Problem Solving. 1. If

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1 Problem Solving If b a = 4 0 5, then a b = O To create a part for a certain piece of machinery, four equal-size wedge-shaped pieces are cut and removed from a circular piece of metal, as illustrated in the figure above. If the unshaded portion of the circle represents the material remaining after the pieces are removed, what percentage of the original circle remains? Crash Course for the GMAT

2 = The number of cells killed by a virus doubles every hour. If the number of cells killed was initially 0 3, what is the number of cells killed after eight hours have passed? ( ) m m n 5. For all numbers m and n, m n =. n What is the value of 3? Math Drills

3 6. In a certain egg-processing plant, every egg must be inspected, and is either accepted for processing or is rejected. For every 96 eggs accepted for processing, 4 eggs are rejected. If additional eggs were accepted on one day, but the overall number of eggs inspected remained the same so that the ratio of accepted eggs to rejected eggs was 99 to, how many eggs does the plant process per day? ,000 4, In a 5-hour race, 6 cars consumed 480 gallons of gas among them. If all the cars consumed gas at the same constant rate, how much gas would be consumed by 7 such cars in an 8-hour race? If a golfer scores an average (arithmetic mean) of p points per round of golf for r rounds, and then scores q points in his next round, which of the following is an expression for the golfer s average score for the r + rounds of golf? pr + q r + p r + q r + p + p + 4 p + ( ) Crash Course for the GMAT

4 9. In the rectangular coordinate system, the line y 3x = 4 passes through each of the four quadrants EXCEPT I II IV I and IV II and IV 0. Of the 40 moving trucks available to rent, 8 have air conditioning, 56 have automatic transmission, and 4 trucks have both air conditioning and automatic transmission. How many of the 40 trucks have neither air conditioning nor automatic transmission? On a certain day, a delivery driver must make 4 deliveries. He departs from the dispatch office and travels 4 miles due west to his first delivery. From there, his second delivery is 7 miles due north, and his third delivery is 9 miles due east of the location of his second delivery. His last delivery is 9 miles due south of his third. What is the distance, in miles, that the driver must travel to return to the dispatch office, if he travels in a straight line via the shortest route? It cannot be determined from the information given. Math Drills 3

5 . A 6-sided die has 3 black sides and 3 white sides. If the die is thrown 4 times, what is the probability that, on at least one of the throws, the die will land with a black side up? A caterer must choose 3 canapés to serve from possible selections. In how many possible combinations can he serve the 3 canapés?,0,440,660,00,30 4 Crash Course for the GMAT

6 4. A group of 0 coworkers has agreed to equally share the cost of a gift costing d dollars. If w of the coworkers later decide not to contribute, how much more must each of the remaining coworkers pay toward the gift? d 0 w ( ) dw 0 0w dw 0( 0 w) 0 w d 0dw 0 w 5. A merchant prices a television at 60 percent above wholesale. For a Presidents Day sale, the merchant marks the television down by 5 percent. If he sells the television during the Presidents Day sale, what percentage over the wholesale price will he have earned? Math Drills 5

7 . A magazine stand owner sells cups of coffee, newspapers, and packs of gum. Compared to the number of cups of coffee he sells, he sells twice as many packs of gum, and three times as many newspapers. If he charges $.5 for a cup of coffee, $0.50 for a newspaper, and $0.35 for a pack of gum, and sells no other items, which of the following could be the amount of his total gross sales on a given day? I. $ II. $58.65 III. $.5 I only I and II only I and III only II and III only I, II and III only 7. Ten strips of paper are numbered from to 0 and placed in a bag. If three numbers are drawn from the bag at random, what is the probability that the sum of the numbers drawn will be odd? Crash Course for the GMAT

8 8. Three actors and two dancers have individual auditions for a musical during the same afternoon. If no two actors are allowed to audition immediately following each other, in how many different orders could the five performers be seen? If a =,48 and b =,5, what is the value of ( a b )? Working together, each at his or her own constant rate, Jeff and Ashley painted their apartment in 6 hours. Working at his constant rate, Jeff could have painted the whole apartment in 0 hours. How many hours would it have taken Ashley, working at her constant rate, to paint the apartment? Math Drills 7

9 . Which of the following fractions has a decimal equivalent that terminates? Jaime has n comic books. He sells one-half of them and then gives one-third of the ones he has left to a friend. If he has 0 comic books left, how many did he have originally? Carol buys x widgets at a cost of y cents per widget. She packages them, q widgets per box, and sells them at a price of z dollars per box. What is the amount of profit, in dollars, that she makes on the sale (profit = sales revenue cost)? 00qz xy xz xy q 00 xy qz 00 00z xy q xz xy q 8 Crash Course for the GMAT

10 4. If w + y = 47, 3y + z =, and w + 3z =, what is the average (arithmetic mean) of w, y, and z? It cannot be determined from the information given. 5. Circle Q has radius r. Circle P has a radius that is 50% greater than r. In terms of r, what is the area of circle P? πr 3πr πr 9πr 4 3πr Math Drills 9