__2015 OG Quant Review PS #3.__ If Mario was 32 years old 8 years ago, how old was he x years ago?

Original equation not counted as a line in the solution.

__Math Lessons__: (1) Algebra is the study of writing and solving equations – and solving equations is the easy part. The hard part of Algebra is to **translate from English to Algebra by writing the first equation**. So learn to write equations because you must write equations to solve hard GMAT questions. The English (non-Math) solution that the Official Guide volunteered above is not widely applicable nor sufficient to solve the five difficult questions below; (2) Learn that x years ago means subtract x; learn that y years from now means add y; and (3) Respect the question! Identify what each question is asking, here Mario’s age x years ago, M – x. For every question, **identify the question asked** so that you improve your likelihood of answering the damn question. All too often when the questions get harder, test takers answer some variation of the question, not the question asked.

__Character count__: The OG writes 99 characters; Shawn Berry writes 12 characters. The OG solution uses 825% as many characters**.** Each line matters; each character matters**.** You don’t have time for the OG’s confusing solutions.

__There’s Joy in Repetition__: Collect like terms has been my first step to solving PS #1, PS #2, and PS #3. In contrast, the Official Guide has written three solutions with three different first steps. Students learn when they are taught simple, repetitive solutions – solutions they can practice over and over. Students get confused and fail to learn when they are taught inconsistent solutions. The OG doesn’t help students to practice any specific solution. Shawn Berry helps students to practice his best solutions over and over again.

__Shawn Berry (550 level).__ If k years ago Leona was n years shy of 40, how old is Leona?

A. 40 + k + n

B. 40 + k – n

C. 40 – k + n

D. 40 – k – n

E. 40 – kn

Shawn Berry (600 level). If Brant was b years ago c years ago, in how many years from now will he be d years old?

A. d – b + c

B. d – b – c

C. d + b – c

D. b + c – d

E. b – c – d

__
Shawn Berry (650 level).__ If in y years Yujie will be x – y years shy of 30, how old is Yujie?

A. 30 – x

B. 30 – y

C. 30 – x – y

D. 30 – x + y

E. 30 + x – y

__Shawn Berry (700 level).__ If m < n and Cynthia was m years ago n years ago, how many years ago was she 2m years old?

A. Cynthia is not yet 2m years old

B. Now

C. m – n

D. n – m

E. (m+n)/2

__Shawn Berry (750 level).__ For 0 < w < x < y < z, if Evan was w years old y – x years ago, in how many years will Evan be z years old?

A. Evan is already z years old

B. z + x + y – w

C. z + x – y – w

D. z – x + y – w

E. z – x – y + w

__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.