GMAT Questions Chat Group

Pipe A and B can fill a tank alone in 48 hours and 24 hours respectively. Another Pipe C can empty the same tank alone in 36 hours. In an empty tank for the first hour, Pipe A is opened alone, second hour pipe B is opened alone, third hour pipe C is opened alone. This process is continued until the tank is filled. Then Pipe B is opened for how many hours?

Can anyone please solve it?

It’s my exam tomorrow.
Any last moment tips ?

About the initial questions or time management ? Any tips would be useful .

Given: Pipe
A fills the tank alone in 48 hours.
Pipe B fills the tank alone in 24 hours.
Pipe C empties the tank alone in 36 hours.

In the first hour,only Pipe A is opened, so it fills 1/48th of the tank.
In the second hour, only Pipe B is opened, so it fills 1/24th of the tank.
In the third hour, only Pipe C is opened, so it empties 1/36th of the tank.

We can observe that in the first three hours, the net amount of water filled in the tank is:
1/48 - 1/24 - 1/36 = (1/48) - (2/48) - (3/48) = -4/48 = -1/12

Since the tank is initially empty, the net amount of water in the tank after the first three hours is negative, which means the tank is not filled yet. Let’s assume that after x hours, the tank is filled.

We can write the equation as: (x/48) - (x/24) - (x/36) = 1

Simplifying the equation, we get: (3x - 6x - 4x) / (48 * 24 * 36) = 1 -7x / (48 * 24 * 36) = 1
Solving for x, we get: x = -48 * 24 * 36 / 7

Since x represents the number of hours, it cannot be negative.

Therefore, we can ignore the negative sign and calculate the value of x as: x = 48 * 24 * 36 / 7 = 82971.4286 hours

Since x represents the number of hours, it cannot be in decimal form.

Therefore, we round it up to the nearest whole number, which is 82972 hours.

To find the number of hours Pipe B is opened, we subtract the first three hours from the total time: 82972 - 3 = 82969 hours Therefore, Pipe B is opened for 82969 hours, which is equivalent to 28 hours and 10 minutes.

Don’t miss answering the last questions. There’s penalty for it.

Go as relaxed as u can.

Getting first few questions correct is really important. It can make or break your score.

Assume total work to be 144 units.
That means -
A fills up 3 units in 1 hour.
B fills up 6 units in 1 hour.
C empties 4 units in 1 hours.
In the first 3 hours, 3+6-4 = 5 units of water filled.
That means 5 units of work done in first shift.
How many shifts like this do we require? The answer is 144/5 = 28.8 hours.

To get accurate answer in minutes - 140 units will be done in 28 hours, that means in the next shift’s first hour will be for A, that js 3 units done. Total 143 units done, 1 unit remains, this 1 unit has to be completed by B, if B does 6 units in 1 hour, it will do 1 unit in 10 minutes. Hence, final answer - 28 hours 10 minutes.

I think at the 81st hour the number of units which were left will be 9. and then A will contribute 3 units and B will be contribute 6 units, thereby making the tank filled at the 28th hr of operation of B

Answer should be 28

But which one is correct?

28 or 28 hours 10 mins

The options won’t probably include both. But if they do, i think 28 hours 10 minutes is accurate.

Think of it like this, at the 28th hour of operation the tank would be filled, therefore the process will stop.

At the completion of 28th hour, the total units filled would be 140 (assuming 144 total units of work in the beginning). 4 units would still be left to be filled, out of which, 3 units will be filled up by A in 1 extra hour, and 1 last unit will be filled up by B in 10 minutes.

Please
I didn’t understand how you solve this question

X^9-X ^7 >0

Why you choose to work with 1/X^9 - 1/X^7 instead and select-2 as result

I think the Question is x^(-9) - x^(-7).... Probably those negative signs in the powers didn’t load while taking the screenshot. That explains the gap too between x and 9 & x and 7

which-of-the-following-is-a-value-of-x-for-which-414715.html

hi

can someone explain this
a-10-kilogram-soil-mixture-containing-30-percent-sand-and-70-percent-424151.html

You have a 10 kg mixture in which 30% is sand and 70% is Humus (not to be confused with Hummus...LOL). This means, you have 3 kg Sand and 7 kg Humus.

The task at hand is to remove some of the mixture and replace it with pure sand, such that we (A) Still have a 10 kg mixture AND (B) Have Sand and Humus in a 50% ratio, i.e., have 5 kg of each.

Basically, it boils down to how much mixture will you replace with same amount of pure sand such that your sand becomes 5 kg (from 3 kg).

Now, let’s say you remove “x” kg of the mixture and replace it with “x” kg of pure sand. We had 3 kg sand. We have added “x” kg sand to it. So now we have (3 + x) kg sand. Also, we have removed “x” kg mixture out during the replacement. This “x” kg mixture contains what? 30% sand and 70% humus......This means, in that “x” kg mixture we have removed, 30% of x = 0.3*x kg was sand.

So all in all, from our 3 kg initial sand, we have added “x” kg sand but removed “0.3*x” kg sand. And why? So that we can have 5 kg sand in total.

Mathematically,

3 + x - 0.3*x = 5
Gives, x = 20/7 ~ 2.9 kg

ALSO, there is a direct way of doing this, which may seem confusing.
Instead of equating sand, we can equate humus. This reduces one step (of adding fresh sand!)

Old humus = 7 kg
New humus = 5 kg

Difference = 2 kg
This is (2/7) of the original humus that needs to be removed from the 10 kg mixture.
So, total mixture removed is (2/7)*10 = 20/7 ~ 2.9 kg

This method may seem confusing and easy to mess up if you don’t understand it well enough. The first one is pretty good and can be easily done under 2 minutes.

how do we know A is the 5% account? Couldn't it be that A is the 3% account but that it collected twice as much interest bc much more money was placed in A than B?

Hey.....I have just started with GMAT.....can anyone please help me with if there is any books/study materials which I can refer for Quant?

if you are starting from scratch, i would recommend to try ttp or e-gmat trial and buy them later if you find useful

if you think you are good with basics, gmat ninja’s playlist and problem solving from forum! expert’s solutions teach you a lot