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On GMAT problems with very large exponents in numerator and denominator, factor the highest power, cancel, then simplify.
Example: (5100 + 599) / (599 + 598) = 598(52 + 5) / [598(5 + 1)] = (25 + 5) / (5 + 1) = 30/6 = 5.
One of the most common ways the GMAT tests higher-order thinking is by presenting intimidating expressions with extremely large powers. At first sight, such problems can look time-consuming, but the trick is to pause and look for what cancels out. The real test here is not your ability to compute massive numbers, but your clarity in spotting simplification. Whenever you see unusually high exponents in both numerator and denominator, the question is often designed so that the largest power can be factored out and cancelled. What initially looks heavy reduces to something very small and easy. This kind of simplification is not just about solving a single question; it builds the habit of looking deeper instead of panicking. Over time, such skills become second nature through regular GMAT preparation and careful analysis during GMAT practice tests, allowing you to approach the exam with calm confidence.
(2100 + 2101 + 2102 + 2103) / (299 + 2100 + 2101 + 2102) = ?
This type of GMAT problem involves very high powers that appear in both the numerator and denominator of a fraction. At first glance, the expression looks unmanageable, but the test-maker deliberately sets it up so that the largest power cancels out, leaving behind something simple.
In the example, the numerator and denominator both contained terms involving 2 raised to high powers. By taking 299 common in both, the intimidating expression reduced immediately. The huge terms cancelled each other, and what remained was a simple value of 2. The principle here is straightforward: factor out the largest common surd, cancel it, and simplify.
Given: (2100 + 2101 + 2102 + 2103) / (299 + 2100 + 2101 + 2102)
Factor the numerator: 2100(1 + 2 + 4 + 8) = 2100 × 15
Factor the denominator: 299(1 + 2 + 4 + 8) = 299 × 15
On cancelling 299 in numerator and denominator we get,
Answer: 2
(3200 + 3201 + 3203) / (3199 + 3201 + 3203) = ?
When faced with 3 raised to very high powers, the same logic applies.
By taking 3199 common from numerator and denominator, the big terms cancel, leaving a small fraction.
What looked complex simplifies to 93/91.
Answer: 93/91
The key learning is that GMAT questions involving massive exponents are rarely about brute calculation. They are about spotting the cancellation opportunity and staying calm under pressure. This is where consistent work with GMAT mock trains your eyes to recognize patterns quickly. Once you internalize this approach, such problems stop feeling threatening and instead become quick wins.
The lesson behind expressions with very large powers is simple: do not fight the size, look for the structure. When you pause, factor out what is common, and let cancellations speak, the chaos fades and a small, clear result appears. This habit is more than a math move; it is a way of thinking. You learn to quiet urgency, see patterns, and choose steps that conserve effort. The same discipline helps in an insightful MBA application process, where careful selection, clear framing, and steady refinement create strength. Clarity grows when you remove what does not matter and highlight what does.
