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?
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?
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?
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?
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.