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Source: — Problem Solving |

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by Brent@GMATPrepNow » Mon Mar 07, 2016 2:35 pm
The age of the Earth is approximately 1.3 x 10^17 seconds, and one year is approximately 3.2 x 10^7 seconds. Which of the following is closest to the age of the Earth in years?

A) 2.5 x 10^9
B) 4.1 x 10^9
C) 1.9 x 10^10
D) 2.5 x 10^11
E) 4.1 x 10^11
If 1 year = 3.2 x 10^7, we need to determine how many time 3.2 x 10^7 divides into 1.3 x 10^17

So, (1.3 x 10^17)/(3.2 x 10^7) = (1.3)/(3.2) x (10^17)/(10^7)
≈ 0.41 x 10^10
This is not one of the answer choices, so we must rewrite our result.
0.41 x 10^10 = (4.1 x 10^-1) x 10^10
= 4.1 x 10^9
= B

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by DavidG@VeritasPrep » Wed Mar 09, 2016 5:42 am
The age of the Earth is approximately 1.3 x 10^17 seconds, and one year is approximately 3.2 x 10^7 seconds. Which of the following is closest to the age of the Earth in years?

A) 2.5 x 10^9
B) 4.1 x 10^9
C) 1.9 x 10^10
D) 2.5 x 10^11
E) 4.1 x 10^11
Note that part of the difficulty of the question comes from the complexity of having to deal with 1.3/3.2. Rather than grapple with this number, we can consider 1/3. 1/3 = .333. (So 1.3/3.2 will be a little bigger.)

Now we can work with .333 * 10^17/10^7
.333 * 10^10
.333 * 10 * 10^9
3.33 * 10^9
(If the answer is a little bigger than this, it must be B
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by GMATGuruNY » Wed Mar 09, 2016 7:26 am
The age of the Earth is approximately 1.3 *10^17 seconds, and one year is approximately 3.2*10^7 seconds. Which of the following is closest to the age of the Earth in years?

2.5*10^9
4.1*10^9
1.9*10^10
2.5*10^11
4.1*10^11
Set up a PROPORTION and round values to the nearest MULTIPLE OF 10.

(3.2)(10�) seconds / 1 year = (1.3)(10¹�) seconds / x years

x =

= (1.3)(10¹�) / (3.2)(10�)

= (13/32)(10¹�)

= (39/96)(10¹�)

≈ (40/100)(10¹�)

≈ (4/10)(10¹�)

≈ 4 * 10�.

The correct answer is B.
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by Matt@VeritasPrep » Thu Mar 17, 2016 9:24 pm
I'd try to work with integers here too, I think that helps:

1.3 * 10¹� / 3.2 * 10� =

130 * 10¹� / 32 * 10� =

(130/32) * (10¹�/10�) =

≈4 * 10�
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