Which of the following values is the largest: 53, 64, 126 or 27612?

Introduction / Context:
This question is a simple comparison of four positive integers. It ensures that learners can quickly identify the largest among a set of values, which is a basic but essential skill in quantitative reasoning. Although this is far easier than many other number problems, it still requires careful reading to avoid mistakes.

Given Data / Assumptions:
- The given numbers are 53, 64, 126 and 27612. - All are positive integers. - We must find the single largest value among them.

Concept / Approach:
- When comparing natural numbers, the number with more digits is automatically larger than any number with fewer digits. - If numbers have the same number of digits, compare digit by digit from left to right. - Here, only one number has five digits while the others have two or three digits.

Step-by-Step Solution:
Step 1: Note the number of digits in each candidate. 53 and 64 are two digit numbers, 126 is a three digit number and 27612 is a five digit number. Step 2: Any five digit number is larger than any three digit number, which in turn is larger than any two digit number because the place value of the leading digit is much higher. Step 3: Since 27612 is the only five digit number in the list, it must be greater than 126, 64 and 53. Step 4: Therefore, 27612 is the largest of the given values.

Verification / Alternative check:
We can also do rough comparisons using magnitude. 53 and 64 are less than 100, 126 is a little more than 100, while 27612 is greater than 27000. Clearly, a number of order tens of thousands is far larger than numbers around 100 or below.

Why Other Options Are Wrong:
Option A (53): This is only a two digit number and is smaller than 64, 126 and 27612. Option B (64): Larger than 53 but still only two digits, so it is far smaller than 126 and especially 27612. Option D (126): This is a three digit number and is larger than 53 and 64, but it is much smaller than 27612. Option E (None of these): Not correct because one of the listed options, namely 27612, is clearly the largest.

Common Pitfalls:
- Overthinking a simple comparison problem and trying to find hidden structure instead of straightforwardly comparing. - Misreading one of the numbers, especially 27612, and assuming it has fewer digits. - Forgetting that digit count is the quickest way to spot the largest among positive integers.

Final Answer:
The largest value among the given numbers is 27612.