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The main ingredient in a certain prescription drug capsule c

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The main ingredient in a certain prescription drug capsule c

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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

Source: GMAT Prep

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BTGmoderatorDC wrote:
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
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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Hi All,

We're told that 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). This is a 'unit conversion' question and comes down to basic Arithmetic. You can do the math in a number of different ways - and if you're concerned about manipulating "big numbers", then you can do several 'smaller decimal shifts' instead.

Since $500 = 1 kilogram = 1,000,000 milligrams
$500 = 1,000,000 milligrams
$50 = 100,000 milligrams
$5 = 10,000 milligrams
$0.50 = 1,000 milligrams

We're asked what 600 milligrams of the drug would cost. Since 600 is less than 1,000 we know that we'll spend LESS than $0.50 on the drug. There's only one answer that fits...

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

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BTGmoderatorDC wrote:
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
Source: GMAT Prep
Perfect opportunity for UNITS CONTROL, one of the most powerful tools of our method!
$${\text{licit}}\,\,{\text{converters}}\,\,:\,\,\,\frac{{\$ \,500}}{{1\,\,{\text{kg}}}}\,\,\,\,\,;\,\,\,\,\,\frac{{1\,\,{\text{capsule}}}}{{600\,\,{\text{mg}}}}\,\,\,\,;\,\,\,\,\,\frac{{1\,\,{\text{kg}}}}{{{{10}^6}\,\,{\text{mg}}}}$$
$$?\,\,:\,\,\,\$ \,\,\,\,{\text{for}}\,\,\,1\,\,{\text{capsule}}$$
$${\text{?}}\,\,\,{\text{:}}\,\,\,\,1\,\,{\text{capsule}}\,\,\left( {\frac{{600\,\,{\text{mg}}}}{{1\,\,{\text{capsule}}}}} \right)\left( {\frac{{1\,\,{\text{kg}}}}{{{{10}^6}\,\,{\text{mg}}}}} \right)\left( {\frac{{\$ \,500}}{{1\,\,{\text{kg}}}}} \right)\,\,\,\, = \,\,\,\,\$ \,\,\frac{{500 \cdot 600}}{{{{10}^6}}}\,\,\, = \,\,\,\$ \,\,\frac{{30 \cdot {{10}^4}}}{{{{10}^6}}}\,\, = \,\,\,\$ \,0.3$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

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Portuguese-speakers :: https://www.gmath.com.br

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BTGmoderatorDC wrote:
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
Each capsule contains 600 milligrams of ingredient.
10⁶ milligrams = 1 kilogram.
1 kilogram of ingredient = 500 dollars.

To determine the cost per capsule, we must use the relationships above to convert 600 milligrams into dollars:
(600 milligrams) * (1 kilogram)/(10⁶ milligrams) * (500 dollars)/(1 kilogram) = (600*500)/10⁶ = 300000/1000000 = 0.3.

The correct answer is A.

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

1kg = 1*10^6 mg. Cost per kg = $500. Therefore cost per mg = $500/10^6 = $5/10^4 .

Multiply this by 600 to get cost per 600mg = (5/10^4)*(6*10^2) = 30*10^-2 = 0.3

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