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viiiQuantitative Question Bank3.17 Inequalities . . . . . . . . . .3.18 Geometry–Lines & Triangles3.19 Geometry–Circles . . . . . .3.20 Geometry–Polygon . . . . . .3.21 Co-ordinate geometry . . . .1021051071081094 Answer key1134.1 Problem Solving Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1144.2 Data Sufficiency Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1175 Solutions – Problem Solving Questions5.1 Number properties . . . . . . . . . . . . . .5.2 Percents . . . . . . . . . . . . . . . . . . . . .5.3 Profit & Loss . . . . . . . . . . . . . . . . . . .5.4 Averages . . . . . . . . . . . . . . . . . . . . .5.5 Ratio & Proportion . . . . . . . . . . . . . . .5.6 Speed, Time & Distance . . . . . . . . . . . .5.7 Time & Work . . . . . . . . . . . . . . . . . .5.8 Computational . . . . . . . . . . . . . . . . .5.9 Interest . . . . . . . . . . . . . . . . . . . . .5.10 Functions . . . . . . . . . . . . . . . . . . . .5.11 Permutation & Combination & Probability5.12 Sets . . . . . . . . . . . . . . . . . . . . . . . .5.13 Statistics & Data Interpretation . . . . . . .5.14 Linear Equations . . . . . . . . . . . . . . . .5.15 Quadratic Equations & Polynomials . . . .5.16 Inequalities . . . . . . . . . . . . . . . . . . .5.17 Geometry: Lines & Triangles . . . . . . . . .5.18 Geometry Circles . . . . . . . . . . . . . . .5.19 Geometry Polygon . . . . . . . . . . . . . .5.20 Geometry 3 Dimensional . . . . . . . . . .5.21 Co-ordinate geometry . . . . . . . . . . . . 502542652702802856 Solutions – Data Sufficiency Questions6.1 Numbers . . . . . . . . . . . . . . . . . . . .6.2 Percents . . . . . . . . . . . . . . . . . . . .6.3 Profit & Loss . . . . . . . . . . . . . . . . . .6.4 Averages (including weighted averages) .6.5 Ratio & Proportion . . . . . . . . . . . . . .6.6 Mixtures . . . . . . . . . . . . . . . . . . . .6.7 Speed, Time, & Distance . . . . . . . . . .6.8 Time & Work . . . . . . . . . . . . . . . . .6.9 Computational . . . . . . . . . . . . . . . .6.10 Interest . . . . . . . . . . . . . . . . . . . .6.11 Functions . . . . . . . . . . . . . . . . . . .6.12 Permutation & Combination . . . . . . . .6.13 Sets . . . . . . . . . . . . . . . . . . . . . . .6.14 Statistics & Data Interpretation . . . . . .6.15 Linear Equations . . . . . . . . . . . . . . .6.16 Quadratic Equations & Polynomials . . .6.17 Inequalities . . . . . . . . . . . . . . . . . .6.18 Geometry–Lines & Triangles . . . . . . . .6.19 Geometry–Circles . . . . . . . . . . . . . .6.20 Geometry–Polygon . . . . . . . . . . . . . 30436454461465www.manhattanreview.com. 1999–2016 Manhattan Review

Quantitative Question Bankix6.21 Co-ordinate geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4697 Talk to Us 1999–2016 Manhattan Review483www.manhattanreview.com

xwww.manhattanreview.comQuantitative Question Bank 1999–2016 Manhattan Review

Chapter 1WelcomeDear Students,Here at Manhattan Review, we constantly strive to provide you the best educational content for standardized test preparation. We make a tremendous effort to keep making things better and better foryou. This is especially important with respect to an examination such as the GMAT. A typical GMATaspirant is confused with so many test-prep options available. Your challenge is to choose a book ora tutor that prepares you for attaining your goal. We cannot say that we are one of the best, it is youwho has to be the judge.There are umpteen books on Quantitative Ability for GMAT preparation. What is so different aboutthis book? The answer lies in its approach to deal with the questions. Solution of each question is dealtwith in detail. There are over hundred questions that have been solved through alternate approaches.You will also find a couple of questions that have been solved through as many as four approaches.The objective is to understand questions from multiple aspects. Few seemingly scary questions havebeen solved through Logical Deduction or through Intuitive approach.The has a great collection of 500 GMAT-like questions: 250 PS and 250 DS.Apart from books on ‘Word Problem,’ ‘Algebra,’ ‘Arithmetic,’ ‘Geometry,’ ‘Permutation and Combination,’ and ‘Sets and Statistics’ which are solely dedicated on GMAT-QA-PS & DS, the book on ‘Fundamentals of GMAT math’ is solely dedicated to develop your math fundamentals. We recommend thatyou go through it before attempting questions from ‘GMAT Quantitative Ability Question Bank.’The Manhattan Review’s ‘GMAT Quantitative Ability Question Bank’ book is holistic and comprehensivein all respects. Should you have any queries, please feel free to write to me at info@manhattanreview.com.Happy Learning!Professor Dr. Joern Meissner& The Manhattan Review Team1

2www.manhattanreview.comQuantitative Question Bank 1999–2016 Manhattan Review

Chapter 2Problem Solving Question Bank3

4Quantitative Question Bank PS Questions2.11.2.3.4.999962 42 (A)1010 8(B)(105 8)2(C)104 (105 8)(D)105 (104 8)(E)105 (105 8)If 5a is a factor of n!, and the greatest integer value of a is 6, what is the largest possible valueof b such that 7b is a factor of n!?(A)2(B)3(C)4(D)5(E)6If a 0.999, b (0.999)2 and c and c?(A)a b c(B)a c b(C)b c a(D)b a c(E)c a b 0.999, which of the following is the correct order of a, bIf p is the product of the reciprocals of integers from 150 to 250, inclusive, and q is the productof the reciprocals of integers from 150 to 251, inclusive, what is the value of (p 1 q 1 ) interms of p?(A)5.Number propertiesp(B)(251)2251 252 p(C)252p(D)252p(E)251 252 p 2If x is the sum of all integers from 51 to 100, inclusive, what is the value of attanreview.com 1999–2016 Manhattan Review

Quantitative Question Bank PS Questions6.If x is the sum of the reciprocals of the consecutive integers from 51 to 60, inclusive and yis the sum of the reciprocals of the consecutive integers from 61 to 70, inclusive, which of thefollowing is correct? 6II.1x1yIII.1y (A)Only I(B)Only II(C)Only III(D)Only II and III(E)I, II and IIII.7.(B)(C)(D)(E)1x1817162552If a and b are real numbers such that a percent of (a 2b) when added to b percent of b, thevalue obtained is 0, then which of the following statements must be true?I.9. 7A number 4p25q is divisible by 4 and 9; where p and q are the thousands and units digits,prespectively. What is the minimum value of q ?(A)8.5a bII.a b 0III.a b 1(A)Only I(B)Only II(C)Only III(D)Only I and III(E)Only II and III A set is such that if m is in the set, m2 3 is also in the set. If 1 is in the set, which of thefollowing is also in the set?I.II. 24III.19(A)Only I(B)Only II 1999–2016 Manhattan Reviewwww.manhattanreview.com

610.11.12.13.14.Quantitative Question Bank PS Questions(C)Only I and II(D)Only II and III(E)I, II and IIIA sequence t1 , t2 , t3 , . . . tn is such that t2 5 and tn 1 2tn 1 for n 1, then what is thevalue of t10 t9 ?(A)29(B)210 1(C)1(D)2(E)4If m, n, p and q are distinct positive integers, greater than 1 such that mnpq 660, how manypossible combination of values exist for m, n, p and q?(A)Two(B)Three(C)Four(D)Five(E)SevenIf x 216 and y 125, what is the value of(A)0(B)1(C)4(D)5(E)10 qq x 2/3 y 2/3 2(xy)1/3 x 2/3 y 2/3 2(xy)1/3 ?If m 0.9, which of the following is a possible value of(A)1.01(B)1.12(C)1.13(D)1.35(E)1.50Given a and b are positive integers and a I.II.III. 1m ?b3, which of the following must be an integer?90a45a90a300www.manhattanreview.com 1999–2016 Manhattan Review

Quantitative Question Bank PS Questions15.16.17.18.(A)Only I(B)Only II(C)Only III(D)Only I and II(E)I, II and III7The following addition operation shows the sum of the two-digit positive integers XY and Y X.If X, Y , and Z are different digits, what is the value of the integer Z?XY YXXXZ(A)8(B)7(C)2(D)1(E)0Suzy saves 20 per month. In each of the next 30 months, she saved 20 more than he saved inthe previous month. What is the total amount she saved during the 30-month period?(A) 3,600(B) 4,800(C) 6,000(D) 9,300(E) 12,000If a sequence of numbers t1 , t2 , . . . tn is such that t1 0, t2 2 and tn t(n 1) 2t(n 1) forn 1, what is the value of t4 ?(A) 2(B)0(C)4(D)6(E)8If n is an integer such that n 9, which of the following could be the remainder when (2 22 23 24 . 2n ) is divided by 3?I.0II.1III.2(A)Only I 1999–2016 Manhattan Reviewwww.manhattanreview.com

8Quantitative Question Bank PS Questions(B)Only II(C)Only III(D)Only I and III(E)I, II and IIIwww.manhattanreview.com 1999–2016 Manhattan Review

Quantitative Question Bank PS Questions2.219.20.21.22.23.9PercentsA machine can be repaired for 1,200 and will last for one year, while the new machine wouldcost for 2,800 and will last for two years. The average cost per year of the new machine is whatpercent greater than the cost of repairing the current machine ?(A)7%(B)10%(C)16.67%(D)18.83%(E)20%An item is levied a sales tax of 10 percent on the part of the price that is greater than 200. If acustomer paid a sales tax of 10 on the item, what was the price of the item?(A) 200(B) 250(C) 300(D) 360(E) 400Item A attracts sales tax rate of 0.54 per 25. What is the sales tax rate, as a percent, for itemB that attracts four times as much as the rate for item A?(A)216%(B)86.4%(C)8.64%(D)2.16%(E)0.135%Cyclist P increases his speed from 10 miles per hour to 25 miles per hour in the last lap, whileanother Cyclist Q increases his speed from 8 miles per hour to 24 miles per hour in the last lap.By what percent is the percent increase in speed of Cyclist Q more than that of Cyclist P?(A)33.33%(B)50%(C)66.67%(D)75%(E)100%In a certain year, Carrier X traveled 101,098 kilometers and consumed 9,890 lites of diesel fuel,while in the same year, Carrier Y traveled 203,000 kilometers and consumed 24,896 lites ofdiesel fuel. The fuel mileage is defined as kilometers per liter of fuel. The mileage of Carrier Xis approximately what percent greater or lesser than that of Carrier Y?(A)20%(B)25%(C)33.33% 1999–2016 Manhattan Reviewwww.manhattanreview.com

1024.25.26.27.28.Quantitative Question Bank PS Questions(D)37.50%(E)40%The price of a bicycle was 456. The trader first decreased the price by 25 percent and thenincreased by 25 percent. Which of the following represents the final percent change in the priceof the bicycle?(A)0%(B)50%(C)66.67%(D)93.75%(E)100%To make a certain color, a paint dealer mixes 3.4 liters of red color to a base that is 68 liters.The paint manufacturer recommends mixing 0.7 liters per 10 liters of base to make that color.By what percent should the mixing be increased to bring it to the %A Business Processing Outsourcing unit recruits 200 employees. Each of them is paid 7.50 perhour for the first 44 hours worked during a week and 1 31 times that rate for hours worked inexcess of 44 hours. What was the total remuneration of the employees for a week in which 30percent of them worked 30 hours, 40 percent worked 44 hours, and the rest worked 50 hours?(A) 25,000(B) 40,500(C) 63,300(D) 70,000(E) 73,400A retail company earned 5 million as commission on the first 35 million in sales and then 11 million as commission on the next 121 million in sales. By what percent did the ratio ofcommissions to sales decrease from the first 35 million in sales to the next 121 million A sales representative earned 8 percent commission on the amount of total sales up to 20,000,inclusive, and x percent commission on the amount of total sales above 20,000. If the salesrepresentative earned a total commission of 2,000 on total sales of 24,000, what was the valueof x?www.manhattanreview.com 1999–2016 Manhattan Review

Quantitative Question Bank PS Questions29.30.31.32.(A)4(B)6(C)8(D)10(E)1211A trader buys a batch of 120,000 computer chips for 3,600,000. He sells 52 of the computerchips, each at 25 percent above the cost per computer chip. Later, he sells the remaining computer chips at a price per computer chip equal to 25 percent less than the cost per computerchip. What was the percent profit or loss on the batch of computer chips?(A)Loss of 1%(B)Loss of 5%(C)Loss of 7.50%(D)Profit of 10%(E)Profit of 22.22%With the increase of 20% in price of milk, a housewife can buy 5 liters less quantity for 60 thanshe was buying before the increase. What was the initial price per liter of milk?(A) 2.00(B) 2.50(C) 2.75(D) 3.00(E) 3.50 thA company was approved to spend a certain sum of money for a year. It spent 14of the sum th1during the first quarter, and 6of the remainder during the second quarter. By what percentis the sum of money that was left at the beginning of the third quarter more than the sum spentin the two 3%David and Suzy each spent 450 in 2013. In 2014, David spent 10 percent more than he did in2013, and together he and Suzy spent a total of 600. Approximately by what percent less didSuzy spend in 2014 than she did in 2013?(A)23%(B)66%(C)77%(D)80%(E)83% 1999–2016 Manhattan Reviewwww.manhattanreview.com

1233.34.35.Quantitative Question Bank PS QuestionsOn day 1, a shopkeeper increases the price of an item by k%, and on day 2, he decreases theincreased price by k%. By the end of the day 2, the price of the item drops by 1. On day 3, heagain increases the decreased price by k%, and on day 4, he again decreases the increased priceby k%. If, at the end of day 4, the price of the item comes to 398, what was the approximateinitial price of the item?(A) 325(B) 350(C) 375(D) 400(E) 450As per the previous year data, y can buy x number of items. If the average cost of each itemincreased by 20 percent this year, then the number of items can be bought with 3y equals(A)x(B)1.50x(C)2.50x(D)3x(E)3.50xA solution consists of 30 percent of water by weight. After boiling the solution for 15 minutes,70 percent water, by weight, was evaporated. There is no weight loss for the other part of thesolution. What percent of the solution’s total remaining weight consists of the remaining 9100%69A mixed juice contains, by volume, 25 percent banana pulp and 75 percent papaya pulp. If thismixed juice costs 20 percent more than an equal quantity of only banana pulp, by what percentare papaya pulp more expensive than banana pulp?(A)22.22%(B)26.67%(C)28%(D)30%(E)33.33%At a lab, bacteria P multiplies itself in every 18 days, while bacteria Q multiplies itself in every15 days. Approximately by what percent is the number of times bacteria Q multiplies itself ismore than the number of times bacteria P multiplies itself in a 3-year period?(A)12%www.manhattanreview.com 1999–2016 Manhattan Review

Quantitative Question Bank PS Questions38.39.(B)16%(C)20%(D)22%(E)33%Jack pur

Long regarded as the gold standard in GMAT prep worldwide, Manhattan Review’s GMAT prep books offer professional GMAT instruction for dramatic score improvement. Now in its updated 6th . their GMAT knowledge and develop a thorough and strategic approach to taking the GMAT. GMAT Math