Web Chat: Quantitative GMAT

GMAT Quantitative SectionOverview, Strategies, and Sample OG Problems

Chat Participants

Angela Bostick, 04MBA Associate Dean of Marketing and Communications Goizueta Business School Emory University

Stephanie Espy, 08MBA Founder and Executive Director MathSP Tutoring & Test Prep www.MathSP.com [email protected]

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GMAT Quantitative Section Overview

• Two question types: – Problem Solving (PS)

• Solve each problem and choose the correct response from 5 answer choices

– Data Sufficiency (DS)• Each problem consists of a question and two statements labeled (1)

and (2), each of which contain data• Determine whether the data given are sufficient for answering the question

• 37 questions total (~21 PS and ~16 DS)• 75 minutes total• Approx. 2 min per question on average

GMAT Quantitative Concepts Tested• Arithmetic Concepts

– Integers (even, odd, positive, negative, consecutive), Number Lines, Digits, Rounding, Prime, Factors, Multiples, Division, Divisibility Rules, Remainders, Fractions, Ratios, Proportions, Percents, Order of Operations, Squares and Powers, Roots, Data Analysis, Operations on Rational Numbers

• Algebra Concepts– Exponents, Scientific Notation, Factor, FOIL, Absolute Value, Solving Equations,

Substitution, Rate, Work, Distance, Inequalities, Translations, Overlapping Sets, Average, Median, Standard Deviation, Range, Probability, Permutations, Combinations, Sets, Linear Functions, Slope, Intercepts, Symbols

• Geometry Concepts– Lines and Angles, Parallel, Perpendicular, Transversal, Circles, Radius, Diameter,

Circumference, Area, Tangent, Triangles, Perimeter, Right Triangles, Isosceles, Equilateral, Similar, Pythagorean Theorem, Triangle Inequality Theorem, Quadrilaterals, Volume, Coordinate Geometry, Shaded Regions

Some Very Useful GMAT Quantitative Strategies

– Diagram-It – Pick-A-Number (PS only)

• Variables in Question and in Choices• “What Fraction”• “How Many”

– Back-Solve (PS only)• Variables in Question but NOT in Choices

– Pattern Recognition– POE using AD/BCE or BD/ACE (DS only)– Stop when you have Enough Info (DS only)– Extremes– Built-in Constraints– Simplify the Given and the Find (DS only)– Don’t Assume Integers Only– Prove-It! (DS only)– Redraw and Label Diagrams

Problem Solving Sample Question #1 from the Official Guide Book by GMAC – 13th Edition

PS 116: If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3k is a factor of p? A) 10 B) 12 C) 14 D) 16 E) 18

Concepts tested: Definitions (product, integer, inclusive, factor), exponents, factors & multiples

Strategy: Diagram-It

Level: Mid 500’s

Problem Solving Sample Solution #1 from the Official Guide Book by GMAC – 13th Edition

PS 116: If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3k is a factor of p?

A) 10 B) 12 C) 14 D) 16 E) 18

Problem Solving Sample Question #2 from the Official Guide Book by GMAC – 13th Edition

PS 151: At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worked on the day crew. If the night crew has 4/5 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load? A) 1/2 B) 2/5 C) 3/5 D) 4/5 E) 5/8

Concepts tested: Translating words into operations, fractions

Strategy: Diagram-It and Pick-A-Number

Level: High 500’s - Low 600’s

Problem Solving Sample Solution #2 from the Official Guide Book by GMAC – 13th Edition

PS 151: At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worked on the day crew. If the night crew has 4/5 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?

A) 1/2 B) 2/5 C) 3/5 D) 4/5 E) 5/8

Problem Solving Sample Question #3 from the Official Guide Book by GMAC – 13th Edition

PS 184: Lois has x dollars more than Jim has, and together they have a total of y dollars. Which of the following represents the number of dollars that Jim has? A) (y-x)/2 B) y-(x/2) C) (y-2)/x D) 2y-x E) y-2x

Concepts tested: Translating words into operations

Strategy: Diagram-It and Pick-A-Number

Level: Mid - High 600’s

Problem Solving Solution Question #3 from the Official Guide Book by GMAC – 13th Edition

PS 184: Lois has x dollars more than Jim has, and together they have a total of y dollars. Which of the following represents the number of dollars that Jim has?

A) (y-x)/2 B) y-(x/2) C) (y-2)/x D) 2y-x E) y-2x

Problem Solving Sample Question #4 from the Official Guide Book by GMAC – 13th Edition

PS 186: Of 30 applicants for a job, 14 had at least 4 years’ experience, 18 had degrees, and 3 had less than 4 years’ experience and did not have a degree. How many of the applicants had at least 4 years’ experience and a degree? A) 14 B) 13 C) 9 D) 7 E) 5

Concept tested: Overlapping sets

Strategy: Diagram-It

Level: Mid - High 600’s

Problem Solving Sample Solution #4 from the Official Guide Book by GMAC – 13th Edition

PS 186: Of 30 applicants for a job, 14 had at least 4 years’ experience, 18 had degrees, and 3 had less than 4 years’ experience and did not have a degree. How many of the applicants had at least 4 years’ experience and a degree?

A) 14 B) 13 C) 9 D) 7 E) 5

Problem Solving Sample Question #5 from the Official Guide Book by GMAC – 13th Edition

PS 215: Xavier, Yvonne, and Zelda each try independently to solve a problem. If their individual probabilities for success are 1/4, 1/2, and 5/8, respectively, what is the probability that Xavier and Yvonne, but not Zelda, will solve the problem? A) 11/8 B) 7/8 C) 9/64 D) 5/64 E) 3/64

Concept tested: Probability

Strategy: Diagram-It

Level: High 600’s – Low 700’s

Problem Solving Sample Solution #5 from the Official Guide Book by GMAC – 13th Edition

PS 215: Xavier, Yvonne, and Zelda each try independently to solve a problem. If their individual probabilities for success are 1/4, 1/2, and 5/8, respectively, what is the probability that Xavier and Yvonne, but not Zelda, will solve the problem?

A) 11/8 B) 7/8 C) 9/64 D) 5/64 E) 3/64

Problem Solving Sample Question #6 from the Official Guide Book by GMAC – 13th Edition

PS 216: 1 1 1

In the equation above, x could be A) 0 B) -1 C) -2 D) -3 E) -4

Concepts tested: Solving equations with fractions with variables in the denominator

Strategy: Back-Solve

Level: High 600’s – Low 700’s

x x+1 x+4

Problem Solving Sample Solution #6 from the Official Guide Book by GMAC – 13th Edition

PS 216: 1 1 1

In the equation above, x could be

A) 0 B) -1 C) -2 D) -3 E) -4

x x+1 x+4

A Statement (1) ALONE is sufficient, but statement (2) alone is not sufficientB Statement (2) ALONE is sufficient, but statement (1) alone is not sufficientC BOTH statements (1) and (2) TOGETHER are sufficient, but NEITHER statement (1) or (2) ALONE is sufficientD Each statement (1) and (2) ALONE is sufficientE Statements (1) and (2) TOGETHER are not sufficientNOTE: In DS problems that ask for a value, the data given in the statements are only

sufficient when it is possible to determine exactly one value.

Data Sufficiency Answer Choices

Eliminating Data Sufficiency Answer Choices

Data Sufficiency Sample Question #1 from the Official Guide Book by GMAC – 13th Edition

DS 72: If m is an integer, is m odd? (1) is not an even integer (2) m-3 is an even integer

Concepts tested: Integers, even and odd rules

Strategy: Don’t assume integers only

Level: 500’s

m2

Data Sufficiency Sample Solution #1 from the Official Guide Book by GMAC – 13th Edition

DS 72: If m is an integer, is m odd? (1) is not an even integer (2) m-3 is an even integer

A BD C E

m2

Data Sufficiency Sample Question #2 from the Official Guide Book by GMAC – 13th Edition

DS 98: Is rst = 1? (1) rs = 1 (2) st = 1

Concepts tested: Integers and fractions

Strategy: Don’t assume integers only

Level: mid 500’s

Data Sufficiency Sample Solution #2 from the Official Guide Book by GMAC – 13th Edition

DS 98: Is rst = 1? (1) rs = 1 (2) st = 1

A BD C

E

Data Sufficiency Sample Question #3 from the Official Guide Book by GMAC – 13th Edition

DS 120: A certain bookcase has 2 shelves of books. On the upper shelf, the book with the greatest number of pages has 400 pages. On the lower shelf, the book with the least number of pages has 475 pages. What is the median number of pages for all of the books on the 2 shelves? (1) There are 25 books on the upper shelf. (2) There are 24 books on the lower shelf.

Concept tested: Median

Strategy: Diagram-It

Level: Low to mid 600’s

Data Sufficiency Sample Solution #3 from the Official Guide Book by GMAC – 13th Edition

DS 120: A certain bookcase has 2 shelves of books. On the upper shelf, the book with the greatest number of pages has 400 pages. On the lower shelf, the book with the least number of pages has 475 pages. What is the median number of pages for all of the books on the 2 shelves? (1) There are 25 books on the upper shelf. (2) There are 24 books on the lower shelf.

A B

D C E

Data Sufficiency Sample Question #4 from the Official Guide Book by GMAC – 13th Edition

DS 154: A report consisting of 2,600 words is divided into 23 paragraphs. A 2-paragraph preface is then added to the report. Is the average (arithmetic mean) number of words per paragraph for all 25 paragraphs less than 120? (1) Each paragraph of the preface has more than 100 words. (2) Each paragraph of the preface has fewer than 150 words.

Concepts tested: Average, manipulating inequalities

Strategy: Simplify the given and the find

Level: High 600’s

Data Sufficiency Sample Solution #4 from the Official Guide Book by GMAC – 13th Edition

DS 154: A report consisting of 2,600 words is divided into 23 paragraphs. A 2-paragraph preface is then added to the report. Is the average (arithmetic mean) number of words per paragraph for all 25 paragraphs less than 120? (1) Each paragraph of the preface has more than 100 words. (2) Each paragraph of the preface has fewer than 150 words.

A B D C E

Data Sufficiency Sample Question #5 from the Official Guide Book by GMAC – 13th Edition

DS 158: If Carmen had 12 more tapes, she would have twice as many tapes as Rafael. Does Carmen have fewer tapes than Rafael? (1) Rafael has more than 5 tapes. (2) Carmen has fewer than 12 tapes.

Concepts tested: Translating words into equations

Strategy: Extremes

Level: High 600’s – Low 700’s

Data Sufficiency Sample Question #5 from the Official Guide Book by GMAC – 13th Edition

DS 158: If Carmen had 12 more tapes, she would have twice as many tapes as Rafael. Does Carmen have fewer tapes than Rafael? (1) Rafael has more than 5 tapes. (2) Carmen has fewer than 12 tapes.

A B D C E

Data Sufficiency Sample Question #6 from the Official Guide Book by GMAC – 13th Edition

DS 162: Is 5k less than 1,000? (1) 5k+1 > 3,000 (2) 5k-1 = 5k - 500

Concepts tested: Exponent rules, equations vs. inequalities

Strategy: Stop when you have enough info

Level: Low 700’s

Data Sufficiency Sample Solution #6 from the Official Guide Book by GMAC – 13th Edition

DS 162: Is 5k less than 1,000? (1) 5k+1 > 3,000 (2) 5k-1 = 5k - 500

A B D C E

Data Sufficiency Sample Solution #7 from the Official Guide Book by GMAC – 13th Edition

DS 166: What is the value of x+y in the figure below? (1) w = 95(2) z = 125

Concepts tested: Lines, angles, and polygons

Strategy: Redraw and Label Diagrams

Level: 700’s

x°

w°

z°

y°

Data Sufficiency Sample Solution #7 from the Official Guide Book by GMAC – 13th Edition

DS 166: What is the value of x+y in the figure below? (1) w = 95(2) z = 125

A B

D C E

x°

w°

z°

y°

Create a Study Plan to Optimize Your GMAT Quantitative Score

Start Early– Commit to a date and schedule the test– Allot 3-6 months of preparation before taking the GMAT

Do something everyday to prepare– “Official Guide for GMAT Review” 13th edition by the GMAC to practice with retired

questions– Computer-adaptive practice exams at www.MBA.com to practice on the computer

with time constraints– Like “MathSP” on Facebook, “MathSP Academy” on Twitter, and “MathSP” on

LinkedIn for questions of the day to practice on the go Be realistic

– Schedule around vacation, birthdays, etc.– Simulate a real testing environment

Write down your plan – Hold yourself accountable and stick to the plan– Amend MathSP’s sample plan to fit your needs!

Sample GMAT Study Plan

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9:30pm at Goizueta Business School• Weekly homework assignments that revisit concepts, reinforce strategies, and evaluate your

understanding of course material• 90-minute homework review each session utilizing MathSP’s Facilitative Approach that

allows you to ask your individualized questions and understand your mistakes• Practice tests throughout the course to familiarize yourself with computer-adaptive testing,

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Contact Information

Stephanie EspyGraduate of MIT, UC Berkeley, and Emory (Goizueta MBA ‘08)

Founder and Executive Director MathSP Tutoring and Test Prep

[email protected]

(678) 628-4650

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