The Value of (10^8-10^2)/(10^7-10^3) is Closest to Which of the Following? GMAT Problem Solving

Question: The value of \(\frac{10^8-10^2}{10^7-10^3}\) is closet to which of the following?

1. 1
2. 10
3. \(10^2\)
4. \(10^3\)
5. \(10^4\)

Answer:

Approach Solution (1):

Yes factoring out \(10^2\) and \(10^3\) and then reducing the fraction by \(10^2\) is one way to deal with this question:

\(\frac{10^8-10^2}{10^7-10^3}=\frac{10^2(10^6-1)}{10^3(10^4-1)}=\frac{10^6-1}{10*(10^4-4)}\)

Now, \(10^6-1\) is very close to \(10^6\) and \(10^4-1\)is very close to \(10^4\), hence

\(=\frac{10^6-1}{10*(10^4-1)} \approx \frac{10^6}{10*10^6} = \frac{10^6}{10^5} = 10\)

Correct Option: B

Approach Solution (2):

You can notice that we need an approximate value of a fraction. Now, \(10^8\) is much, much, much bigger than \(10^2\). So subtracting \(10^2\) from \(10^8\) will be very close to \(10^8\), basically \(10^2\) is negligible in this case. The same for \(10^7\) and \(10^3\). So \(\frac{10^8-10^2}{10^7-10^3} \approx \frac{10^8}{10^7}=10\)

Correct Option: B

“The value of \(\frac{10^8-10^2}{10^7-10^3}\) is closet to which of the following?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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