Of the Following, Which is Least? GMAT Problem Solving

Question: Of the following, which is least?

1. 0.03/0.00071
2. 0.03/0.0071
3. 0.03/0.071
4. 0.03/0.71
5. 0.03/7.1

Correct Answer: E

Solution and Explanation:
Approach Solution 1:
The given problem question requires to find the fraction which is of the least value.
To get the answer to this question, all five options would need to be evaluated and simplified in the following format-

1. 0.03/0.00071
   This can be simplified as follows:
   = 3/71 * \([10^{-2}\)\(/10^{-5}]\)
   = 3/71 * \(10^{-2}\) * \(10^{5}\)
   = 3/71* \(10^3\)
    
2. 0.03/0.0071 
   This can be simplified as follows:
   = 3/71 * \(10^{-2}\)\(/10^{-4}\)
   = 3/71 *\(10^{-2}\) * \(10^4\)
   = 3/71* \(10^2\)
    
3. 0.03/0.071
   This can be simplified as follows:
   = 3/71 * \(10^{-2}\)\(/10^{-3}\)
   = 3/71 * \(10^{-2}\) * \(10^3\)
   = 3/71 * \(10^1\)
    
4. 0.03/0.71
   This can be simplified as follows:
   = 3/71 * \(10^{-2}\)\(/10^{-2}\)
   = 3/71 * \(10^{-2}\) * \(10^2\)
   =3/71 * \(10^0\)
   = 3/71 * 1
    
5. 0.03/7.1
   This can be simplified as follows:
   = 3/71 * \(10^{-2}\)\(/10^{-1}\)
   = 3/71 * \(10^{-2}\) * \(10^1\)
   = 3/71 * \(10^{-1}\)
   = 3/71 * 0.1

Hence, from the above evaluation, it is clear that option E is the least.

Approach Solution 2:
The problem statement asks to find out the fraction which is of the least value.

All 5 numerators given in the options are 0.03
Therefore, we can use the property that states “the bigger the denominator, the smaller the value of the fraction”
For instance, 17/31 is less than 17/30 and 12/6 is less than 12/4.
Now let us inspect the denominators among the answer choices.
The biggest denominator is 7.1, i.e option E – 0.03/7.1

Hence, the fraction which is of the least value is 0.03/7.1

Approach Solution 3:
The problem statement asks to find out the fraction which is of the least value.
Let us form equivalent fractions with the same denominator.
Let's create each denominator 7.1

1. 0.03/0.00071
   To obtain a denominator of 7.1, we must take 0.00071 and move the decimal 4 places to the right.
   Therefore, we will multiply the numerator and denominator by 10,000
   Thus, we get: 300/7.1
    
2. 0.03/0.0071
   To obtain a denominator of 7.1, we must take 0.0071 and move the decimal 3 places to the right.
   Therefore, we will multiply the numerator and denominator by 1,000
   Thus, we get: 30/7.1
    
3. 0.03/0.071
   To obtain a denominator of 7.1, we must take 0.071 and move the decimal 2 places to the right.
   Therefore, we will multiply the numerator and denominator by 100
   Thus, we get: 3/7.1
    
4. 0.03/0.71
   To obtain a denominator of 7.1, we must take 0.71 and move the decimal 1 place to the right.
   Therefore, we will multiply the numerator and denominator by 10
   Thus, we get: 0.3/7.1
    
5. 0.03/7.1
   This already has a denominator of 7.1

Now, since we have the same denominator, we can infer that 0.03/7.1 is the smallest fraction i.e option E.

“Of the following, which is least”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. This topic has been taken from the book “GMAT Official Guide Quantitative Review 2021”. The GMAT Problem Solving questions enhance the candidates’ skills in arithmetic, geometry and algebra. The candidates can go through GMAT Quant practice papers to improve their mathematical proficiency and knowledge.

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