The value of (10^8-10^2)/(10^7-10^3) is closest to which

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

by VJesus12 » Sat Jan 05, 2019 7:25 am

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The value of (10^8-10^2)/(10^7-10^3) is closest to which of the following?

A. 1
B. 10
C. 10^2
D. 10^3
E. 10^4

[spoiler]OA=B[/spoiler]

Source: GMAT Prep

Source: Beat The GMAT — Problem Solving | Sat Jan 05, 2019 7:25 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat Jan 05, 2019 7:56 am

VJesus12 wrote:The value of (10^8-10^2)/(10^7-10^3) is closest to which of the following?

A. 1
B. 10
C. 10^2
D. 10^3
E. 10^4

Since the answer choices are so spread out, we can be quite aggressive with out estimation.

First, 10â�¸ - 10Â² can be rounded to 10â�¸

Is this reasonable? Well, 10â�¸ equals 100,000,000, so subtracting 10Â² (aka 100) from 100,000,000 still leaves us with approximately 100,000,000

Similarly, 10â�· - 10Â³ can be rounded to 10â�· (10,000,000 - 1000 is pretty close to 10,000,000)

So, by estimating, we get:
(10â�¸ - 10Â²)/(10â�· - 10Â³) â‰ˆ (10â�¸)/(10â�·) = 10Â¹ = 10 = B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8132; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Fri Feb 01, 2019 5:39 pm

VJesus12 wrote:The value of (10^8-10^2)/(10^7-10^3) is closest to which of the following?

A. 1
B. 10
C. 10^2
D. 10^3
E. 10^4

[spoiler]OA=B[/spoiler]

Source: GMAT Prep

We see that since 10^2 is MUCH SMALLER than 10^8 and 10^3 is MUCH smaller than 10^7, subtracting 10^2 from 10^8 does not appreciably change the value, and subtracting 10^3 from 10^7 does not appreciably change the value. Thus, the approximate value of (10^8-10^2)/(10^7-10^3) is:

(10^8)/(10^7) = 10

Answer: B

Scott Woodbury-Stewart
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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sat Feb 02, 2019 12:00 pm

Hi All,

We're asked to choose the answer that is CLOSEST in value to (10^8-10^2)/(10^7-10^3). While you might be tempted to try lots of 'math steps', if you consider how the answer choices are written, you can use a bit of estimation and logic to get to the correct answer without doing too much math.

To start, when the answer choices are based around increased exponents, it's worth noting that those answers are NOT "close" to one another. Each of the answers here is a 'power of 10', and each answer is 10 TIMES greater than the one immediately above it.

With the numerator of the given fraction, instead of factoring, consider how 10^8 compares to (10^8 - 10^2)....

10^8 = 100,000,000
10^2 = 100

Difference = 99,999,900

100,000,000 is essentially the same as 99,999,900. Next, we can think about the denominator in the same terms...

10^7 = 10,000,000
10^3 = 1,000

Difference = 9,999,000

This means that 10,000,000 is essentially the same as 9,999,999...

Thus, we're essentially just asked to divide 10 million by 1 million... and that equals 10.

Final Answer: B

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

Contact Rich at [email protected]

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