Cracking GMAT's most difficult Quant Word Problems - www.manyagroup.com

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27. Jun 2019
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Cracking GMAT's most difficult Quant Word Problems - www.manyagroup.com

• 1. ‘Saraswati before Lakshmi’ 1 Cracking GMAT's most difficult Quant Word Problems
• 2. ‘Saraswati before Lakshmi’ GMAT Exam format & Timing 2 GMAT Test Section # of Questions Question Types Duration Analytical Writing Assessment 1 Topic Analysis of an Argument 30 Minutes Integrated Reasoning 12 Questions Multi-Source Reasoning Graphics Interpretation Two-Part Analysis Table Analysis 30 Minutes Quantitative 31 Questions Data Sufficiency Problem Solving 62 Minutes Verbal 36 Questions Reading Comprehension Critical Reasoning Sentence Correction 65 Minutes Total Exam Time, not including breaks or tutorials 3 hours 7 minutes
• 3. ‘Saraswati before Lakshmi’ GMAT Scoring 3 Section Type Score Composite Score AWA – Argument based topic 0-6 N.A. Integrated Reasoning Section 1-8 Quantitave (Math) 0 – 60 (8-51) 200 - 800 Verbal 0 – 60 (9 – 51)
• 4. ‘Saraswati before Lakshmi’ 4 GMAT-Quant Topics Arithmetic 1. Property of Integers 2. Fractions 3. Decimals 4. Real Numbers 5. Ratio & Proportion 6. Percents 7. Power & Roots of Numbers 8. Descriptive Statistics 9. Sets 10. Counting Methods 11. Discrete Probability. Algebra 1. Simplifying Algebraic Expressions 2. Equations 3. Solving Linear Equations 4. Quadratic Equations 5. Exponents 6. Inequalities & Modulus 7. Functions. Geometry 1. Lines and Angles 2. Triangles 3. Quadrilaterals 4. Polygons(Convex) 5. Circles 6. Rectangular Solids and Cylinders 7. Co-ordinate Geometry. Word Problems 1. Work & Rate problems 2. Mixture Problems 3. Interest Problems 4. Profit & Discount 5. Geometry word problems 6. Measurement Problems 7. Data Interpretation.
• 5. ‘Saraswati before Lakshmi’ GMAT Quant Questions Format 5 There can be two types of difficult word based questions : PS & DS Let’s start with PS questions first :
• 6. ‘Saraswati before Lakshmi’ Work on a miniature version 6 List T consist of 30 positive decimals, none of which is an integer, and the sum of the 30 decimals is S. The estimated sum of the 30 decimals, E, is defined as follows. Each decimal in T whose tenths digit is even is rounded up to the nearest integer, and each decimal in T whose tenths digits is odd is rounded down to the nearest integer. If 1/3 of the decimals in T have a tenths digit that is even, which of the following is a possible value of (E – S)? [Q. 225 (O.G.- 19)] I. -16 II. 6 III. 10 A. I only B. I and II only C. I and III only D. II and III only E. I, II, and III Say, there are 3 decimals (i.e. 1/10th) So, the tenth digit is even in 1 decimal & odd in 2 decimals. Min values are : 0.2, 0.1, 0.1 So, S = 0.4 ; E = 1+0+0 = 1 E – S = 1 -0.4 = 0.6 So, for 30 decimals = E – S = 0.6 * 10 = 6 Max. values are : 0.8, 0.9, 0.9 So, S = 2.6 ; E = 1+ 0 + 0 = 1 E – S = 1 – 2.6 = -1.6 So, for 30 decimals = E – S = -1.6 * 10 = -16
• 7. ‘Saraswati before Lakshmi’ See Variables? Use Numbers! 77 Last Sunday a certain store sold copies of Newspaper A for \$1.00 each and copies of Newspaper B for \$1.25 each, and the sold no other newspaper that day. If r percent of the store’s revenue from Newspaper sales was from Newspaper A and p percent of the newspapers that the store sold were copies of Newspaper A, which of the following expresses r in terms of p ? [Q.215 -O.G.- 19] A)(100p)/(125-p) B) (150p)/(250-p) C) (300p)/(375-p) D) (400p)/(500-p) E) (500p)/(625-p) Say, total copies of Newspapers = 100. And # of copies of A= p = 20 Now, r = %age of revenue from A = (20/120) × 100 = (100/6) %. Now, putting p = 20 in the options : A) (100× 20)/105 B) (150× 20)/230 C) (300 × 20)/355 D) (400 × 20)/480) = (100/6)% E) (500 × 20)/ 605 A B Total Cost/unit \$1.00 \$1.25 # of Units Revenue 20 80 100 \$20 \$100 \$120
• 8. ‘Saraswati before Lakshmi’ Organize the data systematically. 8 A photography dealer ordered 60 Model X cameras to be sold for \$250 each, which represents a 20 percent markup over the dealer’s initial cost for each camera. Of the cameras ordered, 6 were never sold and were returned to the manufacturer for a refund of 50 percent of the dealer's initial cost. What was the dealer's approximate profit or loss as a percent of the dealer’s initial cost for the 60 cameras? [Q.210 – O.G.-19] A. 7% loss B. 13% loss C. 7% profit D. 13% profit E. 15% profit
• 9. ‘Saraswati before Lakshmi’ Organize the data systematically. 9 A photography dealer ordered 60 Model X cameras to be sold for \$250 each, which represents a 20 percent markup over the dealer’s initial cost for each camera. # 60 SP 250 Profit 20% CP 250/1.2 Of the cameras ordered, 6 were never sold and were returned to the manufacturer for a refund of 50 percent of the dealer’s initial cost. 6 - 50% 50% of (250/1.2)What was the dealer’s approximate profit or loss as a percent of the dealer’s initial cost for the 60 cameras? 54 + 20% 250 ? Solution 6x(-50) + 54x20 (6+54) = 13 6 20 - m -- = ----------- 54 m - (-50) -50 20 6 54 m54 x 250 + 6 x (250/1.2)x 0.5 – 60 x (250/1.2) ----------------------------------------------------------- x 100 60 x 250 1.2
• 10. ‘Saraswati before Lakshmi’ Use numbers in the Options: 10 At his regular hourly rate, Don had estimated the labor cost of a repair job as \$336 and he was paid that amount. However, the job took 4 hours longer than he had estimated and, consequently, he earned \$2 per hour less than his regular early rate. What was the time Don had estimated for the job, in hours ? [Q.188; O.G. – 2019] A) 28 B) 24 C) 16 D) 14 E) 12 Time Rate/hr New time 21 20 NR/hr 16.8 Difference 4.2 14 28 12 2.0
• 11. ‘Saraswati before Lakshmi’ 11 Running at their respective constant rates, Machine A takes 4 days longer to produce x widgets than Machine B. At these rates, if the two machines work together to produce 2x widgets in 3 days, how many days would it take Machine A alone to produce (5/2)x widgets? A) 1 B) 3 C) 5 D) 7 E) 15 A[5/2x] A(x) 2 B(x) -2 6 2 A & B together(2x) 3
• 12. At a loading dock, each worker on the night crew loaded (3/4)th as many boxes as each worker on the day crew. If the night crew has (4/5)th as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load ? [O.G.- 2018] A) 1/2 B) 2/5 C) 3/5 D) 4/5 E) 5/8 Day Crew Night Crew Total # of boxes by each worker # of workers Total boxes 4 3 5 4 20 12 32 # of boxes unloaded by day crew Total # of boxes = (20) ÷ (32) = 5/8 Use your own number
• 13. ‘Saraswati before Lakshmi’ Use the Grid 13 Of the 645 speckled trout in a certain fishery that contains only speckled and rainbow trout, the number of males is 45 more than twice the number of females. If the ratio of female speckled trout to male rainbow trout is 4:3 and the ratio of male rainbow trout to all trout is 3:20, how many female rainbow trout are there? A)192 B)195 C)200 D)205 E)208 Speckled Rainbow Total Males Females Total 645 x 2x+45 So, (2x+45) + x = 645 x = 200 200 445 FS : MR = 4:3 => 200/MR = 4:3 => MR = 150 150 MR : Total = 3: 20  150/Total = 3/20  Total = 1000 1000355 205
• 14. ‘Saraswati before Lakshmi’ Data Sufficiency (DS) Questions 14 Now, let’s talk look at a few DS questions
• 15. ‘Saraswati before Lakshmi’ Data Sufficiency: The format and the approach 15 Mark (A) if Statement (1) ALONE is sufficient, but statement (2) is not sufficient. Mark (B) if Statement (2) ALONE is sufficient, but statement (1) is not sufficient. Mark (C) if BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. Mark (D) if EACH statement ALONE is sufficient. Mark (E) if statements (1) and (2) TOGETHER are not sufficient. What is the value of x? 1) 10% of x is 0.2. 2) x is the only even prime number. If statement (1) alone is sufficient….Answer could be A/D If statement (1) alone is not sufficient…Answer could be B/C/E A D
• 16. ‘Saraswati before Lakshmi’ Value DS 16 At a certain college, students can major in Science, Math, History or Linguistics. If there are one-third as many Science majors as there are History major and two-third as many Math majors as there are History majors, how many of the 2000 students major in Linguistics ? 1) There are as many Linguistics majors as there are Math majors. 2) There are 250 more Math majors than there are Science majors. # of majors in Linguistics ? Know : 1) Only S, M, H, L 2) S = 1/3 (H) 3) M = 2/3 (H) 4) S + M + H + L = 2000 Need: H =? 1) L = M => 1/3(H) + 2/3(H) + H + 2/3(H) = 2000 AD 2) M – S = 250 => 2/3(H) – 1/3(H) = 250
• 17. ‘Saraswati before Lakshmi’ Yes-No DS: 17 A school administrator will assign each student in a group of n students to one of m classrooms. If 3 < m < 13 < n, is it possible to assign each of the n students to one of the m classrooms so that each classroom has the same number of students assigned to it ? [Q.390-OG-19] 1) It is possible to assign each of 3n students to one of m classrooms so that each classroom has the same number of students assigned to it. 2) It is possible to assign each of 13n students to one of m classrooms so that each classroom has the same number of students assigned to it. Is n divisible by m ? 1) 3n is divisible by m n = 14 ; m = 7 YES n = 14 ; m =6 NO B C E 2) 13n is divisible by m n = 14 ; m = 7 YES n = 20 ; m =10 YES See Variables? Plug in.
• 18. ‘Saraswati before Lakshmi’ What do we need to figure out? 18 Beginning in January of last month, Carl made deposits of \$120 into his account on the 15th of each month for several consecutive months and then made withdrawals of \$50 from the account on the 15th of the each of remaining months of the last year. There were no other transactions in the account last year. If the closing balance of Carl’s account for May of last year was \$2600, what was the range of the monthly closing balances of Carl’s account last year? 1) Last year the closing balance of Carl’s account for April was less than \$2625. 2) Last year the closing balance of Carl’s account for June was less than \$2675. J F M … … 120 +120 |… … - 50 - 50 … … When ? (1) If withdrawal started in May or earlier Balance in April 2650 Balance in May \$2600 If withdrawal started after May 2480 Therefore, withdrawal started after May If withdrawal started in June or earlier Balance in June 2550 Balance in May \$2600 If withdrawal started in July or later 2720 (2) Therefore, withdrawal started in June or earlier B C E Withdrawal started in June (1) and (2) together
• 19. ‘Saraswati before Lakshmi’ 19 The GMAT is scored on a scale of 200 to 800 in 10 point increments. (Thus 410 and 760 are real GMAT scores but 412 and 765 are not). A first-year class at a certain business school consists of 478 students. Did any students of the same gender in the first-year class who were born in the same-named month have the same GMAT score? (1) The range of GMAT scores in the first-year class is 600 to 780. (2) 60% of the students in the first-year class are male. Know: 1) Total # of students = 478 2) Total Genders = 2 3) # of months = 12 1) Score range = 600 to 780 => 19 possible scores. Number of different Combinations = 19 * 2 * 12 = 456 Since, 456 < 478 ; We will have at least one repeat of the same gender and birth month. A D 2) # of males = 60% of 478 = 287