Speed when both pipes work together = 1/x
Speed A alone = 1/(x+a)
Speed B alone = 1/(x+b)
1/(x+a)+1/(x+b) = 1/x
x = sqrt(ab)
more than x minutes
- ronnie1985
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Started with the work formula and realized it might get messy. So plugged in values and did not choose the best values. Eventually ended up with D but took way above 2 mins. ![Sad :(](./images/smilies/sad.png)
Nevertheless, like explained previously here, plugging in the right numbers can come only with practice. Working on applying plugging numbers.
![Sad :(](./images/smilies/sad.png)
Nevertheless, like explained previously here, plugging in the right numbers can come only with practice. Working on applying plugging numbers.
My attempt to capture my B-School Journey in a Blog : tranquilnomadgmat.blocked
There are no shortcuts to any place worth going.
There are no shortcuts to any place worth going.
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This is a parallel rates question, so we need to find the rates and add them. Tables help with these by providing a scaffold:
W(ork) = R(ate) x T(ime)
Both pipes 1 = ? x
->1/x
A alone 1 ? x+a
->1/(x+a)
B alone 1 ? x+b
->1/(x+b)
Then we have a bit of algebra to do. We know the both pipes speed is equal to the sum of the others, so:
1/x = 1/(x+a) + 1/(x+b)
Multiply through by all the denominators:
(x+a)(x+b) = x(x+b) + x(x+a)
Distribute:
x^2 + (a+b)x + ab = x^2 + bx + x^2 + ax
ax + bx + ab = x^2 + ax + bx
x^2 = ab
x = sqrt(ab)
W(ork) = R(ate) x T(ime)
Both pipes 1 = ? x
->1/x
A alone 1 ? x+a
->1/(x+a)
B alone 1 ? x+b
->1/(x+b)
Then we have a bit of algebra to do. We know the both pipes speed is equal to the sum of the others, so:
1/x = 1/(x+a) + 1/(x+b)
Multiply through by all the denominators:
(x+a)(x+b) = x(x+b) + x(x+a)
Distribute:
x^2 + (a+b)x + ab = x^2 + bx + x^2 + ax
ax + bx + ab = x^2 + ax + bx
x^2 = ab
x = sqrt(ab)
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Hi, great eplanation.harshavardhanc wrote:Gmatmachoman..buddy, I know you are very experienced on this forum and I think you have a strong prep too.gmatmachoman wrote:heheheh!! U logic wont work bro....Try for other values of X where a is not equal to b...harshavardhanc wrote:since this relation is a generic one, it should be satisfied by all the values.sanju09 wrote:If two pipes A and B together can fill a cistern in x minutes and if A alone can fill it in a minutes more than x minutes and B alone can fill it in b minutes more than x minutes, then what is x equal to?
(A) √ (a^2 + b^2)
(B) √ (a^2 - b^2)
(C) a b
(D) √ (a b)
(E) a b - a^2 - b^2
Let's take equal and simple values, and then go about it.
let A and B each fill the cistern in 4 mins. therefore, together they will take half the time , i.e. 2 mins to fill the cistern.
according to the question X= 2, a=2, b=2
put the values, check for correctness.
Only the straight method wrks as posted by @truplayer256.
But, this CR has made me so adamant that I cannot take a plain no. I need solid reasoning for any argument.
now coming to my previous response, there is NO logic involved in my first post. None at all.
it's like saying : if you have an equation of line as X+Y = 2, sum of every set of value on this line will be 2 . Simple.
Now let me show you how this is true. I'll take some difficult numbers, calculation verification for which is left to you .
Let A take 4 mins to fill the cistern and B take 5 mins. So working together, they well take 20/9 mins to fill the cistern
Hence, per the question 'a' becomes 4-(20/9) = (16/9) and 'b' becomes 5-(20/9) = 25/9
therefore X = 20/9 = sqrt( 16/9 * 25/9)
no option other than D will give you the correct answer.
plugging in the values ALWAYS works. Sometimes it gives two probable answers. You then need to take another set which eliminates the wrong choice.
I just didn' catch this passage "Hence, per the question 'a' becomes 4-(20/9) = (16/9) and 'b' becomes 5-(20/9) = 25/9" . Why you get 'a' by subtracting the fraction, since we already have a?
Thank you
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1/ x = 1(x+a) +1/(x+b)
x^2 + ax + bx + ab = (x+b + a + x ) x
x^2 + ax + bx + ab = x^2+bx + ax + x^2
ab = x^2
x = sqrt ( ab)
Answer D
x^2 + ax + bx + ab = (x+b + a + x ) x
x^2 + ax + bx + ab = x^2+bx + ax + x^2
ab = x^2
x = sqrt ( ab)
Answer D