2015 OG Quant Review PS #2. If x/4 is 2 more than x/8, then x = .
Note: Original equation is not counted as a line in the solution.
Math Lesson: (1) Given 1st line x/4 = x/8 + 2, find in your head the least common denominator of 4 & 8, lcd(4,8)=8. Amend the first fraction x/4 by multiplying both the numerator (top) and denominator (bottom) by 2. The 1st line now reads 2x/8 = x/8 + 2. Collect like terms in 2nd line x/8 = 2. Cross-multiply in 3rd line: x = 16. D/C.
To Add/Subtract Fractions: Write 1st line a/2 + a/3 = 10 and in your head find lcd(2,3)=6. Amend the first fraction by multiplying top & bottom by 3 and the second fraction by multiplying top & bottom by 2. Your 1st line now reads 3a/6 + 2a/6 = 10. Collect like terms in 2nd line 5a/6 = 10. Cross-multiply in 3rd line; find a =12. D/C.
Write 1st line k/3 – k/5 = 40 and in your head find lcd(3,5)=15. Amend the first fraction by multiplying top & bottom by 5 and the second fraction by multiplying top & bottom by 3. Your amended 1st line should now read
5k/15 – 3k/15 = 40. Collect like terms in 2nd line, 2k/15 = 40. Cross-multiply in 3rd line; find k = 300. Double-check.
Character count: The OG writes 3 lines and 25 characters; Shawn Berry writes 2 lines and 9 characters. The OG solution uses 278% as many characters as necessary. Each line matters because you can waste 60 seconds to get a second 6-page workbook. Each character matters because you must answer 37 Quant questions in 75 minutes.
There’s Joy in Repetition: Collect like terms and then Cross-multiply is the same solution that I taught in PS #1. In contrast, the Official Guide’s solutions to PS #1 and PS #2 vary. Students learn best when they are taught simple, repetitive solutions. Students get confused and fail to learn when they are taught varying solutions.
Shawn Berry (550 level). Two less than a/3 is two more than a/2 for what value of a?
Shawn Berry (600 level). One-half subtracted from c/3 is one-half added to c/12 for what value of c?
Shawn Berry (600 level). For what value of k does k divided by the quantity k divided k/2 equal to 2?
Shawn Berry (650 level). For what value of n does one-eight less than one-seventh of n equal one-fifth less than one-sixth of n?
Shawn Berry (750 level). Five less the quantity b/3 less b/6 is two less than b for what value of b?
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.