Question: Which of the following is closet to \(\frac{4}{2.001}\)?

1. 1.997
2. 1.998
3. 1.999
4. 2.000
5. 2.001

Answer:

Approach Solution (1):

\(\frac{4}{2.001}=\frac{4}{2+0.001}=\frac{4(2-0.001)}{(2+0.001)(2-0.001)}=\frac{4(2-0.001)}{4-0.001^2}\)

Now, since \(0.001^2\) is very small number then \(4-0.001^2\) is very close to 4 itself, so \(0.001^2\) is basically negligible in this case and we can write:

\(\frac{4(2-0.001)}{4-0.001^2}\approx\frac{4(2-0.001)}{4}=2-0.001=1.999\)

Correct option: C

Approach Solution (2):

To make this calculation easier let’s round down 2.001 to 2.

Then it will be \(\frac{4}{2}=2\)

But, we know that the larger the denominator, the smaller is the number.

Comparing: \(\frac{4}{2.001}\)  is a little bit smaller than \(\frac{4}{2}\)

This way, the answer choice has to be a little bit smaller than 2

The answer will be 1.999

Correct option: C

“Which of the following is closet to \(\frac{4}{2.001}\)?”- 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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