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

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

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Updated on: 26 Aug 2018, 02:42
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Difficulty:

55% (hard)

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

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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.
Director
Joined: 08 Jun 2013
Posts: 560
Location: France
GMAT 1: 200 Q1 V1
GPA: 3.82
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Re: If m = 3x + 4y for x, y > 0. Find the minimum value of m.  [#permalink]

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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!!
_________________
Everything will fall into place…

There is perfect timing for
everything and everyone.
Never doubt, But Work on
improving yourself,
Keep the faith and
It will all make sense.

Originally posted by Helium on 25 Aug 2018, 20:44.
Last edited by Helium on 25 Aug 2018, 20:57, edited 1 time in total.
Director
Joined: 31 Jul 2017
Posts: 516
Location: Malaysia
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
Re: If m = 3x + 4y for x, y > 0. Find the minimum value of m.  [#permalink]

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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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Joined: 02 Aug 2009
Posts: 7671
Re: If m = 3x + 4y for x, y > 0. Find the minimum value of m.  [#permalink]

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

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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 ?
_________________
Everything will fall into place…

There is perfect timing for
everything and everyone.
Never doubt, But Work on
improving yourself,
Keep the faith and
It will all make sense.
Re: If m = 3x + 4y for x, y > 0. Find the minimum value of m.   [#permalink] 25 Aug 2018, 22:56
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