2015 OG Quant Review PS #20. (1 + √5) (1 – √5) =
Math Lessons: (1) Factor a difference of squares, a² – b² = (a+b)(a–b) and apply it in either direction. Don’t mindlessly use FOIL (as the Official Guide did) when a simpler solution applies; (2) Similarly, know that a² + 2ab + b² = (a+b)(a+b), that a² – 2ab + b² = (a–b)(a–b), and that a² + b² does not factor in the real numbers; (3) Know FOIL – wherein you find first*first + outer*outer + inner*inner + last*last – and be ready to use it if a simpler method, such as one listed above, does not apply; and (4) Study what mathematics fits where. To date, in just the tenth OG solution that I’ve criticized, I have started to train you to (i) collect like terms on the side where they are positive, (ii) use fractions, not decimals, so that you can cross-multiply, (iii) multiply numerator and denominator by the same quantity to achieve the common denominator and then read the given fraction interchangeably with the fraction converted to a common denominator, (iv) translate from English to Algebra wherein the Noun-subject is the left-hand side of the equation, the Verb is the equal to sign, and the Noun after the Verb is the right-hand side of the equation, (v) rewrite any fraction as a percent by forcing the denominator = 100, (vi) add or subtract two equations with two variables to simplify to one equation with one variable, (vii) double-check your answer to guarantee accuracy, (viii) use a meaningful variable to make sense of what you write, (ix) notice that the words “per”, “each”, “every”, “for”, and “a” indicate the fractional units of a Rate, (x) upon noticing a Rate, write Rate*Time=Distance, (xi) draw a 2×2 chart when you see two partitions, such as Men versus Women (sex) and College grads versus ∼College grads (education), and (xii) factor a difference of squares. Because I repeatedly use the same solutions – only the best solutions – you will see these lessons demonstrated over and over again.
Character count: The OG’s solution uses 2 lines and 57 characters; Shawn Berry writes 1 line and 19 characters. The OG solution uses 300% as many characters as necessary. Each line matters; each character matters.
Shawn Berry (600 level) What is value of (2√2 + √50) (√18 + √98)?
Shawn Berry (650 level) Approximate each root to the tenths place and then evaluate (√2 + √3) (√4 + √5).
Shawn Berry (700 level) Factor x² – (y²)².
A. (x + y)(√x + y)(√x – y)
B. (x + y)(√x – y)(√x – y)
C. (x + y²)(√x – y)(√x – y)
D. (x + y²)(√x + y)(√x – y)
E. (x – y²)²
Shawn Berry (750 level) Factor a³ – b³ = 0.
A. (a – b)³ = 0
B. (a – b)(a² + ab + b²) = 0
C. (a – b)(a² + 2ab + b²) = 0
D. (a + b)(a² – ab + b²) = 0
E. (a + b)( a² – 2ab + b²) = 0
Shawn Berry (750 level) Factor p³ + q³ = 0.
A. (p + q)(p² – pq + q²) = 0
B. (p + q)(p² – 2pq + q²) = 0
C. (p – q)(p² + pq + q²) = 0
D. (p – q)(p² + 2pq + q²) = 0
E. No factoring exists within the real numbers
Legal Note: “The Graduate Management Admissions Council (GMAC) firmly believes that the Official Guide for GMAT Review is all that you need to perform your best on the GMAT … and that no additional techniques or strategies are needed to do well.” I, Shawn Berry, know better. I have twice earned a perfect 800 on the GMAT-CAT. I document that the Official Guide writes inconsistent, inefficient, and downright confusing solutions that take longer than the allotted 2 minutes/question. Herein I make fair use of GMAC copyrighted material – mostly its confusing solutions – for the transformative educational purpose of teaching students the clear, consistent, and efficient Mathematics, Grammar, and Logic needed to answer GMAT questions in less than 2 minutes.