more than x minutes

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Mon Mar 08, 2010 1:54 am

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) âˆš (a^2 + b^2)
(B) âˆš (a^2 - b^2)
(C) a b
(D) âˆš (a b)
(E) a b - a^2 - b^2

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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Source: Beat The GMAT — Problem Solving | Mon Mar 08, 2010 1:54 am

truplayer256: Master | Next Rank: 500 Posts; Posts: 392; Joined: Thu Jan 15, 2009 12:52 pm; Location: New Jersey; Thanked: 76 times

by truplayer256 » Mon Mar 08, 2010 5:24 am

1/(a+x)+1/(b+x)=1/x

(a+x)(b+x)/(a+b+2x)=x

ax+bx+2x^2=ab+ax+bx+x^2

x^2=ab

x=âˆšab

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harshavardhanc: Legendary Member; Posts: 526; Joined: Sat Feb 21, 2009 11:47 pm; Location: India; Thanked: 68 times; GMAT Score:680

by harshavardhanc » Mon Mar 08, 2010 6:01 am

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) âˆš (a^2 + b^2)
(B) âˆš (a^2 - b^2)
(C) a b
(D) âˆš (a b)
(E) a b - a^2 - b^2

since this relation is a generic one, it should be satisfied by all the values.

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.

Regards,
Harsha

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gmatmachoman: Legendary Member; Posts: 2326; Joined: Mon Jul 28, 2008 3:54 amFollowed by: 2 members; Thanked: 173 times; GMAT Score:710

by gmatmachoman » Mon Mar 08, 2010 6:12 am

harshavardhanc wrote:
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) âˆš (a^2 + b^2)
(B) âˆš (a^2 - b^2)
(C) a b
(D) âˆš (a b)
(E) a b - a^2 - b^2
since this relation is a generic one, it should be satisfied by all the values.

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.

heheheh!! U logic wont work bro....Try for other values of X where a is not equal to b...

Only the straight method wrks as posted by @truplayer256.

R&D on GMAT algorithm:

https://www.beatthegmat.com/r-d-on-gmat- ... tml#305739

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harshavardhanc: Legendary Member; Posts: 526; Joined: Sat Feb 21, 2009 11:47 pm; Location: India; Thanked: 68 times; GMAT Score:680

by harshavardhanc » Mon Mar 08, 2010 9:58 am

gmatmachoman wrote:
harshavardhanc wrote:
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) âˆš (a^2 + b^2)
(B) âˆš (a^2 - b^2)
(C) a b
(D) âˆš (a b)
(E) a b - a^2 - b^2
since this relation is a generic one, it should be satisfied by all the values.

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.
heheheh!! U logic wont work bro....Try for other values of X where a is not equal to b...

Only the straight method wrks as posted by @truplayer256.

Gmatmachoman..buddy, I know you are very experienced on this forum and I think you have a strong prep too.

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.

Regards,
Harsha

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gmatmachoman: Legendary Member; Posts: 2326; Joined: Mon Jul 28, 2008 3:54 amFollowed by: 2 members; Thanked: 173 times; GMAT Score:710

by gmatmachoman » Mon Mar 08, 2010 10:06 am

agreed Bro!!

Seems some Hitch in my statement!!

Apologies from my end bro!!

R&D on GMAT algorithm:

https://www.beatthegmat.com/r-d-on-gmat- ... tml#305739

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harshavardhanc: Legendary Member; Posts: 526; Joined: Sat Feb 21, 2009 11:47 pm; Location: India; Thanked: 68 times; GMAT Score:680

by harshavardhanc » Mon Mar 08, 2010 10:19 am

gmatmachoman wrote:agreed Bro!!

Seems some Hitch in my statement!!

Apologies from my end bro!!

not a prob ...to err is human

Regards,
Harsha

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Mon Mar 08, 2010 11:32 pm

harshavardhanc wrote:
gmatmachoman wrote:
harshavardhanc wrote:
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) âˆš (a^2 + b^2)
(B) âˆš (a^2 - b^2)
(C) a b
(D) âˆš (a b)
(E) a b - a^2 - b^2
since this relation is a generic one, it should be satisfied by all the values.

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.
heheheh!! U logic wont work bro....Try for other values of X where a is not equal to b...

Only the straight method wrks as posted by @truplayer256.
Gmatmachoman..buddy, I know you are very experienced on this forum and I think you have a strong prep too.

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.

great advocacy of plugging in, this helps you foresee without pen sometimes, but a fair practice that is enough to decide where to apply plugging in policy, is always must.

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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harshavardhanc: Legendary Member; Posts: 526; Joined: Sat Feb 21, 2009 11:47 pm; Location: India; Thanked: 68 times; GMAT Score:680

by harshavardhanc » Tue Mar 09, 2010 1:56 am

sanju09 wrote: great advocacy of plugging in, this helps you foresee without pen sometimes, but a fair practice that is enough to decide

where to apply plugging in policy, is always must.

yes, I missed the *conditions apply part in my post. Thanks for supplementing my response with it !

Anyway, as the normal equation method had already been posted, I chose to reply with the plugging-in method. In that way, the readers are aware of another method which, in some cases, might be faster.

But as Sanju said, it's totally depends on the users discretion whether to apply that method in the actual exam.

Regards,
Harsha

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tgou008: Senior | Next Rank: 100 Posts; Posts: 43; Joined: Sat Jan 15, 2011 11:26 am; Thanked: 9 times

by tgou008 » Sun May 22, 2011 3:36 pm

harshavardhanc wrote:
gmatmachoman wrote:
harshavardhanc wrote:
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) âˆš (a^2 + b^2)
(B) âˆš (a^2 - b^2)
(C) a b
(D) âˆš (a b)
(E) a b - a^2 - b^2
since this relation is a generic one, it should be satisfied by all the values.

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.
heheheh!! U logic wont work bro....Try for other values of X where a is not equal to b...

Only the straight method wrks as posted by @truplayer256.
Gmatmachoman..buddy, I know you are very experienced on this forum and I think you have a strong prep too.

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 too used this plugging approach; but it is very time consuming and the numbers are messy. Is there an easier and faster method we can use?

Thanks

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Mon May 23, 2011 1:35 am

tgou008 wrote:
harshavardhanc wrote:
gmatmachoman wrote:
harshavardhanc wrote:
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) âˆš (a^2 + b^2)
(B) âˆš (a^2 - b^2)
(C) a b
(D) âˆš (a b)
(E) a b - a^2 - b^2
since this relation is a generic one, it should be satisfied by all the values.

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.
heheheh!! U logic wont work bro....Try for other values of X where a is not equal to b...

Only the straight method wrks as posted by @truplayer256.
Gmatmachoman..buddy, I know you are very experienced on this forum and I think you have a strong prep too.

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 too used this plugging approach; but it is very time consuming and the numbers are messy. Is there an easier and faster method we can use?

Thanks

In 1 minute, A alone can fill 1/ (x + a) of the cistern, B alone can fill 1/ (x + b) of the same cistern, whereas A and B together can fill 1/x of the same cistern.

That way

1/ (x + a) + 1/ (x + b) = 1/x

Â» (2 x + a + b)/ (x^2 + a x + b x + a b) = 1/x

Â» 2 x^2 + a x + b x = x^2 + a x + b x + a b

Â» x^2 = a b

Â» [spoiler]x = âˆš (a b)

D[/spoiler]

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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sushantgupta: Senior | Next Rank: 100 Posts; Posts: 40; Joined: Sun Mar 27, 2011 9:54 am; Thanked: 2 times

by sushantgupta » Sat Jul 16, 2011 9:12 pm

1/x = 1/(x+a) + 1/x+b
=> x(x+a+x+b) = (x+a)(x+b)
> x^2 = ab > x = sqrt(ab).

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Bek: Senior | Next Rank: 100 Posts; Posts: 68; Joined: Fri Dec 03, 2010 10:29 pmFollowed by: 1 member; Thanked: 5 times

by Bek » Fri Aug 12, 2011 9:41 pm

The easiest way is to plug in.

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tailoc: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Wed Jun 15, 2011 11:38 am; Thanked: 1 times

by tailoc » Wed Sep 28, 2011 5:54 am

Formula: Ra+Rb=Rx
<=> 1/(a+x) + 1/(b+x) = 1/x
=> x = sqrt(ab)

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prashant misra: Master | Next Rank: 500 Posts; Posts: 101; Joined: Thu Aug 25, 2011 9:39 pm

by prashant misra » Fri Dec 02, 2011 11:16 am

The answer to this question is option D picking numbers would be the bets possible approach if anyone know which values would approximately nearby to the squareroot xy

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