Column A: \(\frac{24}{23} + \frac{101}{100}\)
Column B: 2
Column B: 2
Show Hint
- Quantity A is greater
- Quantity B is greater
- The two quantities are equal
- The relationship cannot be determined from the information given
The Correct Option is A
Solution and Explanation
This question asks to compare a sum of two fractions to an integer. A quick way to solve this is by estimation, without calculating the full sum.
Step 2: Detailed Explanation:
Let's analyze the fractions in Column A.
The first fraction is \(\frac{24}{23}\). Since the numerator is greater than the denominator, this fraction is greater than 1. We can rewrite it as:
\[ \frac{24}{23} = \frac{23+1}{23} = 1 + \frac{1}{23} \] The second fraction is \(\frac{101}{100}\). This fraction is also greater than 1. We can rewrite it as:
\[ \frac{101}{100} = \frac{100+1}{100} = 1 + \frac{1}{100} \] Now, let's find the sum in Column A:
\[ \text{Column A} = \left(1 + \frac{1}{23}\right) + \left(1 + \frac{1}{100}\right) = 2 + \frac{1}{23} + \frac{1}{100} \] Step 3: Comparing the Quantities:
Column A: \(2 + \frac{1}{23} + \frac{1}{100}\)
Column B: 2
Since \(\frac{1}{23}\) and \(\frac{1}{100}\) are both positive numbers, their sum is positive. Therefore, the value in Column A is 2 plus a small positive amount, which is definitively greater than 2.
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Questions Asked in GRE exam
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