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### 28 Cards in this Set

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 What are 3 easy manipulations that are the key to solving most COMBO problems M: Multiply / divide the whole equation by a certain number. U: Unsquare / square both sides. D: Distribute and factor. Absolute value equations have ____ solutions. What is the exception to this rule? Absolute value equations must be solved for positive and negative cases inside the brackets. The exception is when the solution is zero. Even exponents are dangerous because ____________________ They hide the sign of the base. Mismatch problems are_________. What do you do? Problems in which the number of variables does NOT correspond to the number of given equations. All MISMATCH problems must be solved on a case by case basis. What form of exponential equations have no real solution? x^2 + 9 = 0 The square of any number cannot be ____________? The square of any number cannot be a NEGATIVE number In problems involving exponential expressions on BOTH sides of the equation, it is imperative to REWRITE the bases so that _________.... So that either the SAME BASE or the SAME EXPONENT appears on both sides of the exponential equation. Then you can ELIMINATE THE BASES or EXPONENTS and rewrite the remainder as an equation. All quadratic equations on the GMAT can be _____. You'll never need _______ All GMAT quadratics can be FACTORED. You will never need to use the quadratic formula. A fraction can never have _________. This would make the problem ___. Fractions can never have a denominator of 0. This would make the problem undefined. x^2 - y^2 = (x+y)(x-y) x^2 + 2xy + y2 = (x+y)(x+y) x^2 - 2xy + y^2 = (x-y)(x-y) If the difference between successive terms is always the same, the rule will take the form: kn + x where k and x are real numbers and k = difference between successive terms. Ex: 16, 20, 24, 28 => 4n + x => 4(1) + x = 16. x = 12. 4n + 12. If the difference between the difference between successive terms is always the same, the rule will take the form: an^2 + bn + c, where a,b,c are real numbers. N = term number. 18, 27, 38, 51. Differences - 9,11,13 Difference between differences - 2,2,2 Name the two equations for two classic sequence equations: kn + x OR an^2 + bn + c Simple additive sequence method? Ex: If each # in a sequence is 3 more than the previous number, and the 6th number Is 32, what is the 100th number? From the 6th to the 100th term, there are 94 jumps of three. 94 x 3 - 282, there is an increase of 282 from the 6th term to the 100th term. 32 + 282 = 314. If S(n) = 3 ^ n, what is the units digit of S(65)? Can you do 3 ^ 65 easily? Look for patterns in the powers of three. 3^1 = 3, 3^2 = 9, 3^3 = 27, 3^4 = 81, etc. When you multiply / divide an inequality by a negative number, ____________ The inequality sign flips! Given that xy < 3y, what is the range of possible values for x? In order to isolate x in the equation, ti seems we would divide both sides of the inequality by y. Ths would yield x < 3. x^2 < 4 x < 2 and x > -2 OR -2 < x < 2 x^2 > 81 x > 9, and x < -9. X can by any number except for those between -9 and 9. Equations with absolute value have ___ solutions. How do you do it? 2 solutions. Solve by removing brackets. Reverse signs of terms inside brackets and solve again. How do you combine inequalities? Solve them, simplify w/ all inequality symbols in the same direction, line up common variables, combine by taking more limiting upper and lower extremes. What is the best way of solving GMAT inequality problems? Focus on extreme values of given inequality. Test them… Data sufficiency problems that involve algebraic equations / inequalities can usually be solved through ___________________ Algebraic manipulations. Either manipulate original question or statements. DS: Rephrase where helpful: Is p > q? I. -3p < -3q II. p - r > q - r D. Both sufficient. I. p > q II. p > q Rephrase Statements by dividing out -3 (swap sign) and add r. DS: Rephrase where helpful: What is the value of r + u? I. rs - ut = 8 + rt - us II. s - t = 6 I. rs - rt - ut + us = 8 next: r(s-t) + u(s-t) = 8 next: (r+u)(s-t) = 8 so: r + u = 8 / (s - t) -- II. S - t = 6 C DS: Rephrase where helpful: If ab = 8, is a greater than b? I. -3b > -18 II. 2b > 8 B.