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

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 - https://www.gmatprepnow.com/module/gmat- ... /video/805

Cheers,
Brent
_________________

You can convert 215 as a % of 750 or convert 40% and 20% as values.
Always choose what saves your time.
40% of 750 is 300, so 20% is 150.

Weighted average method is best suited now.

………………A……………Avg……….….B
…………….300…….….215………...150

\(\frac{B}{Total}=\frac{300-215}{300-150}=\frac{85}{150}\)

Quantity of B in 750 mixture = \(750*\frac{85}{150}=5*85=425\)


D
_________________

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
_________________

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

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

Hope this helps !!
_________________

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
_________________

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

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

40%A + 20%B = 215
2/5 + 1/5B = 215
2A + B = 215

and if A + B = 750; then A = 325 & B = 425

Hi chetan2u , Bunuel , i worked with percentages
………………A……………Avg……….….B
…………….40…….….86/3………...20

I got 17:13 as the ratio .
30x=750
x=25

13x= 25*13=325. How is the answer 425 . The question is asking ml of medication B.

You have taken the ratios opposite. The quantity is more of the solution that has average closer. More quantity pulls the average closer to itself.
Here, 86/3 is closer to 20, so ratio of B will be more => \(\frac{B}{A}=\frac{40-28.7}{28.7-20}=\frac{11.3}{8.7}=\frac{17}{13}\)
_________________

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________