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A. Exponents and Multiple Answers
B. Simplifying Bases
C. The Products of Monomials and/or Polynomials
D. Quadratic Equations: Multiplying Binomials
E.
Factoring Algebraic Equations
A. Exponents and Multiple Answers
Life is never easy for MBA applicants. One of the GMAT's more difficult tricks is the "dual answer". You would think that a question like x2 = 25 would be simple, but it is not because there are two answers: -5 and +5. Any number raised to an even numbered exponent will always be positive. The reason for this is that -5 × -5 is 25.
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The "no answer" trick
x2 + 25 = 0
This is a "trick" statement because there isn't an answer to it. This breaks down into x2 = -25. x2 can't be a negative number.
Therefore, x2 + 25 = 0 can't have a real answer. |
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Solving for Dual Answers
Absolute value and even exponent equations questions will make any negative value positive, so they require you to construct two possible answers.
- Try to isolate the expressions within the absolute value or the even exponent.
- Solve for two scenarios, one where the value within the absolute value/even exponent is negative, one where it is positive.
- Solve for the negative value by replacing the absolute value with a parenthesis and a negative sign outside of it.
Try to solve this equation for both solutions: 6 - 5|x - 1| = 1
6 - 5|x - 1| = 1 |
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-5|x - 1| = -5 |
Subtract 6 from both sides. |
|x - 1| = 1 |
Divide by -5 from both sides.
Once you have isolated the absolute value, get rid of absolute value sign by creating two scenarios (one negative and one positive). |
Set to negative |
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Set to positive |
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-(x - 1) = 1 |
Negative scenario |
(x - 1) = +1 |
Add 1 |
-x + 1 = 1 |
Minus 1 from both sides |
x = 2 |
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x = 0 |
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