If 100,000 microns = 1 decimeter, and 1,000,000,000 angstroms = 1 decimeter, how many angstroms equal 1 micron? GMAT Problem Solving

Question: If 100,000 microns = 1 decimeter, and 1,000,000,000 angstroms = 1 decimeter, how many angstroms equal 1 micron?

1. 0.00001
2. 0.0001
3. 0.001
4. 10,000
5. 100,000

“If 100,000 microns = 1 decimeter, and 1,000,000,000 angstroms = 1 decimeter, how many angstroms equal 1 micron?”- 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 number of qualitative skills. GMAT Quant section consists of 31 questions in total. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:

Approach Solution 1:

The problem statement informs that:

Given:

• 100,000 microns = 1 decimeter
• 1,000,000,000 angstroms = 1 decimeter

Find Out:

• How many angstroms equal 1 micron?

Hence, we get that 100,000 microns = 1 decimeter
So, on solving, we get: 1 micron = (1 * 1)/100,000
= 1/100,000 decimeter
Also, 1 decimeter = 1,000,000,000 angstorm
So, on solving, we get:
1/100,000 decimeter = [(1/100,000) * 1,000,000,000]/1
= 10,000

Correct Answer: D 

Approach Solution 2:

As per the problem statement, it is given that:
1 dm (decimeter) = 10^5 microns - (i)
1 dm = 10^9 angstroms - (ii)
Hence, from (i) and (ii) we get:
10^5 microns = 10^9 angstroms
=> 1 micron = 10^4 angstroms

Correct Answer: D 

Approach Solution 3:

In this approach , we will go by a=c and b=c ; therefore a =b

Given:

• 100,000 microns = 1 decimeter
• 1,000,000,000 angstroms = 1 decimeter

Find Out:

• How many angstroms equal 1 micron?

We know,

100,000 microns = 1,000,000,000 angstroms
We will cancel out 5 zeros from both sides
Therefore, we get:
1 micron = 10,000 angstroms.

Correct Answer: D 

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