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# 2.5 million is what percent of 10 billion?

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Intern
Joined: 20 Jun 2019
Posts: 44
Location: United States (DC)
Schools: UVA Darden
GPA: 3.4
WE: Sales (Computer Software)
2.5 million is what percent of 10 billion?  [#permalink]

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19 Mar 2020, 07:43
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65% (hard)

Question Stats:

47% (01:23) correct 53% (01:28) wrong based on 45 sessions

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2.5 million is what percent of 10 billion?

a) $$\frac{1}{40,000}$$ percent

b) $$\frac{1}{25,000}$$ percent

c) $$\frac{1}{15,000}$$ percent

d) $$\frac{1}{4,000}$$ percent

e) $$\frac{1}{40}$$ percent
GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4871
GMAT 1: 770 Q49 V46
Re: 2.5 million is what percent of 10 billion?  [#permalink]

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19 Mar 2020, 07:53
Top Contributor
whollymoses wrote:
2.5 million is what percent of 10 billion?

a) $$\frac{1}{40,000}$$ percent

b) $$\frac{1}{25,000}$$ percent

c) $$\frac{1}{15,000}$$ percent

d) $$\frac{1}{4,000}$$ percent

e) $$\frac{1}{40}$$ percent

Let x = the desired percent

In other words: 2.5 million is x percent of 10 billion
In other words: 2,500,000 = x% of 10,000,000,000
In other words: 2,500,000 = (x/100)(10,000,000,000)
Divide both sides by 100,000 to get: 25 = (x/100)(100,000)
Simplify to get: 25 = 1000x
Divide both sides by 1000 to get: x = 25/1000 = 1/40

Cheers,
Brent
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Intern
Joined: 20 Jun 2019
Posts: 44
Location: United States (DC)
Schools: UVA Darden
GPA: 3.4
WE: Sales (Computer Software)
Re: 2.5 million is what percent of 10 billion?  [#permalink]

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19 Mar 2020, 07:56
Having some issues figuring out what I did wrong. ScottTargetTestPrep or JeffTargetTestPrep care to share any light?

step 1] Set up equation

2,500,000 = $$\frac{x}{100} * 10,000,000,000$$

I simplified the equation as follows

2,500,000 = 25 x $$10^5$$
10,000,000,000 = 10 x $$10^9$$

25 x $$10^5$$ = $$\frac{x}{10^2} * 10^9$$

Then
25 x $$10^5$$ = x * $$10^{11}$$

$$\frac{25 x 10^5 }{10^{11} }$$ = x

25 x $$10^ {-6}$$ = x

Which is equivalent to
$$\frac{25}{1,000,000}$$ = x

$$\frac{1}{40,000}$$ = x
GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4871
GMAT 1: 770 Q49 V46
Re: 2.5 million is what percent of 10 billion?  [#permalink]

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19 Mar 2020, 08:04
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Top Contributor
whollymoses wrote:
Having some issues figuring out what I did wrong. ScottTargetTestPrep or JeffTargetTestPrep care to share any light?

step 1] Set up equation

2,500,000 = $$\frac{x}{100} * 10,000,000,000$$

I simplified the equation as follows

2,500,000 = 25 x $$10^5$$
10,000,000,000 = 10 x $$10^9$$

25 x $$10^5$$ = $$\frac{x}{10^2} * 10^9$$

Then
25 x $$10^5$$ = x * $$10^{11}$$

$$\frac{25 x 10^5 }{10^{11} }$$ = x

25 x $$10^ {-6}$$ = x

Which is equivalent to
$$\frac{25}{1,000,000}$$ = x

$$\frac{1}{40,000}$$ = x

I have highlighted your mistake above.

$$(\frac{x}{10^2})(10^9)=(\frac{x}{10^2})(\frac{10^9}{1}) = \frac{(x)(10^9)}{10^2} = (x)(10^7)$$
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Re: 2.5 million is what percent of 10 billion?  [#permalink]

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21 Mar 2020, 15:18
whollymoses wrote:
Having some issues figuring out what I did wrong. ScottTargetTestPrep or JeffTargetTestPrep care to share any light?

step 1] Set up equation

2,500,000 = $$\frac{x}{100} * 10,000,000,000$$

I simplified the equation as follows

2,500,000 = 25 x $$10^5$$
10,000,000,000 = 10 x $$10^9$$

25 x $$10^5$$ = $$\frac{x}{10^2} * 10^9$$

Then
25 x $$10^5$$ = x * $$10^{11}$$

$$\frac{25 x 10^5 }{10^{11} }$$ = x

25 x $$10^ {-6}$$ = x

Which is equivalent to
$$\frac{25}{1,000,000}$$ = x

$$\frac{1}{40,000}$$ = x

-------------------------------------------

There are two mistakes in your work: First, you correctly wrote 10 billion as 10 x 10^9, but in the equation you wrote just 10^9. That should have been 10^10. Next, when you cancelled the 10^2 in the denominator, you increased the exponent of 10^9 (which should have been 10^10) by 2 instead of decreasing it by 2.

Correcting the first mistake, the equation should have been 25 * 10^5 = (x/10^2)*10^10.

Correcting the second mistake, the next line should have been 25 * 10^5 = x * 10^8. If you solve this equation, you'll get x = 25/1000 = 1/40, which is the correct answer.
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Re: 2.5 million is what percent of 10 billion?   [#permalink] 21 Mar 2020, 15:18