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Between 1990 and 2000, the number of Americans aged 45 to 64

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Between 1990 and 2000, the number of Americans aged 45 to 64 [#permalink] New post 28 Jan 2013, 12:31
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58% (02:41) correct 42% (01:29) wrong based on 71 sessions
Between 1990 and 2000, the number of Americans aged 45 to 64 was projected to increase from 47 million to 61 million, while the number of Americans aged 18 to 24 was projected to decrease from 26 million to 25 million. According to this projection, which of the following is closest to the ratio of the percent increase in the 45-to-64 age group to the percent decrease in the 18-to-24 age group?

A) 5 to 1
B) 6 to 1
C) 8 to 1
D) 10 to 1
E) 14 to 1

This question is from GMAT Focus.
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Re: Between 1990 and 2000, the number of Americans aged 45 to 64 [#permalink] New post 28 Jan 2013, 23:48
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deoljasms wrote:
Between 1990 and 2000, the number of Americans aged 45 to 64 was projected to increase from 47 million to 61 million, while the number of Americans aged 18 to 24 was projected to decrease from 26 million to 25 million. According to this projection, which of the following is closest to the ratio of the percent increase in the 45-to-64 age group to the percent decrease in the 18-to-24 age group?

A) 5 to 1
B) 6 to 1
C) 8 to 1
D) 10 to 1
E) 14 to 1

This question is from GMAT Focus.


My answer is C.

Given:
1990 - 2000 (one year)
Age 45 to 64 = 47 to 61
Age 18 to 24 = 26 to 25

Find: % increase in 45 to 65 / % decrease in 18 to 24

General formula: % increase or % decrease = (new number - old number ) / old number

That being said, we have:

% increase in 45 to 65 = (65 - 45) / 45 = 14 / 47

% decrease in 18 to 25 = (25 - 26) / 26 = - 1 / 26 or 1 / 26 (we can remove the negative sign because we are talking about changes here)

Now we use the two values:

= (14 / 47) / (1 / 26)

= (14 / 47) * ( 26)

= 364 / 47

~ 7.7...

7.7 is closest to 8, which is answer choice (C)

There you have it. :) Kudos please? :)
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Re: Between 1990 and 2000, the number of Americans aged 45 to 64 [#permalink] New post 11 Jun 2013, 16:15
While the answer was still right in the above post the numbers are reversed...but here's my approach, quick and simple:


Americans 45-64: Increase 47M to 61M
Americans 18-24: Decrease 26M to 25M

Percent change = \frac{New-Old}{Old}

So we have \frac{61-47}{47} and \frac{25-26}{25}

Our ratio becomes \frac{14}{47}:\frac{1}{25} which leads us to a factor of 14 in the numerator and almost a factor of 2 in the denominator: Since the answer choices were 5, 6, 8, 10, and 14 we know that it must be either 6 or 8 (around 7) and since the denominator isn't quite a factor of 2 different then we would be closer to 8>>Answer C
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Re: Between 1990 and 2000, the number of Americans aged 45 to 64 [#permalink] New post 11 Jun 2013, 16:35
Hey,

I took a similar approach to the others, but since I assume most people aren't good at doing arithmetic, and even those who are usually aren't lighting fast, I think the following approximation is very useful:

When comparing 14/47 to 1/26, this can seem a little difficult. We can easily compare this though if we bring each of the bases to be around 100:

If we multiply 14/47 by 2/2, we can approximately 30/100.
If we multiply 1/26 by 4/4, we get something a tad smaller than 4/100.

The closest, by far, to <4 : 30, is 8.

Hope that helps.
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Re: Between 1990 and 2000, the number of Americans aged 45 to 64 [#permalink] New post 11 Jun 2013, 22:40
Expert's post
Nwsmith11 wrote:
While the answer was still right in the above post the numbers are reversed...but here's my approach, quick and simple:


Americans 45-64: Increase 47M to 61M
Americans 18-24: Decrease 26M to 25M

Percent change = \frac{New-Old}{Old}

So we have \frac{61-47}{47} and \frac{25-26}{25}

Our ratio becomes \frac{14}{47}:\frac{1}{25} which leads us to a factor of 14 in the numerator and almost a factor of 2 in the denominator: Since the answer choices were 5, 6, 8, 10, and 14 we know that it must be either 6 or 8 (around 7) and since the denominator isn't quite a factor of 2 different then we would be closer to 8>>Answer C


Actually the post above had it right.

Change 45-64 = \frac{14}{47}
Change 18-24 = \frac{(25 - 26)}{26}

And yes, I would use the same approximation too.

14*\frac{26}{47}
26/47 is approx 1/2 but actually 2 is 1.8 or 1.9 something

When you divide 14 by 2, you get 7 but when you divide it by less than 2, you get more than 7. Hence 8 would be the answer.
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Re: Between 1990 and 2000, the number of Americans aged 45 to 64 [#permalink] New post 26 Oct 2013, 01:23
deoljasms wrote:
Between 1990 and 2000, the number of Americans aged 45 to 64 was projected to increase from 47 million to 61 million, while the number of Americans aged 18 to 24 was projected to decrease from 26 million to 25 million. According to this projection, which of the following is closest to the ratio of the percent increase in the 45-to-64 age group to the percent decrease in the 18-to-24 age group?

A) 5 to 1
B) 6 to 1
C) 8 to 1
D) 10 to 1
E) 14 to 1

This question is from GMAT Focus.


Thirty Seconds approach:

increase in aged 45 to 64: 14 million in 47 or approximately 30%
decrease in aged 18 to 24: 1 million in 26 or approximately 4%

Therefore their ratio is 30%/4% = 7.5 to 1, which is nearest to C
Re: Between 1990 and 2000, the number of Americans aged 45 to 64   [#permalink] 26 Oct 2013, 01:23
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