Percentage Problem

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Joy Shaha: Senior | Next Rank: 100 Posts; Posts: 59; Joined: Thu May 05, 2016 4:20 am; Thanked: 3 times

by Joy Shaha » Mon Sep 19, 2016 1:13 pm

Q. 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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Source: Beat The GMAT — Problem Solving | Mon Sep 19, 2016 1:13 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Sep 19, 2016 1:56 pm

Joy Shaha wrote:Q. 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

Answer: D

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Brent Hanneson - Creator of GMATPrepNow.com

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MBA Challengers: Senior | Next Rank: 100 Posts; Posts: 51; Joined: Fri Sep 09, 2016 11:59 pm; Thanked: 20 times

by MBA Challengers » Wed Sep 21, 2016 11:28 pm

Slightly different approach:
First divide the body weight by 15 to understand how many of the 2 cubic centimentres dose.
120/15 = 8
Thus, he should have been prescribed 8 x 2 cubic centimetre dosages = 16 cubic centimetre dosage.

However, the prescription is for 18 cubic cm, which is 2 cubic cm more than the adequate dosage of 16 cubic cm. This excess should be calculated on the base of 16 cubic cm.
Thus, we need to know the percentage for 2/16 = 1/8. It is ideal to know the percentages of a few fractions on your fingertips to know that 1/8 translates to 12.5% directly.

Thus, the answer is D 12.5%

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