\(999,999^2\)−1 equals? GMAT Problem Solving

Question: \(999,999^2\)−1 equals?

1. \((9^2) (11^2)\)
2. \((10^6) (10^5-2)\)
3. \((10^6) (10^6-2)\)
4. \((10^5)^2\)
5. \((10^6)^2\)

‘\(999,999^2\)−1 equals ?’ - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “Official Guide for GMAT Reviews”. To solve GMAT Problem Solving examiners measure how well the candidates make analytical and logical approaches to solve numerical problems. In this section, candidates have to evaluate and interpret data from given graphical representation. In this section, mostly one finds out mathematical questions. Five answer choices are given for each GMAT Problem solving question.

Solution and Explanation:

Approach Solution 1:

There is only one approach to solve the problem statement.
This is a simplification problem. We can use the factorize formula to solve the given problem.

\(x^2 - y^2\) = (x+y)(x-y)

So, the given question can be solved using the above formula

\(999,999^2\)−1

= \(999,999^2\)−\(1^2\)

=(999,999 +1)(999,999-1)
=(1,000,000)(999,998)

= \((10^6) (10^6-2)\)

Hence option C is the correct answer.

Correct Answer: C

Suggested GMAT Problem Solving Questions

• Is quadrilateral ABCD a rectangle GMAT Problem Solving 
• If x is positive, which of the following could be the correct ordering of 1/x, 2x and x^2 GMAT Problem Solving
• What is the angle between the minute and the hour hand of the clock which shows 12:24 GMAT Problem Solving
• What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 3 GMAT Problem Solving
• Two varieties of sugar are mixed together in a certain ratio GMAT Problem Solving
• y varies directly as x and when x = 6, y = 24. What is the value of y, when x = 5? GMAT Problem Solving
• How many factors does 36^2 have? GMAT Problem Solving
• Walking at 6/7 th of his usual speed, a man is 25 min too late GMAT Problem Solving
• A number when divided successively by 4 and 5 leaves remainder 1 and 4 GMAT Problem Solving
• A jet is flying 2400 miles from Hawaii to San Francisco. In still air, it flies at 600 mph. There is a 40 mph tailwind in the same direction GMAT Problem Solving
• If a carton containing a dozen mirrors is dropped, which of the following cannot be the ratio of broken mirrors to unbroken mirrors GMAT Problem Solving
• Two solutions having milk and water in the ratios 3 : 5 and 4 : 7 are mixed in the ratio 2 : 3. GMAT Problem Solving
• A mixture of 40 liters of milk and water contains 10% water GMAT Problem Solving
• A Train Travelling at 100 kmph Overtakes a Motorbike Travelling at 64 kmph in 40 seconds GMAT Problem Solving
• Eight litres of wine is drawn from a cask full of wine and is replaced with water GMAT Problem Solving
• The closing price of Stock X changed on each trading day last month The percent change in the closing price of Stock X GMAT Problem Solving 
• If P and Q are positive integers, is P divisible by 12? GMAT Problem Solving
• At a certain laboratory, chemical substances are identified by an unordered combination of three different colours GMAT Problem Solving
• Iqbal Dealt Some Cards to Mushtaq and Himself From a Full Pack of Playing Cards and Laid the Rest Aside GMAT Problem Solving
• If a and b are integers, and b > 0, does (a - 1)/(b + 1) = a/b? GMAT Problem Solving