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A patient is given exactly 750 milliliters of a mixture of two medicat

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A patient is given exactly 750 milliliters of a mixture of two medicat [#permalink]

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A patient is given exactly 750 milliliters of a mixture of two medications daily. Medication A contains 40% pain killer and medication B contains 20% pain killer. If the patient receives exactly 215 milliliters of pain killer daily, how many milliliters of medication B are in the mixture?

A. 150
B. 225
C. 325
D. 425
E. 550
[Reveal] Spoiler: OA

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Re: A patient is given exactly 750 milliliters of a mixture of two medicat [#permalink]

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Let there be A milliliters of Medication A
and B milliliters of Medication B

A+B = 750 -- 1

Medication A contains 40% pain killer and medication B contains 20% pain killer.

(40/100)*A + (20/100)*B = 215
=> (2/5)*A + (1/5)*B = 215
Multiplying by 5 , we get

2A + B = 1075 -- 2

Equation 2- Equation 1 , we get
A = 325
B = 425

Answer D
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A patient is given exactly 750 milliliters of a mixture of two medicat [#permalink]

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New post 19 Nov 2015, 13:26
I tried algebra first but messed up and didn't get an answer choice so then I used this method but I'm not sure if it's the quickest. I probably took 3 minutes because of my mess up.

If mixture was all A it would be (2/5)750= 300
If it was all B the mixture would be (1/5)(750) = 150

A----------given--------B
300--------215-------150
-----85----------65-----

85+65=150
so B is (85/150)(750) = 85*5 = 425



My algebra looked like this. Could someone tell me where I went wrong?

A+B = 750
(2/5)A+(1/5)B=215

(2/5)(750-B)+(1/5)B = 215
300-(2/5)B + (1/5)B = 215
(-1/5)B = -115
B=575 WRONG!!!!!!! Please Help
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A patient is given exactly 750 milliliters of a mixture of two medicat [#permalink]

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New post 19 Nov 2015, 14:22
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Bunuel wrote:
A patient is given exactly 750 milliliters of a mixture of two medications daily. Medication A contains 40% pain killer and medication B contains 20% pain killer. If the patient receives exactly 215 milliliters of pain killer daily, how many milliliters of medication B are in the mixture?

A. 150
B. 225
C. 325
D. 425
E. 550


Medication A: 40% pain killer
Medication B: 20% pain killer
We combine medications to get TOTAL of 750 ml that's approximately 29% pain killer (215/750 ≈ 29%)

Important, if we combine EQUAL AMOUNTS of medications A and B (i.e., 375 mls of each), the TOTAL mixture is 30%.
Since the ACTUAL mixture is 29% , we know that this mixture has MORE of medication B (20%) than medication A (40%)

However, since 29% is very close to 30%, we know that a BIT MORE than half the mixture is medication B.
Check the answer choices to see that D (425) is a bit more than half.

Answer: D

For more on this concept, please see our free video on weighted averages - http://www.gmatprepnow.com/module/gmat- ... /video/805

Cheers,
Brent
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Last edited by GMATPrepNow on 19 Nov 2015, 22:39, edited 1 time in total.
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Re: A patient is given exactly 750 milliliters of a mixture of two medicat [#permalink]

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New post 19 Nov 2015, 18:55
DJ1986 wrote:
I tried algebra first but messed up and didn't get an answer choice so then I used this method but I'm not sure if it's the quickest. I probably took 3 minutes because of my mess up.

If mixture was all A it would be (2/5)750= 300
If it was all B the mixture would be (1/5)(750) = 150

A----------given--------B
300--------215-------150
-----85----------65-----

85+65=150
so B is (85/150)(750) = 85*5 = 425



My algebra looked like this. Could someone tell me where I went wrong?

A+B = 750
(2/5)A+(1/5)B=215

(2/5)(750-B)+(1/5)B = 215
300-(2/5)B + (1/5)B = 215
(-1/5)B = -115 --- you made an error here
B=575 WRONG!!!!!!! Please Help [/b]


Hi DJ1986 ,
300-(2/5)B + (1/5)B = 215
=> -(1/5)B = 215 - 300 = -85
=>B = 425

Hope this helps !! :)
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When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long
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Re: A patient is given exactly 750 milliliters of a mixture of two medicat [#permalink]

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GMATPrepNow wrote:
Bunuel wrote:
A patient is given exactly 750 milliliters of a mixture of two medications daily. Medication A contains 40% pain killer and medication B contains 20% pain killer. If the patient receives exactly 215 milliliters of pain killer daily, how many milliliters of medication B are in the mixture?

A. 150
B. 225
C. 325
D. 425
E. 550


Medication A: 40% pain killer
Medication B: 20% pain killer
We combine medications to get TOTAL of 750 ml that's approximately 29% pain killer (215/750 ≈ 29%)

Important, if we combine EQUAL AMOUNTS of medications A and B (i.e., 375 mls of each), the TOTAL mixture is 30%.
Since the ACTUAL mixture is 29% , we know that this mixture has MORE of medication A (20%) than medication B (40%)
However, since 29% is very close to 30%, we know that a BIT MORE than half the mixture is medication B.
Check the answer choices to see that D (425) is a bit more than half.

Answer: D

For more on this concept, please see our free video on weighted averages - http://www.gmatprepnow.com/module/gmat- ... /video/805

Cheers,
Brent


Hi Brent,
Really nice logic solution. However, I think there is type error. Please review the highlighted part. it should be Medicine B (20%) and A (40%)
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Re: A patient is given exactly 750 milliliters of a mixture of two medicat [#permalink]

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New post 19 Nov 2015, 22:40
Mo2men wrote:
GMATPrepNow wrote:
Bunuel wrote:
A patient is given exactly 750 milliliters of a mixture of two medications daily. Medication A contains 40% pain killer and medication B contains 20% pain killer. If the patient receives exactly 215 milliliters of pain killer daily, how many milliliters of medication B are in the mixture?

A. 150
B. 225
C. 325
D. 425
E. 550


Medication A: 40% pain killer
Medication B: 20% pain killer
We combine medications to get TOTAL of 750 ml that's approximately 29% pain killer (215/750 ≈ 29%)

Important, if we combine EQUAL AMOUNTS of medications A and B (i.e., 375 mls of each), the TOTAL mixture is 30%.
Since the ACTUAL mixture is 29% , we know that this mixture has MORE of medication A (20%) than medication B (40%)
However, since 29% is very close to 30%, we know that a BIT MORE than half the mixture is medication B.
Check the answer choices to see that D (425) is a bit more than half.

Answer: D

For more on this concept, please see our free video on weighted averages - http://www.gmatprepnow.com/module/gmat- ... /video/805

Cheers,
Brent


Hi Brent,
Really nice logic solution. However, I think there is type error. Please review the highlighted part. it should be Medicine B (20%) and A (40%)


Good catch, Mo2men!
I have edited my response.

Cheers,
Brent
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Re: A patient is given exactly 750 milliliters of a mixture of two medicat [#permalink]

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New post 20 Nov 2015, 05:12
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Bunuel wrote:
A patient is given exactly 750 milliliters of a mixture of two medications daily. Medication A contains 40% pain killer and medication B contains 20% pain killer. If the patient receives exactly 215 milliliters of pain killer daily, how many milliliters of medication B are in the mixture?

A. 150
B. 225
C. 325
D. 425
E. 550


Total mixture = 750 mL
Milliliters of medication B in the mixture = B
Milliliters of medication A in the mixture = (750 - B)

Medication A contains 40% pain killer, B contains 20% pain killer, and the patient receives 215 mL.

0.4 (750 - B) + 0.2 (B) = 215
300 - 0.4*B + 0.2*B = 215
0.2*B = 85
B = 425

Answer D
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A patient is given exactly 750 milliliters of a mixture of two medicat [#permalink]

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New post 07 May 2016, 14:18
A patient is given exactly 750 milliliters of a mixture of two medications daily. Medication A contains 40% pain killer and medication B contains 20% pain killer. If the patient receives exactly 215 milliliters of pain killer daily, how many milliliters of medication B are in the mixture?

A. 150
B. 225
C. 325
D. 425
E. 550


equation1: A+B=750 ml
equation2: .4A+.2B=215 ml
multiplying e2 by 2.5,
A+.5B=537.5 ml
subtracting from equation1,
.5B=212.5 ml
B=425 ml
D

Last edited by gracie on 06 Aug 2017, 15:58, edited 3 times in total.
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Re: A patient is given exactly 750 milliliters of a mixture of two medicat [#permalink]

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Re: A patient is given exactly 750 milliliters of a mixture of two medicat   [#permalink] 06 Aug 2017, 01:06
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