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)
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more than x minutes
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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. 
Nevertheless, like explained previously here, plugging in the right numbers can come only with practice. Working on applying plugging numbers.
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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willrc
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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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rajeshsinghgmat
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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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jaspreetsra
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nikhilgmat31
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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
