__2015 OG Quant Review PS #1.__ The maximum recommended pulse rate R, when exercising, for a person who is x years of age is given by the equation R = 176 – 0.8x. What is the age, in years, of a person whose maximum recommended pulse rate when exercising is 140?

Original equation is not counted as a line in the solution.

__Math Lessons__: (1) **Collect like terms** by putting the variable on the side where it’s positive. In contrast, using negatives leads to sign errors; (2) **Convert decimals to fractions** because fractions allow you to perform cross-multiplication that decimals do not allow; and (3) **Cross-multiply** by dividing first and multiplying second.

__OG Calculator__: The Official Guide for GMAT Review writes solutions that require a Calculator – which is absolutely not permitted on the GMAT! If you use a calculator, your test will be cancelled, your $250 test fee will be forfeited, and you will be evaluated for further punishment. I can’t know why the authors of The Official Guide use a calculator, but I conjecture that the authors are embarrassed by their already long and inefficient solutions and hope that nobody criticizes them for shaving a few lines off by inappropriately using a calculator.

__Character count__: The OG solution uses 5 lines and 38 characters, including 4 negatives; Shawn Berry writes 2 lines and 11 characters, including 0 negatives. The OG solution uses 345% as many characters as necessary. Each line matters; each character matters. You don’t have extra time on test day.

__Legal Note__: The maximum recommended pulse rate is a medical term that has been in wide use for decades.

__Shawn Berry (550 level).__ The maximum recommended pulse rate of 176 – 0.8x is 20 percent less than the maximum pulse rate of

A. 200 – x

B. 210 – 0.8x

C. 210 – x

D. 220 – 0.8x

E. 220 – x

__Shawn Berry (600 level).__ The maximum recommended pulse rate for a person x years of age is 176 – 0.8x. By what fraction would a 40-year old man exceed his maximum recommended pulse rate if his pulse reached the maximum recommended pulse rate for a man half his age?

A. 1/10

B. 1/9

C. 1/8

D. 1/7

E. 1/6

__Shawn Berry (650 level).__ The maximum recommended pulse rate for a person x years of age is 176 – 0.8x. If the pulse of a 20-year old woman reached the maximum recommended pulse rate for a 30-year old woman, by which percentage would she be shy of her maximum recommended pulse rate?

A. 5%

B. 10%

C. 15%

D. 20%

E. 25%

__Shawn Berry (750 level).__ The maximum recommended pulse rate for a person x years of age, 176 – 0.8x, is 80 percent of the maximum pulse rate for a person of that age. For which pair is the maximum recommended pulse rate of the first age equal to the maximum pulse rate of the second age?

A. (25, 65)

B. (30, 70)

C. (35, 70)

D. (40, 75)

E. (45, 80)

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.