__2015 OG Quant Review PS #15.__ If 60 percent of a rectangular floor is covered by a rectangular rug that is 9 feet by 12 feet, what is the area, in square feet, of the floor?

__Math Lessons__: (1) Translate from English to Algebra by partitioning sentences into phrases. To translate from English to Algebra, I will rewrite the passive clause “60 percent of a rectangular floor is covered by a rectangular rug that is 9 feet by 12 feet.” with the active voice “__A rectangular rug that is 9 feet by 12 feet__ __covers__ __60 percent of a rectangular floor__.” The Noun-subject = “A rectangular rug that is 9 feet by 12 feet” becomes the left-hand side of our equation. The Verb = “covers” means “is” and thus becomes our equal-to sign. The Noun-direct object = “60 percent of a rectangular floor” becomes the right-hand side of the equation; (2) As you progress, you won’t need to rewrite a clause with active voice to translate from English to Algebra. Let’s now translate the original “__60 percent of a rectangular floor__ __is covered__ __by a rectangular rug that is 9 feet by 12 feet__.” The Noun-subject = “60 percent of a rectangular floor” = left-hand side, the passive verb = “is covered” = equal, and “by a rectangular rug that is 9 feet by 12 feet” = right-hand side; and (3) Convert decimals to fractions because fractions enable cross-multiplication; (4) Cross-multiply by dividing first and multiplying second; (5) Divide 108 by 3 by knowing that 90 is 30*3 and the remaining 18 is 6*3. Thus 108 = 36*3; and (6) Multiply by 5 is *10 and 2.

__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 cheats with a calculator and still uses 4 lines and 297 characters, including “x = area of the floor”. Why not use a meaningful variable? Shawn Berry writes 2 lines and 55 characters, including the meaningful variable ‘Floor’. The OG solution uses 540% as many characters but provides less know-how.

__There’s Joy in Repetition__: In both PS#1 & PS#15, I used fractions and then cross-multiplied. The Official Guide twice used decimals and a calculator. On the bright side, at least we’ve seen the OG use the same solution twice!

__Shawn Berry (600 level).__ Inside an equilateral triangle of area A, a smaller equilateral triangle has vertices placed at the midpoints of the legs of the larger triangle. What is the area of the smaller equilateral triangle?

A. A/9

B. A/8

C. A/6

D. A/4

E. A/3

__Shawn Berry (650 level).__ At the center of a circle is a bulls eye with a radius equal to 20% of the circle’s radius. If the area of the circle excluding the bulls eye is 48 square inches, what is the area, in square inches, of the bulls eye?

A. 2

B. 4

C. 6

D. 8

E. 12

__Shawn Berry (700 level).__ If a cube of side length s centimeters and uniform thickness t centimeters has its interior surface area equal to 81% of its external surface area, what is the ratio of s to t?

A. 6:1

B. 8:1

C. 9:1

D. 10:1

E. 20:1

__Shawn Berry (750 level).__ A sphere of uniform thickness has its interior volume equal to 50% of its external volume. Given that the volume of a sphere is 4πr³/3, the inside radius is approximately what portion of the outside radius?

A. 60%

B. 65%

C. 70%

D. 75%

E. 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.