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A certain country had a total annual expenditure of $1.2 x 1

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A certain country had a total annual expenditure of $1.2 x 1 [#permalink]

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New post 17 Dec 2012, 07:12
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A certain country had a total annual expenditure of $1.2 x 10^12 last year. If the population of the country was 240 million last year, what was the per capita expenditure?

(A) $ 500
(B) $1,000
(C) $2,000
(D) $3,000
(E) $5,000
[Reveal] Spoiler: OA
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Re: A certain country had a total annual expenditure of $1.2 x 1 [#permalink]

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New post 17 Dec 2012, 07:16
Expert's post
Walkabout wrote:
A certain country had a total annual expenditure of $1.2 x 10^12 last year. If the population of the country was 240 million last year, what was the per capita expenditure?

(A) $ 500
(B) $1,000
(C) $2,000
(D) $3,000
(E) $5,000


240 million = 24*10^7, thus the per capita expenditure = \(\frac{1.2 * 10^{12}}{24*10^7}=\frac{12 * 10^{11}}{24*10^7}=0.5*10^4=5000\).

Answer: E.
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Re: A certain country had a total annual expenditure of $1.2 x 1 [#permalink]

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New post 18 Dec 2012, 21:38
\(=\frac{1.2x10^{12}}{240x10^{6}}\)
Notice that 1.2 and 240 we could manipulate to make it to \(120/240\)

\(=\frac{120x10^{10}}{240x10^{6}}=0.5x10^{10-6}=0.5x10^{4}=5,000\)

Answer: E
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Re: A certain country had a total annual expenditure of $1.2 x 1 [#permalink]

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New post 21 Jun 2016, 10:22
Walkabout wrote:
A certain country had a total annual expenditure of $1.2 x 10^12 last year. If the population of the country was 240 million last year, what was the per capita expenditure?

(A) $ 500
(B) $1,000
(C) $2,000
(D) $3,000
(E) $5,000


The key to solving this problem is to accurately translate what is being asked to a mathematical expression. We need to determine the “per capital expenditure”. As an expression this is:

(Total annual expenditure)/(Total population)= per capita expenditure

The easiest first step is to express 240 million as a number times a power of 10 since the other number is in this format.

240 million = 240,000,000

Since we have a 24 with 7 zeroes we can write this as:

24 x 10^7

Next, we should adjust 1.2 x 10^12 to make it a more usable number in our expression.

1.2 x 10^12 = 120 x 10^10

We now can solve:

(Total annual expenditure)/(Total population)

(120 x 10^10)/(24 x 10^7)

5 x 10^3

5 x 1,000 = 5,000

Answer E.
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Re: A certain country had a total annual expenditure of $1.2 x 1   [#permalink] 21 Jun 2016, 10:22
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