The value of $$\left(10^8-10^2\right)\div\left(10^7-10^3\right)$$ is closest to which of the following?

A) 1

B) 10

C) 10^2

D) 10^3

E) 10^4

Answer is C 10^2. How are they able to simply subtract the like bases with different exponents than divide. Aren't you only allowed to multiple and divide like bases with different exponents? $$\left(10^8-10^2\right)\div\left(10^7-10^3\right)$$

## GMAT Official Practice Tes #6

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- Marty Murray
- Legendary Member
**Posts:**2074**Joined:**03 Feb 2014**Location:**New York City Metro Area and Worldwide Online**Thanked**: 955 times**Followed by:**138 members**GMAT Score:**800

You are correct. You can't add or subtract like bases with different exponents.simpm14 wrote:The value of $$\left(10^8-10^2\right)\div\left(10^7-10^3\right)$$ is closest to which of the following?

A) 1

B) 10

C) 10^2

D) 10^3

E) 10^4

Answer is C 10^2. How are they able to simply subtract the like bases with different exponents than divide. Aren't you only allowed to multiple and divide like bases with different exponents? $$\left(10^8-10^2\right)\div\left(10^7-10^3\right)$$

However, in this case, the question is asking which of the answers the value of $$\left(10^8-10^2\right)\div\left(10^7-10^3\right)$$ is CLOSEST to. So, we don't need an exact answer.

Notice, 10â�¸ is much greater than 10Â², and 10â�· is much greater than 10Â³.

In fact, the larger numbers in the parentheses are so much greater than the smaller numbers that we can ignore the smaller numbers and consider the expression approximately equal to 10â�¸/10â�·.

Of course 10â�¸/10â�· = 10.

So, $$\left(10^8-10^2\right)\div\left(10^7-10^3\right)$$ = approximately 10.

The correct answer is B.

Marty Murray

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https://infinitemindprep.com/

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### GMAT/MBA Expert

- ceilidh.erickson
- GMAT Instructor
**Posts:**2094**Joined:**04 Dec 2012**Thanked**: 1443 times**Followed by:**245 members

Since we're asked what the value is *closest* to, Marty is right - we don't have to do complicated math, we can just estimate with the larger numbers.

But, for a lot of exponent questions with addition or subtraction, we can't simply add or subtract the bases, but we can FACTOR:

\(10^8-10^2\) ---> \(10^2(10^6-1)\)

and

\(10^7-10^3\) ---> \(10^3(10^4-1)\)

So, we can rewrite the problem as:

$$\frac{10^2\left(10^6-1\right)}{10^3\left(10^4-1\right)}$$

$$\frac{\left(10^6-1\right)}{10^1\left(10^4-1\right)}$$

$$\frac{10^6-1}{10^5-10}$$

Since \(10^6\) is so much greater than 1, \(10^6-1\) is effectively equal to \(10^6\) for the purposes of estimating. So, we essentially have \(\frac{10^6}{10^5-10}\) . Again, the -10 makes very little impact, so for the purposes of estimating, this is very close to \(\frac{10^6}{10^5}\), which would equal \(10^1\).

The answer is B.

But, for a lot of exponent questions with addition or subtraction, we can't simply add or subtract the bases, but we can FACTOR:

\(10^8-10^2\) ---> \(10^2(10^6-1)\)

and

\(10^7-10^3\) ---> \(10^3(10^4-1)\)

So, we can rewrite the problem as:

$$\frac{10^2\left(10^6-1\right)}{10^3\left(10^4-1\right)}$$

$$\frac{\left(10^6-1\right)}{10^1\left(10^4-1\right)}$$

$$\frac{10^6-1}{10^5-10}$$

Since \(10^6\) is so much greater than 1, \(10^6-1\) is effectively equal to \(10^6\) for the purposes of estimating. So, we essentially have \(\frac{10^6}{10^5-10}\) . Again, the -10 makes very little impact, so for the purposes of estimating, this is very close to \(\frac{10^6}{10^5}\), which would equal \(10^1\).

The answer is B.

Ceilidh Erickson

EdM in Mind, Brain, and Education

Harvard Graduate School of Education

EdM in Mind, Brain, and Education

Harvard Graduate School of Education