1/8)B
Expand: A/12 = B/8
Cross multiply to get: 8A = 12B
Divide both sides by 8 to get: A = (3/2)B
In other words, A = 1.5B
In other words, the capacity of A is 1.5 TIMES the capacity of B.
In other words, flask A has a greater capacity than flask B.

Does that help?

How are you able to label the values inside the flask as "x", if each x value (1/6 and 1/8, respectively) is different?
greenlight-admin's picture

x = the VOLUME of water that's initially poured into each flask.

We're told that "EQUAL volumes of water were poured into the 3 empty flasks," so we can use the variable x to describe the VOLUME of water in each flask.

"if 1/2 of the water from each of the two smallest flasks..." This section of the problem led me to the wrong pathway to solve it because it should be made clear that the value to be taken out of the two flasks is 1/2 of the initial volume that was poured into each one. Following the quoted instructions, it allows for the interpretation that 1/2 of the water from each flask's capacity is to be taken... which wouldn't be a value of 1/2(x) as it explains in the video. For the 1/8 flask it is, in my judgement, instructing me to pour water into the largest flask so that it will be left 1/16 full (half of 1/8). This was a challenging problem, but the wording can be improved.
greenlight-admin's picture

I'm not sure I agree with the assessment that "it allows for the interpretation that 1/2 of the water from each flask's capacity is to be taken"

The instructions say "Then 1/2 of the water from each of the two smallest flasks is then poured..."

Since we're removing half of the water, the flask's capacity doesn't really come into play.

That said, we can agree to disagree :-)

Hi, This is how I solved it.

I assumed volume in each flask is 2 (easy number)
So total volumes of each of the flasks must be - 12,16 and 24 respectively.

Then as half the water from two of the smallest flasks go to the largest - 1 and 1 is removed. And volume of largest flask become 4.

Finally, 4/24 = 1/6.

Is this a fine approach?
greenlight-admin's picture

Excellent approach!

How did SSS get the values 12 16 and 24
greenlight-admin's picture

SS started by saying each flask contained 2 units of water.

We're told that the first flask is 1/6 full.
So, the CAPACITY of the first flask must be 12 units (since 2/12 = 1/6)

We're also told that the second flask is 1/8 full.
So, the CAPACITY of the second flask must be 16 units (since 2/16 = 1/8)

Finally, we're told that the third flask is 1/12 full.
So, the CAPACITY of the second flask must be 24 units (since 2/24 = 1/12)

Does that help?

Cheers,
Brent

I did the exact measure, and was real quick in getting to the answer. I assumed the number 24 though, as a LCM.
greenlight-admin's picture

Perfect!

Hi Brent,
For this could please help me in understanding the half water removal and adding it into large flask
how did she get 4/24

and also in the video at last how you told that it got doubled.

Thanks
greenlight-admin's picture

If we say each flack ORIGINALLY contains 2 units of water, then:

The CAPACITY of the smallest flask is 12 units (since 2/12 = 1/6)
The CAPACITY of the middle flask must be 16 units (since 2/16 = 1/8)
The CAPACITY of the largest flask must be 24 units (since 2/24 = 1/12)

At this point, we're told to pour HALF of the water from each of the two smaller containers into the largest container.

Since each flask originally contained 2 units of water, we will pour 1 unit of water from EACH of the two smaller containers.

So, 1 unit of water is poured from the smallest flask into the largest flask.
And 1 unit of water is poured from the middle flask into the largest flask.

Since we're adding 2 units of water to the largest flask (which ORIGINALLY contained 2 units of water), the largest flask now contains 4 units of water.

Does that help?

Cheers,
Brent

ss's method is easy and quick.
greenlight-admin's picture

Agreed!

Hi Brent,

I solved it as this : Since equal volumes were poured in all 3 flasks, taking 1/2 of water from other two flasks is equal to taking another 1/12 of water. So the largest flask now is filled with 1/12+1/12 = 1/6 water

Is this right approach ?

Thanks :)
greenlight-admin's picture

Perfect approach!

Where can i find similar questions like this to solve
greenlight-admin's picture

The question doesn't really belong to a specific category of questions.
I'd loosely place it in the family of general word problems.
You will find general word problems in the Reinforcement Activities boxes of the following videos:
- https://www.greenlighttestprep.com/module/gre-word-problems/video/902
- https://www.greenlighttestprep.com/module/gre-word-problems/video/903
- https://www.greenlighttestprep.com/module/gre-word-problems/video/907

Cheers,
Brent

This was my approach. I assumed that 4L of water was added to each flasks. So flask 1 got 4L of water, flask 2 got 4L of water, and flask 3 got 4L of water. Then, we were told that half of the water was removed from flask 1 and 2. So, 2L + 2L (4L) was removed from both flask 1 and 2. This 4L was added to flask 3, which already had 4L of water from before. Due to the original 4L of water, flask 3 became 1 / 12 full. Now since we add another 4L of water means that another 1 / 12 of space was taken by the added 4L. This 4L (1 / 12 capacity) + 4L (1 / 12 capacity)...1 / 12 + 1 / 12 = 1 / 6 full.
greenlight-admin's picture

That approach works perfectly - well done!

Cheers,
Brent

Can you help in solving this

Taylor earns $2,500more in 6 months than Pete. If Pete gets a 10% raise, their earnings would be equal for 6months. How much money does Pete earn a year?
greenlight-admin's picture

GIVEN: Taylor earns $2,500 more in 6 months than Pete.
Let P = the amount Pete makes in 6 months
So, P + 2500 = the amount Taylor makes in 6 months

GIVEN: If Pete gets a 10% raise, their earnings would be equal for 6 months.
After the 10% raise, the amount Pete earns = P + (10% of P)
= P + 0.1P
= 1.1P

This 10% increase makes their earnings EQUAL.
We can write: 1.1P = P + 2500
Subtract P from both sides: 0.1P = 2500
Solve: P = 2500/0.1 = 25,000

So, Pete presently earns $25,000 in 6 months

Cheers,
Brent

Thank you so much

I assumed that the other two flasks were equal in size to the largest flask, since the volume of water is equal in all three, it doesn't matter what size the flasks are. Now we have three flasks filled 1/12 of the way full. Now take half from two of the flasks and add it to the third. 1/24+1/24+2/24=4/24==> 1/6
greenlight-admin's picture

Totally valid approach - nice work!

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