The main ingredient in a certain prescription drug capsule

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AAPL: Moderator; Posts: 2599; Joined: Sun Oct 29, 2017 2:08 pm; Followed by:2 members

The main ingredient in a certain prescription drug capsule

by AAPL » Wed Jul 31, 2019 7:44 am

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The main ingredient in a certain prescription drug capsule cost $500 per kilogram. If each capsule contains 600 milligrams of ingredient, what is the cost of the ingredient in a capsule? (1-kilogram $= 10^6$ milligrams)

A. $0.30
B. $0.83
C. $1.20
D. $3.00
E. $3.33

OA A

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Source: Beat The GMAT — Problem Solving | Wed Jul 31, 2019 7:44 am

swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

by swerve » Wed Jul 31, 2019 12:15 pm

Find the cost per mg, and multiply that by 600 mg.

1kg $= 1\cdot 10^6$ mg. Cost per kg $= \$500$. Therefore cost per mg $= \frac{500}{10^6} = \frac{5}{10^4}$.

Multiply this by 600 to get cost per 600mg $= \frac{5}{10^4}\cdot 6\cdot 10^2 = 30\cdot 10^{-2} = 0.3$

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Mon Aug 05, 2019 4:11 pm

AAPL wrote:GMAT Prep

The main ingredient in a certain prescription drug capsule cost $500 per kilogram. If each capsule contains 600 milligrams of ingredient, what is the cost of the ingredient in a capsule? (1-kilogram $= 10^6$ milligrams)

A. $0.30
B. $0.83
C. $1.20
D. $3.00
E. $3.33

OA A

We can use a proportion to solve this problem. Letting x be the cost, in dollars, per 600-mg capsule, we have:

$500/1 kg = $x/600 mg

Before we can cross multiply, we need the denominators to have the same units. Since we are given 1 kg = 10^6 mg, we have:

$500/10^6 mg = x/600 mg

500/10^6 = x/600

(10^6)(x) = 500(600)

1,000,000(x) = 300,000

10x = 3

x = 0.3

Thus, the cost is $0.30 per capsule.

Answer: A

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