__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 1^{st} 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 1^{st} line now reads 2x/8 = x/8 + 2. Collect like terms in 2^{nd} line x/8 **= **2. Cross-multiply in 3^{rd} line: x = 16. D/C**.**

__To Add/Subtract__ __Fractions:__ Write 1^{st} 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 1^{st} line now reads 3a/6 + 2a/6 = 10**.** Collect like terms in 2^{nd} line 5a/6 = 10. Cross-multiply in 3^{rd} line; find *a* =12. D/C**.**

Write 1^{st} 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 1^{st} line should now read

5k/15 – 3k/15 = 40**.** Collect like terms in 2^{nd} line, 2k/15 = 40**.** Cross-multiply in 3^{rd} 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?

A. 24

B. 12

C. 0

D. –12

E. –24

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Shawn Berry (600 level).__ One-half subtracted from c/3 is one-half added to c/12 for what value of c?

A. 2

B. 3

C. 4

D. 5

E. 6

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Shawn Berry (600 level).__ For what value of k does k divided by the quantity k divided k/2 equal to 2?

A. 1/4

B. 1/2

C. 1

D. 2

E. 4

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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?

A. 2.70

B. 2.85

C. 3.00

D. 3.15

E. 3.30

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Shawn Berry (750 level).__ Five less the quantity b/3 less b/6 is two less than b for what value of b?

A. 3

B. 4

C. 5

D. 6

E. 7

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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.