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# A doctor prescribed 18 cubic centimeters of a certain drug to a patien

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A doctor prescribed 18 cubic centimeters of a certain drug to a patien  [#permalink]

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15 Jun 2016, 00:24
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Difficulty:

15% (low)

Question Stats:

81% (01:38) correct 19% (02:12) wrong based on 1471 sessions

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A doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 120 pounds. If the typical dosage is 2 cubic centimeters per 15 pounds of the body weight, by what percent was the prescribed dosage greater than the typical dosage?

A) 8%
B) 9%
C) 11%
D) 12.5%
E) 14.8%

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Re: A doctor prescribed 18 cubic centimeters of a certain drug to a patien  [#permalink]

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13 Jan 2018, 08:47
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Top Contributor
1
Bunuel wrote:
A doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 120 pounds. If the typical dosage is 2 cubic centimeters per 15 pounds of the body weight, by what percent was the prescribed dosage greater than the typical dosage?

A) 8%
B) 9%
C) 11%
D) 12.5%
E) 14.8%

We can use equivalent ratios to determine what the dosage SHOULD have been.
We'll use the ratio of drug dosage (in cubic centimeters)/body weight (in pounds)

Let x = the dosage (in cubic centimeters) the patient SHOULD have received

We get: 2/15 = x/120
Cross multiply to get: 15x = (2)(120)
Simplify: 15x = 240
Solve: x = 16
So, the patient SHOULD have received a dosage of 16 cubic centimeters
Instead, the patient was prescribed a dosage of 18 cubic centimeters

Percent increase = 100(new - original)/original
= 100(18 - 16)/16
= 200/16
= 12.5

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##### General Discussion
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Re: A doctor prescribed 18 cubic centimeters of a certain drug to a patien  [#permalink]

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15 Jun 2016, 02:11
2
typical dosage = 2 cubic centimetres per 15 pounds of the body weight
or,
1200/75= 16 cubic centimetres for a body weight of 120 pounds
doctor prescribed 18 cubic centimetres
greater by (2/16)= 12.5%
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Posts: 236
Re: A doctor prescribed 18 cubic centimeters of a certain drug to a patien  [#permalink]

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15 Jun 2016, 02:27
2
Bunuel wrote:
A doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 120 pounds. If the typical dosage is 2 cubic centimeters per 15 pounds of the body weight, by what percent was the prescribed dosage greater than the typical dosage?

A) 8%
B) 9%
C) 11%
D) 12.5%
E) 14.8%

Typical dosage is Dose : weight :: 2: 15.

Now if weight is 120 (Multiplying factor is 8: (120/15)) then typical dosage would be 2 *8 = 16 cc.

Dosage = 18 cc. Dosage is greater by 2 cc.

% disage is greater: (2 / 16)*100 = 12.5 %

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Re: A doctor prescribed 18 cubic centimeters of a certain drug to a patien  [#permalink]

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16 Jun 2016, 01:32
1
2
Typical dosage per 15 pound of the body weight = 2 c.c
Typical dosage per 120 pound of the body weight = 2 *(120/15)
= 2 * 8
= 16 c.c
Dosage prescribed by doctor for 120 pound patient = 18 c.c
% prescribed dosage greater than the typical dosage = (18-16/16) *100%
=(2/16) *100%
= 12.5%
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Re: A doctor prescribed 18 cubic centimeters of a certain drug to a patien  [#permalink]

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16 Jun 2016, 03:34
1
Bunuel wrote:
A doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 120 pounds. If the typical dosage is 2 cubic centimeters per 15 pounds of the body weight, by what percent was the prescribed dosage greater than the typical dosage?

A) 8%
B) 9%
C) 11%
D) 12.5%
E) 14.8%

typical dosage: for 15p -- 2 cc
=> for 1p -- 2/15 cc
=> for 120p -- (2/15)*120 = 16cc
so, (18-16)/16 % = 12.5% -- option d.
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Re: A doctor prescribed 18 cubic centimeters of a certain drug to a patien  [#permalink]

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16 Jun 2016, 05:14
2
Bunuel wrote:
A doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 120 pounds. If the typical dosage is 2 cubic centimeters per 15 pounds of the body weight, by what percent was the prescribed dosage greater than the typical dosage?

A) 8%
B) 9%
C) 11%
D) 12.5%
E) 14.8%

Ideal prescription is 2 cubic centimeters for 15 pounds of body weight.

for 120 pounds, it will be= 2*120/15= 16 cubic centimeters

Prescribed dosage= 18 cubic centimeters

% increase= 18-16/16*100= 12.5%

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Re: A doctor prescribed 18 cubic centimeters of a certain drug to a patien  [#permalink]

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12 Dec 2017, 09:29
2
1
Bunuel wrote:
A doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 120 pounds. If the typical dosage is 2 cubic centimeters per 15 pounds of the body weight, by what percent was the prescribed dosage greater than the typical dosage?

A) 8%
B) 9%
C) 11%
D) 12.5%
E) 14.8%

The typical dosage is 2 cubic centimeters (cc) per 15 pounds of body weight. We can set up a proportion to determine what the typical number of cc of the drug would be for a patient with a body weight of 120 pounds:

2/15 = x/120

240 = 15x

240/15 = x

16 = x

Thus, the typical dose for this 120-pound patient is 16 cc. To determine the percent greater than this dose that 18 cc would be, we can use the percent change formula.

(Doctor dose – typical dose)/typical dose x 100%

(18 – 16)/16 x 100% = 2/16 x 100% = 0.125 x 100% = 12.5%

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Re: A doctor prescribed 18 cubic centimeters of a certain drug to a patien  [#permalink]

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17 Jan 2018, 12:32
2
Hi All,

This question is essentially about working through the necessary arithmetic. Thankfully, the math itself isn't that tough, but you do have to stay organized to make sure that you're setting up the proper calculations.

We're told that a typical dose of a drug is 2 cm^3 per 15 pounds. With a 120 pound person, there are 8 15-pound "sets", so the typical dose would be 8(2 cm^3) = 16 cm^3. Since the doctor prescribed 18 cm^3 of the drug, the dose was clearly larger than the typical dose. The question asks by what percent greater was that dose.

Since 18 is "2 more" than 16, we can know that the prescribed dose was 2/16 = 1/8 = 12.5% greater than it typically would be.

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A doctor prescribed 18 cubic centimeters of a certain drug to a patien  [#permalink]

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12 Sep 2018, 23:53
Recommended dose,
2cc/15 lbs

Doctor did,
18cc/120 lbs

Since we know 2 will nicely go over 18, 18/2 = 9

At 9 times, 2cc will be suitable for 9*15 = 135 lbs. This doctor has given a dosage for someone who is 15 lbs lesser

So,
(difference / original) * 100 = Percentage increase

(15/120) * 100 = 12.5% increase in dosage
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Re: A doctor prescribed 18 cubic centimeters of a certain drug to a patien  [#permalink]

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29 Jan 2019, 21:57
1
Prescribed Ratio = 18/120 = 3/20
Typical Ratio = 2/15
% Change (Greater) = (Prescribed Ratio - Typical Ratio) / (Typical Ratio) = (3/20-2/15) / (2/15) = (1/8)
Converting to %:
1/8 is 0.125 = 0.125*100 = 12.5%
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Re: A doctor prescribed 18 cubic centimeters of a certain drug to a patien  [#permalink]

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31 Jan 2019, 04:58
Bunuel wrote:
A doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 120 pounds. If the typical dosage is 2 cubic centimeters per 15 pounds of the body weight, by what percent was the prescribed dosage greater than the typical dosage?

A) 8%
B) 9%
C) 11%
D) 12.5%
E) 14.8%

Perfect opportunity for UNITS CONTROL, one of the most powerful tools carefully explained in our course!

$${\rm{atypical}}\,\,\left( {120\,\,{\rm{pounds}}} \right)\,\,\,:\,\,\,18\,{\rm{c}}{{\rm{m}}^3}$$

$${\rm{typical}}\,\,\,{\rm{:}}\,\,\,120\,{\rm{pounds}}\,\, \cdot \,\,\left( {{{2\,{\rm{c}}{{\rm{m}}^3}} \over {15\,{\rm{pounds}}}}} \right)\,\,\, = \,\,\,16\,\,{\rm{c}}{{\rm{m}}^{\rm{3}}}$$

$$16\mathop \to \limits^{?\, = \,\Delta \% } 18\,\,\,\,\left[ {{\rm{c}}{{\rm{m}}^{\rm{3}}}} \right]$$

$${\rm{?}}\,\, = \,\,\Delta \% \,\, = \,\,{{18 - 16} \over {16}}\,\,\, = \,\,\,{1 \over 8} \cdot 100\% \,\,\, = \,\,\,12.5\%$$

The correct answer is therefore (D).

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: A doctor prescribed 18 cubic centimeters of a certain drug  [#permalink]

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Re: A doctor prescribed 18 cubic centimeters of a certain drug   [#permalink] 24 Jul 2020, 03:25