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If m = 3x + 4y for x, y > 0. Find the minimum value of m.

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If m = 3x + 4y for x, y > 0. Find the minimum value of m.  [#permalink]

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New post Updated on: 26 Aug 2018, 02:42
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Question Stats:

55% (00:58) correct 45% (01:20) wrong based on 11 sessions

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If m = 3x + 4y for x, y > 0. Find the minimum value of m.


(1) When m is minimum distance between X and Y intercepts in a co-ordinate plane is 15/2 .

(2) xy = 27/4

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Originally posted by Harshgmat on 25 Aug 2018, 19:36.
Last edited by Bunuel on 26 Aug 2018, 02:42, edited 5 times in total.
Renamed the topic and edited the question.
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Re: If m = 3x + 4y for x, y > 0. Find the minimum value of m.  [#permalink]

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New post Updated on: 25 Aug 2018, 20:56
Harshgmat wrote:
If m = 3x + 4y Find the minimum value of m.

1) When minimum distance between X and Y intercepts in a co-ordinate plane is 15/2 .

2) xy = 27


Hi Harshgmat

Statement I:

\(25 m^2/16*9 = 225/4\)

m = 18

Statement II:

\(x = 27/4y\)
\(m = 81/4y + 4y\)
\(y = 9/4, x = 3\)
\(m = 18\).

Hence, D.
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Originally posted by rahul16singh28 on 25 Aug 2018, 20:06.
Last edited by rahul16singh28 on 25 Aug 2018, 20:56, edited 3 times in total.
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Re: If m = 3x + 4y for x, y > 0. Find the minimum value of m.  [#permalink]

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New post Updated on: 25 Aug 2018, 20:57
rahul16singh28 wrote:
Harshgmat wrote:
If m = 3x + 4y Find the minimum value of m.

1) When minimum distance between X and Y intercepts in a co-ordinate plane is 15/2 .

2) xy = 27


Hi Harshgmat

Not sure, if we are missing anything in the question or if there is any flaw in my logic.

Statement I:

\(25 m^2/16*9 = 225/4\)

m = 18

Statement II:

\(x = 27/y\)
\(m = 81/y + 4y\)
\(y = 9/2, x = 6\)
\(m = 36\).

For the same value of m, I am getting two different answers from the two statements. But as Statement I says, the distance is minimum between the two Intercepts - so, m(min) = 18. Hence, A.


Hi rahul16singh28

Thanks...Edited the typo.

Does it make sense now...

Your approach for statement 2) is elegant!!
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Originally posted by Harshgmat on 25 Aug 2018, 20:44.
Last edited by Harshgmat on 25 Aug 2018, 20:57, edited 1 time in total.
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Re: If m = 3x + 4y for x, y > 0. Find the minimum value of m.  [#permalink]

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New post 25 Aug 2018, 20:50
Harshgmat wrote:
rahul16singh28 wrote:
Harshgmat wrote:
If m = 3x + 4y Find the minimum value of m.

1) When minimum distance between X and Y intercepts in a co-ordinate plane is 15/2 .

2) xy = 27


Hi Harshgmat

Not sure, if we are missing anything in the question or if there is any flaw in my logic.

Statement I:

\(25 m^2/16*9 = 225/4\)

m = 18

Statement II:

\(x = 27/y\)
\(m = 81/y + 4y\)
\(y = 9/2, x = 6\)
\(m = 36\).

For the same value of m, I am getting two different answers from the two statements. But as Statement I says, the distance is minimum between the two Intercepts - so, m(min) = 18. Hence, A.


Hi rahul16singh28

Thanks...Edited the typo.

Does it make sense now...

Your approach for sentence 2) is elegant!!


Yeah.. now the answer should be D:).. Thanks..!!
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Re: If m = 3x + 4y for x, y > 0. Find the minimum value of m.  [#permalink]

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New post 25 Aug 2018, 22:38
Harshgmat wrote:
If m = 3x + 4y Find the minimum value of m.

1) When minimum distance between X and Y intercepts in a co-ordinate plane is 15/2 .

2) xy = 27/4



The question is flawed. It is nowhere mentioned that x and y are positive so xy =27/4 can mean x= -1000 and y = -27/4000
So 3x+4y = 3*-1000+4*(-27/4000)=-3000-27/1000
Ofcourse the value can go to ' - infinity'

Also statement I is awkward
1) WHEN min distance ....
When seems to be giving some scenario and not a condition..
So it should have been merely
1) min distance....
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Senior Manager
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Re: If m = 3x + 4y for x, y > 0. Find the minimum value of m.  [#permalink]

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New post 25 Aug 2018, 22:56
chetan2u wrote:
Harshgmat wrote:
If m = 3x + 4y Find the minimum value of m.

1) When minimum distance between X and Y intercepts in a co-ordinate plane is 15/2 .

2) xy = 27/4



The question is flawed. It is nowhere mentioned that x and y are positive so xy =27/4 can mean x= -1000 and y = -27/4000
So 3x+4y = 3*-1000+4*(-27/4000)=-3000-27/1000
Ofcourse the value can go to ' - infinity'

Also statement I is awkward
1) WHEN min distance ....
When seems to be giving some scenario and not a condition..
So it should have been merely
1) min distance....


chetan2u

You are right...

if it is given that x, y >0 then does that make given statements sufficient ?
_________________

It seems Kudos button not working correctly with all my posts...

Please check if it is working with this post......

is it?....

Anyways...Thanks for trying :cool:

Re: If m = 3x + 4y for x, y > 0. Find the minimum value of m. &nbs [#permalink] 25 Aug 2018, 22:56
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If m = 3x + 4y for x, y > 0. Find the minimum value of m.

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