99,999^2−1^2 = ? GMAT Problem Solving

Question: 99,999^2 − 1^2 = ?

1. 10^10-2
2. (10^5–2)^2
3. 10^4(10^5–2)
4. 10^5(10^4–2)
5. 10^5(10^5–2)

“99,999^2 − 1^2 = ?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:

Approach Solution 1:

This question can be solved by only this approach.

It is asked in the question to find out the value of 99,999^2−1^2
It should be noted that this question does not require us to square both the terms and then subtract.
It can be seen that this equation is of the form
\(a^2\)-b2
Therefore we can write this equation as,
(a-b)(a+b)
For example, if a = 4 and b = 2
\(a^2\)-\(b^2\)= \(4^2\)-\(2^2\)= 16-4=12
(a-b)(a+b) = (4-2)(4+2) = 2*6=12
Both are same.
In this question we are asked to solve 99,999^2−1^2
a = 99999 and b = 1
(a2-b2) = (a-b)(a+b)
(\(99999^2\)-\(1^2\)) = (99999+1)(99999-1)
= (100000)(99998)
= \(10^5 \)(\(10^5 \)- 2)

Correct Answer: E

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