Question of the day. 31st October 2015

Profit and Loss

PROFIT AND LOSS

1.       Ms Rogers bought an electric range on the installment plan . The cash price of theb range was $400.The amount she paid was $120 down and 12 monthly payments of $28 each.

Column A : The amount she paid for the electric range in excess of the cash price

Column B : $56

2.       Column A : A bonus of $450 plus a 9 percent increase in annual salary.

       Column B : A bonus of $500  plus a 8.5 percent increase in annual salary.

3.       A discount of 40 percent of the original selling price of an item reduces the price to $72.

Column A : The original selling price of the item          Column B: $120

4.       The cost,  in dollars, of manufacturing x refrigerators is 9000 + 400x . The amount received when selling these x refrigerators is 500x   dollars. What is the least number of refrigerators that must be manufactured and sold so that the amount received is atleast equal to the manufacturing cost?

(A)   10     (B) 18   (C) 45    (D) 90    (E) 100

5.       The toll for a certain bridge is $0.15 or 1 token.

Tokens are sold in packs of 40 for $4.00.

Column A : The percent saved on 40 trips across the bridge if a token, rather than $0.15, is used to pay each toll

Column B: 66 2/3 %

6.                                   d>0

Column A : The total interest earned on d dollars invested for 3 months at 11 percent simple annual interest .

Column B :  (60) dollars

7.       Maria’s weekly net salary of $85 is 65 percent of her weekly gross salary.

Column A : Maria’s weekly gross salary                     Column B : $900

8.       Three individuals contributed $800 each towards purchase of a computer. If they bought the computer on sale for $1950 plus 10 percent sales tax, how much money should be refunded to each individual?

(A)   $65      (B) $85         (C) $150          (D)$195          (E) $255  

9.       A hardware store purchased identical snow shovels at a cost of $9 a piece and sold each of them for 20 percent above cost.

Column A : The price at which the hardware store sold each shovel     Column B : $10.80

10.   The price of a pen is (10x + y ) cents, the price of a notebook is (10y + x ) cents, and the sum of the two prices is $1.43.

Column A : x                       Column B :  y

11.   Karl’s net income is always 80 ppercent of his gross income. What will be the increase in Karl’s net income when his gross income increases from $20,000 to $25,000 ?

(A)   $5,000      (B) $4,000         (C) $3,000          (D)$2,000          (E) $1,000

12.   The selling price of a certain book is $12.00. For each copy of the book sold, the author receives $2.40. What percent of the selling price does the author receive?

(A)   20%          (B)   5 %     (C)  2 %    (D) 0.5 %   (E) 0.2 %

13.   If checks of $455 and x dollars are deducted from a  checking account that has a balance of $800, then  $305 of the balance will be left.

Column A :  x                   Column B : 45

14.   A purchase plan for a stereo receiver requires 20 percent of the total cost as a  down payment and monthly payments of $30.

Column A :  The total cost of the stereo receiver          Column B : $450

15.   Lila purchased a hat and a scarf for a total of $40.She received a 25  percent discount on the price of the scarf and a 15 percent discount on the price of the hat .

 Column A :  The amount Lila saved on the scarf    Column B : The amount Lila saved on the hat

16.   For each home in Town X , the amount of property tax is p percent of the value of the home . The property tax on a home whose value is $45,000 is $1,200.

Column A :The property tax on a home in Town X whose value is $54,000      Column B : $1,300

17.   Betty spent $75 for a bicycle and she also spent $27 repairing it.She then sold for $120.

Column A : The money Betty received in excess of the total amount she spent

Column B : $20

18.   The price per pair of brand X socks is $2 and the price per pair of brand Y socks is $3. If there is no sales tax and a customer chooses only among two brands , What is the greatest number of pairs of socks that he can buy with exactly $25 ?

(A) 9         (B) 10        (C) 11       (D) 12       (E) 20

19.   A decrease in the number of sales personnel in Company K to 85 percent of the original sales force resulted in a decrease of 500 in the number of monthly sales.

Column A : The percent decrease in the number of company K’s monthly sales

Column B : The percent decrease in the number of company k’s sales personnel.

20.   A merchant made a profit of $2.75 on the sales price of a sweater that cost the merchant $12.25

Column A : The profit expressed as a percent of the cost to the merchant

Column B : The profit expressed as a percent of the sale price

21.   A consumer insulates a house with material bought at 20 percent off the list price of $370.If the consumer also receives a rebate of $25 from the manufacturer of the material , how much does the material cost the consumer?

(A)   $238       (B) $240          (C) $263          (D)$271          (E) $325

22.   A band is paid $700 per concert. The leader receives 25 percent of this amount and the other 5 members share the rest equally. How much does each of the 5 members  receive?

(A)   $525        (B) $175          (C) $140          (D)$112          (E) $105

23.   In a certain shipment 2 percent of the boxes shipped were damaged. If the loss per damaged box was $35 and the total loss due to damage was $700, how many boxes were shipped?

(A) 2,000         (B) 1,000        (C) 200      (D) 100       (E) 20

  

  

          

Rate Problems

  RATE PROBLEMS

1.                                                 ds≠0

Column A : The time required to travel d miles at s miles per hour

Column B : The time required to travel d/2 miles at 2s miles per hour

2.       Column A : The time that it takes Jim to drive 300 miles at a speed of 52 miles per hour.

Column B : The time that it takes Lila to drive 240 miles at a speed of 40 miles per hour.

3.       A distillate flows in to an empty 64 –gallon drum at spout A and out of the drum at spout B. If the rate of flow through A is 2 gallons per hour, how many gallons per hour must flow out at spout B so that the drum is full in exactly 96 hours?

4.                                                       X > 0

                        Quantity A:                   Quantity B: 

5.        Column A :  The total number of liters of water in x tanks, each containing 20 liters of water, and   2x tanks , each containing 35 liters of water.

          Column B : The total number of liters of water in x tanks , each containing 25 liters of water, and 2x     tanks , each containing 30 liters of water.

6.     

(1)  Two  tanks , X and Y, are filled to capacity with jet fuel. Tank X holds 600 gallons more than Tank

Y. If 100 gallons of fuel were to be pumped from each tank, tank X would then contain 3 times as much fuel as tank Y. What is the total number of gallons of fuel in the two full tanks?

(A) 1,400      (B) 1,200      (C) 1,000    (D) 900     (E) 800

(2)  A certain machine fills a bag with 7 ounces of potato chips in 3.5 seconds. At this rate how many seconds will it take the machine to fill a bag with 15 ounces of potato chips?

(A)   6.5    (B) 7.0    (C) 7.5    (D) 8.0    (E) 11.5

7.       One bacterial cell of a certain type is placed in a petri dish. Cells of this type divide once every day.

Column A : The total number of bacterial cells in the dish at the end of 4 days if no cells die

Column B : 6

8.       An aviator in Mexico flew 300 kilometers in a straight line due east from point P to point Q and then 400 kilometers in a straight line due north to point R .

Column A :  The shortest distance from point P to point R           Column B : 550  kilometers

                                  x>0

9.       Column A : The number of minutes in x+ 100 hours

Column B : The number of seconds in 60(x+100) minutes

10.   If a small juice contains 200 milliliters of juice, how many liters of juice are there in a case containing 48 small cans? (1 liter = 1,000 milliliters)

(A) 0.96     (B) 9.6    (C) 96    (D) 960   (E) 9,600

11. If a certain object has been moving at the constant rate of x meters per minute, how many meters has the object moved in the last y seconds?

(A)      (B)     (C)     (D)    (E) 60xy

12. A secretary typed 6 letters, each of which had either 1 or 2 pages. If the secretary typed 10 pages in all, how many of the letters had 2 pages?

(A) 1        (B) 2       (C)3        (D) 4       (E) 5

13. At 9:00 a.m. train T left the train station and two hours later train S left the same station on a parallel track. If train T averaged 60 kilometers per hour and train S averaged 75 kilometers per hour until S passed T , at what time time did S pass T ?

(A) 2:00 p.m.        (B) 5: 00 p.m.       (C)6:00 p.m.       (D) 7: 00 p.m.       (E) 9:00 p.m.

14. Seven cars were used to transport the members of a chess team to their match , and each car contained either 4 team members or 3 team members.

Column A : The total number of members on the chess team                Column B : 25

15. A train travels 60 miles per hour for 3 hours and then 45 miles per hour for 2 hours. What is the train’s average speed in miles per hour during the 5-hour period?

(A) 1        (B) 2       (C)3        (D) 4       (E) 5

16. Two people were hired to mow a lawn for a total of $45 . They completed the job with one person working for 1 hour and 20 minutes and the other working 40 minutes. If they split the $45 in proportion to the amount of time each spent working on the job, how much did the person who worked longer receive?

(A)    $33.75      (B) $30.00         (C) $27.50         (D)$25.00       (E) $22.50

17. In a certain country , a person is born every 3 seconds and a person dies every 10 seconds. Therefore , the birth and death rates account for a population growth rate of one person every

(A) 3  sec         (B) 4  sec        (C) 7 sec         (D) 11  sec       (E) 13 sec

18. The price of a pen is (10x + y ) cents, the price of a notebook is (10y + x ) cents, and the sum of the two prices is $1.43.

Column A : x                       Column B :  y

19.   If 15 pies cost a total of $11.50 , then at this rate , what is the cost of 9 pies?

(A)      $6.75       (B) $ 6.90         (C) $7.50          (D)$8.50          (E) $9.45  

20.   At the rate of 3,000 revolutions per minute , how many revolutions will a wheel make in k seconds ?

21.  On map X each centimeter represents 20 kilometers.

Column A : The actual distance, in kilometers, between two locations that  are 17 centimeters apart on map X

Column B :  300

21.   Pencils have the same unit unit cost regardless of the number sold. x pencils cost a total of $0.50 , and n pencils cost a total of y dollars.

Column A :n                            Column B :  2xy

22.   The daily rate for a hotel room that sleeps 4 people is $39 for one person and x  dollars for each additional person. If 3 people take the room for one day and each pays $21 for the room , what is the value of x?

(A) 6        (B) 8       (C)12        (D) 13       (E) 24

23. If a person  can save $380 in 5 weeks , in how many weeks, at this same rate , can the person save 2.6 times this amount?

(A) 13        (B) 12.5        (C) 11       (D) 10.6       (E) 8

24. A car travelling at a constant sped of 50 miles per hour k gallons of fuel each hour .

Column A : The number of gallons of fuel this car uses to travel 200 miles at a constant speed of 50 miles per hour.

Column B :  4k

25. A buzzer sounds every 15 minutes. If the buzzer sounded at 12:40 , which of the following could be a time at which the buzzer sounded?

(A) 4: 05         (B) 5: 30    (C) 6: 45        (D) 7: 15       (E) 8: 10

26. A  cyclist travels x miles in w hours and z minutes.What is the cyclist’s speed in miles per hour?

27. Maria purchased 3 pounds of candy X for $ 7.98 and 5 pounds of candy Y for $10.95.

Column A : The price Maria paid per pound for candy X

Column B :   The price Maria paid per pound for candy Y

28. A student can purchase a research report for $5.00, or reproduce the x pages of the report at accost of $0.15 per page.

Column A :  The greatest possible value of x if the cost of reproducing the x pages is less than the cost of purchasing the report

Column B :  34

29. Column A : The cost of x apples at a cost of y + 2 cents a piece

       Column B :  The cost of y oranges at a cost of x + 2 cents a piece

30. A watch gains 7 minutes and 6 seconds every 6 days. If the rate of gain is constant , how much does the watch gain in one day?

(A) 1 min 1 sec  (B) 1 min 6 sec (C) 1min 11 sec    (D) 1 min 16 sec  (E) 1 min 21 sec

31. The distance from point X to point Y is 20 miles, and the distance from point X to point Z is 12 miles. If d is the distance , in miles, between points Y and Z , then the range of possible values for d is indicated by

(A)  8  ≤  d  ≤ 20   (B) 8  ≤  d  ≤ 32   (C)12  ≤  d  ≤ 20   (D) 12  ≤  d  ≤ 32   (E) 20  ≤  d  ≤ 32

32. A machine packages milk at the rate of q quarts per hour.

  Column A : The number of hours required for the machine to package 5,000 quarts of milk

Column B : 8

33. The cost of 48 cans of soda is $20 .

Column A :  At the same rate, the cost, in dollars, of n of these cans of soda

Column B :  (0.24)n

34. A manufacturer packages soap powder in containers of three different sizes. The amount of soap powder in a full large container could fit exactly 3 of the medium containers or exactly 5 of the small containers . If an equal number of small and large containers are to be filled with the amount of soap powder that would fill 90 medium containers, how many small containers will be filled?

(A) 25        (B) 27        (C) 30       (D) 45       (E) 54

35. Each of the following numbers has two digits blotted out. Which of the numbers could be the number of hours in x days, where x is an integer?

(A) 25- , - 06        (B) 50- , -26      (C) 56-,-02       (D) 62-,-50        (E) 65-,-20

36. Team X scored 10 points in the first half of a certain game . In the second half of the game, team Y scored 15 points more than team X .

Column A :  The number of points scored by team X I the first half of the game

Column B : The number of points scored by team Y I the first half of the game.

37. Column A :  The cost of x pounds of meat at y dollars per pound

Column B :  The cost of y yards of material at x dollars per yard

38. Column A :   The cost per gram of carrots if 3 cans of carrots cost $0.90

Column B : The cost per gram of onions if 5 cans of onions cost $1.50

39. A certain car gets 24 miles per gallon of gasoline for city driving, which is 60 % of the number of miles per gallon of gasoline the car gets for highway driving.

Column A :  The number of gallons of gasoline used to drive this car 30 miles in the city

Column B :    The number of gallons of gasoline used to drive this car 45 miles on the highway

40.  Column A :  The number of minutes in y weeks

       Column B :   The number of hours in 60y weeks

41.  A certain writer noted that , on an average , 3 pages of a manuscript were equivalent to 1 page of the published book. If the writer has a 302-page manuscript , about how many pages will the published book have ?

(A)100         (B) 150        (C) 300       (D) 600       (E) 900\

42. The Acme Rent- a- car agency charges $10.00 per day and $0.10 per mile to rent a car. The super Rent-a- car agency charges $20.00 per day and $0.05 per mile to rent a car . If a car is rented for 1 day, at how many miles would the rental charges of the two agencies be equal?

(A) 50        (B) 100        (C) 150       (D) 175       (E) 200

43.  When Fred drives from his home to the nearest mountain resort, it takes 4 hours at an average speed of 50 miles per hour. When Fred drives from his home to beach house , it takes 3.5 hours at an average speed of 55 miles per hour.

Column A :  Fred’s driving distance  from his home to the nearest mountain resort

Column B :  Fred’s driving distance from his home to his beach house

44. At a grocery store Ray paid $1.85 for 5 pounds of potatoes and $1.29 for 3 pounds of apples.

Column A :  The amount Ray paid per pound for the potatoes

Column B : The amount Ray paid per pound for the apples

45. A certain form letter is to be sent to prospective customers .If 4 model-X computers working independently can do a combined total of  4 of the letters in 4 minutes, then 100  model-X computers working independently can do a combined total of 100  of the letters in exactly how many minutes?

 (A)  4 min         (B) 10 min         (C) 25 min       (D) 40 min      (E) 100 min

46. Column A :  The number of minutes in y weeks

Column B :   The number of hours in 60y weeks

47. A train travels from C ity X to City Y in 3 hours and 30 minutes at an average speed of 60 miles per hour. If the train returns at an average speed of 50 miles per hour, how long does the return trip take ?

(A) 2 hr 55 min      (B) 3 hr 40 min    (C) 4 hr 12 min   (D) 4 hr 32 min   (E) 4 hr 40 min

48. A certain store sells each pencil at the same price regardless of the number of pencils sold. K of these pencils have a total price  of q cents , and r of these pencils have a total price of s cents.

Column A :  ks                         Column B : qr

49. If 18 identical machines required 40 days to complete a job, how many fewer days would have been required to do the job if 6 additional machines of the same type had been used from the beginning?

  (A) 10           (B) 13         (C) 16      (D) 26        (E) 36

49. Toni bought n dozen eggs for $12 and m half gallons of milk for $6.

Column A  : The price Toni paid for a dozen eggs

Column B  : The price Toni paid for a half gallon of milk

50. A printer numbered consecutively the pages of a book, beginning with 1 on the first page .In numbering the  pages , he printed a total of 189 digits.

Column A : The number of pages in the book          Column B : 100

51. When  walking , a certain person takes 16 complete steps in 10 seconds. At this rate, how many complete steps does the person take in 72 seconds?

(A) 45         (B) 78        (C) 86       (D) 99       (E) 115

52. Working  at constant rates , machine R completely presses x records in 0.5 hour and machine S completely presses x records in 0.75 hour( x > 0)

Column A : The number of records completely pressed by R in 3 hours .

Column B  : The number of records completely pressed by S in 4  hours .

53. A spraying machine uses 5 full gallon buckets of fungicide every 20 minutes.

Column A: The number of gallons of fungicide the machine uses during 8 hours of spraying .

Column B : 720

54. A contractor can purchase paint at $19.50  per gallon or at the bulk rate of 20 gallons for $335.00

Column A: The amount saved per gallon by purchasing 20 gallons of the paint at the bulk rate rather than by the gallon

Column B: $2.75

55. A school district has 1,989 computers, which is approximately one computer for every 68.6 students. Of the following , which is the closest approximation of students in the school district?

(A) 30         (B) 120        (C) 140       (D) 160       (E) 200

56.  An emergency vehicle travels 10 miles at a speed of 50 miles per hour. How  fast must the vehicle on the return trip if the round- trip travel time Is to be 20 minutes?

(A) 55 mph     (B) 60 mph   (C) 65 mph    (D) 70 mph   (E) 75 mph

57.  For each of n people, Margie bought a hamburger and a soda at a restaurant .For each of n people, Paul bought 3 hamburgers and a soda at the same restaurant. If Margie spent a total of $5.40 and Paul spent a total of $12.60 , how much did Paul spent just for hamburgers ?  (Assume that all hamburgers cost the same and all sodas cost the same .)  

(A)  $ 10.80     (B) $ 9.60    (C) $7.20      (D) $3.60    (E) $2.40

58. If a certain company purchased its computer terminals for a total of $40,400 and each of the terminals was purchased for $350 , how many terminals did the company purchase?

(A) 1,624          (B) 1,544         (C) 1,434       (D) 1,384       (E) 1,264

59.  x copies of sports magazine X cost a total of $12.

Column A : The total cost, in dollars, of m copies of fashion magazine M

Column B : 100

60. Sue drives 10 miles from home to work. If she could average 50 miles per hour , how many minutes would it take her to drive from home to work?

(A)  20     (B) 18    (C) 15     (D) 12    (E) 10

61. Column A : The number of minutes it takes a car going 50 miles an hour to go 30 miles

       Column B :  The number of seconds  it takes  a car going 50 miles an hour to go 30 miles

  62. A time-study specialist has set the production rate for each worker on a certain job at 22 units every 3 hours. At this rate what is the minimum  number of workers that should be put on the job if atleast 90 units are to be produced per hour?

(A) 5         (B) 8        (C) 12       (D) 13       (E) 30

63 . Column A :  The number of hours to travel 1,500 miles at an average speed of 400 miles per hour.

Column B : The number of hours required to travel 200 miles at an average speed of 50 miles per hour

64.    Column A : The number of shares of stock X purchased for $1,581,000

Column B :  The number of shares of stock Y purchased for $1,603,000

65.   A certain photocopying machine can make 10 copies every 4 seconds. At this rate , how many copies can the machine make in 6 minutes?

(A)   900     (B) 600     (C) 360     (D) 240    (E) 150

66.   Worker W produces n units 5 hours. Workers  V and  W  , working independently but at the same time , produce n units in 2 hours. How long would it take V alone to produce n units?

(A)   1 hr 26 min      (B) 1 hr 53min    (C) 2 hr 30 min   (D) 3 hr 20  min   (E) 3 hr 30 min

67.                      Andy earns $5 per hour.

                   Susan earns $6 per hour.

Column A : The amount Andy earns in 6  hours.

Column B :   The amount Susan earns in 5    hours.

68.   The cost of strawberries is $0.45 per pint if piced by the customer and $1.25 per quart already picked(2 pints = 1 quart)

Column A : The cost of 8 quarts of strawberries picked by the customer.

Column B : The cost of 6 quarts of strawberries already picked