2015 OG Quant Review PS #17. The value of –3 – (–10) is how much greater than the value of –10 – (–3)?
Math Lessons: (1) Translate from English to Algebra; partition sentence into phrases N-Subject, Verb, and Pred-N. The value of –3 – (–10) is how much greater than the value of –10 – (–3) is underlined as you should read it. You may not realize it, but you don’t read sentences in words. That is, you don’t break stride at random places. Instead you read in phrases, which I am underlining above to show how you translate from English to Algebra. The Noun-subject = “The value of –3 – (–10)” becomes the left-hand side of our first equation. Verb “is” means equals. The Predicate–Noun = “how much greater than the value of –10 – (–3)” becomes the right-hand side; (2) As you progress, you won’t need to underline. My goal is to train you so that, with due practice, you translate the English “The value of –3 – (–10) is how much greater than the value of –10 – (–3)” to the Algebra 7 = –7 + h, where h is the meaningful variable ‘how much greater’; and (3) In contrast, the Official Guide doesn’t translate from English to Algebra. The OG uses no variable for “how much greater”. The OG fails to capture the sentence (equation) in its entirety – the OG’s first line is the N-subject and the second line is part (not all) of the Pred-N. Finally, the OG’s third line comes out of nowhere, only works because the question is easy, and is not scalable. Translate from English to Algebra: Write meaningful variables by using the first letter. Set C = cats and D = dogs. In contrast, in PS #15 the Official Guide wrote “let x = area of the floor”. That’s like letting X = cats. How would you remember that? Now without looking to the right of the page, translate from English to Algebra. English: “y is how much greater than 100.” Algebra: y = 100 + h, because ‘how much greater’ means you add h. English: “a is how much less than b.” Algebra: a = b – h, because ‘how much less’ means that you subtract h. English: “m is what percent less than n.” Algebra: m=[(100–p)/100]n because ‘p% less’ multiplies by (100–p)/100.
Character count: The OG’s solution uses 4 lines and 45 characters. Notice that the OG doesn’t translate from English to Algebra, failing to teach you how to write the first equation needed to solve GMAT questions. Shawn Berry writes 2 lines and 10 characters. The OG solution uses twice as many lines and 450% as many characters.
There’s Joy in Repetition: I always translate from English to Algebra – and so should you! In contrast, the Official Guide has written wildly different solutions for PS #15 and PS #17, which were probably written by two different authors. To solve each, partition the English into Noun-subject, Verb, and Noun-Direct Object (or Noun-Subject, Verb, and Predicate-Noun) to determine the Algebra left-hand side = right-hand side (lhs = rhs).
Shawn Berry (550 level). –1² is how much greater than the reciprocal of –1?
Shawn Berry (600 level). For operation defined by a⊕b = a(b–a), a⊕b is how much greater than b⊕b?
Shawn Berry (650 level). For operation defined by x⊗y =x(x+y), x⊗y is how much greater than y⊗x?
A. x + y
B. x – y
C. (x + y)(x – y)
D. x² + y²
E. y² – x²
Shawn Berry (750 level). For operation defined by mΘn = m+n+mn, mΘn is how much less than mΘ2n?
C. (mΘn) – mn
D. (mΘn) – m
E. (mΘn) – n
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.