__2015 OG Quant Review PS #13.__ The number of rooms at Hotel G is 10 less than twice the number of rooms at Hotel H. If the total number of rooms at Hotel G and Hotel H is 425, what is the total number of rooms at Hotel G?

__Math Lessons__: (1) Because the GMAT uses integer coefficients, add or subtract **two equations with two variables** to find one equation with one variable, a simpler process than substitution; (2) Cancel either G or H because you want to solve for both G and H so that you can **double-check** that the two original equations hold true. The flexibility to cancel either G or H gives you twice as many options on how you proceed. In contrast, the Official Guide substitution solution forces you substitute for H. Notice that in this question, G was easier to substitute; and (3) Double-checking the original equations guarantees that you find the correct G and H values! The OG solution does not find H and thus fails to double-check, a serious strike against its already-inefficient solution.

__Character count__: The OG’s solution uses 6 lines and 279 characters; Shawn Berry writes 3 lines and 90 characters. The OG solution writes twice as many lines and 310% as many characters as necessary.

__There’s Joy in Repetition__: Although two equations with two variables may obscure matters, again our first step was to collect like terms by collecting H on the right-hand side (rhs), where H is positive. Collect like terms has been my first step in PS #1, PS #2, PS #3, and now PS #13. In contrast, the Official Guide has written four different first steps (PS#1 Put variable on side where it’s negative!; PS #2 Multiplying by lcd to clear fractions; PS #3 English (non-Algebra) solution; and PS #13 Substitute). Compare and contrast – I will teach you Collect like terms, Collect like terms & Collect like terms — and you will learn to Collect like terms. The OG will teach you different solution after different solution after different solution. You might never see the same solution twice.

__Shawn Berry (600 level).__ Before a diet, a boyfriend weighed fifty pounds more than his girlfriend. But reducing his calories consumed reduced his metabolic rate, causing him to gain 15 pounds. If after the diet the boyfriend weighs 50% more than his girlfriend, whose weight did not change, how many pounds does he now weigh?

A. 180

B. 195

C. 210

D. 225

E. 240

__Shawn Berry (650 level).__ If the number of cars rented by Company A doubled, then A would have rented 75 more cars than Company B, not 75 fewer. How many cars have the two companies rented?

A. 325

B. 375

C. 425

D. 475

E. 525

__Shawn Berry (750 level).__ M increased one-half is twelve more than N increased one-fifth. M decreased two-fifths is twelve less than N decreased one-third. What is the difference between M and N?

A. – 10

B. – 5

C. 0

D. 5

E. 10

__Shawn Berry (800 level).__ Let x be one-sixth less than y and z exceed x by three-fifths. If y and z average to 10 more than the average of x, y and z, what is the average of x, y, and z?

A. 75

B. 80

C. 85

D. 90

E. 95

__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.