34. Find the square root of 3534400.5. 35. A platform bears a weight of 100 lb. per square foot; what is the weight in kilograms per square meter? 36. A horse that cost 6 per cent of $25000, was sold for $1000; what was the loss per cent? College of City of New York, 1880, '81. 37. Reduce of 4 of 11 to a decimal, carrying out the operation to four places. 38. If two men, working 8 hours, can carry 12000 bricks to the height of 50 feet, how many bricks can one man, working 10 hours, carry to the height of 30 feet? 39. I buy goods to the amount of $4,978.70, payable in 4 mo., with interest at 5%, and give my note without interest. What must be the face of the note ? 40. A man lost 1, 1, and of his money, and then had $2600 left; what sum had he originally, and how much per cent had he lost? 41. Sold a fire engine for $7050, and lost 6% on its cost; for how much ought I to have sold it to gain 12% ? 42. What sum of money put at interest 6 yr. 5 mo. 11 da., at 7%, will gain $3159.14? 43. For what sum must a note be drawn at 60 days to net $1200 when discounted at 5% ? 44. Extract the square root of 3286.9835 to the fourth decimal place. 45. Extract the cube root of 30.625. Amherst College, 1881. 46. Find the greatest common divisor of 1263 and 1623. 47. Find the least common multiple of 18, 24, 36, and 126. 48. A cable that weighs one ton per mile weighs how much per foot? 49. When it is 10 o'clock in Boston what time is it in Amherst, the longitude of Boston being 71° 7' 45" W. from Greenwich, that of Amherst being 72° 31' 50"? 50. Reduce 1 hr. 25 min. 30 sec. to the decimal of a day. 51. Of what number is the part? 52. What must be the face of a note which discounted at a bank at 6% for 30 days and grace, would yield $200 ? 53. Sold a house for $5000 and thereby gained 20%. Should I have gained or lost, and how much per cent, if I had sold it for $4000 ? 54. Find the square root of 5.6169. 55. The meter is 39.37 inches. Find how many kilometers there are in a mile. 57. Multiply 48 ten thousandths by two and one thousandth, and divide the result by one million. 58. Express 462 mm. in higher denominations. 59. What is % of 140 books? What per cent of 30 ft. is 25 inches? 60. If I lose 10% by selling goods at 28 cents per yard, for what should they be sold to gain 20%? 61. What principal will yield an interest of $339.20 in 5 yr. 4 mo. at 6% ? 62. What must be the length of a box, 1 meter wide and 1 meter deep, to contain 4500 liters ? 63. Cube .01. Square 1.001. 64. Extract the square root of 4.932841. 65. A can do a piece of work in 10 days; A and B can do the same work together in 7 days; in how many days can B working alone do the work? New York Normal College, 1880. 66. What will it cost to floor a room 17 ft. long and 16 ft. wide, at the rate of $1.10 per sq. yd.? 67. A man has a capital of $12500; he puts 15% of it in stocks, 33% in land, and 25% in mortgages; how many dollars has he left? 68. A grocer bought 500 bags of coffee, each bag containing 494 pounds, at 12 cents a pound, and sold at a profit of 16%; for what did he sell it? 69. If I buy a house for $5620 and receive $1803 for rent in 2 yr. 3 mo. 15 da., what rate of int. do I get for my money? 70. Find the face of a note payable in 90 da. at 7%, so that the proceeds shall be $2050 ? 71. A merchant owes $2400, of which $400 is payable in 6 mo., $800 in 10 mo., and $1200 in 16 mo.; what is the equated time? 72. If it costs $7.20 to transport 181 cwt. 5 miles, what will it cost to transport 1123 tons 62 miles? 73. Extract the square root of 1051 to three places of decimals. 74. What is the cube root of 403583419 ? Cornell University, 1880, 75. What is the value of 50 lb. 8 oz. of gold, at $20.591 per ounce? 76. Given the metre equal to 39.37 inches, reduce one mile to kilometers. Give the metric table of weights. 77. Divide of 74 by 4 of 1211. Prove the result by reducing the fractions to decimals and working the example anew. 78. How long must $125 be on interest at 7 per cent to gain $15? 79. Received 6 per cent dividend on stock bought at 25 per cent below par; what rate of interest did the investment pay ? 80. How many liters in 20 bu. 3 pk. 4 qt., the bushel being 2150.42 cubic inches, and the metre 39.37 inches? 82. If one kilometer equals five-eighths of a mile, how many turns will a wheel make in 20 miles, the circumference of the wheel being 4 meters 5 millimeters? 83. What is the difference between the true and bank discount of $250, due 10 mo. hence, at 7%? 84. If 8 men spend $32 in 13 weeks, what will 24 men spend in 52 weeks? Trinity College, 1880. 85. Subtract thirty million twenty-six thousand three from 45007021. Find what number must be added to the difference to make one hundred million, and write the answer in words. 86. The sum of and is diminished by. How many times does the difference contain of the sum of 1,, and ? 87. Divide 375 by .75, and .75 by 375, and find the sum and the difference of the quotients. 88. A loaded wagon weighs 2 T. 3 cwt. 48 lb.; the wagon itself weighs 18 cwt. 75 lb. The load consists of 215 packages, each of the same weight. Find the weight of each, and reduce it to grams and kilograms. 89. Define interest, and give and explain the rule for computing the interest on any sum of money, for any time, and at any rate per cent. 90. Extract the square root of 184.2 to 3 decimals. 91. How many hektoliters of oats can be put into a bin that is 2 meters long, 1.3 meters wide, and 1.5 meters deep? 92. Add Wesleyan University, 1881. of 21 21 +31 93. If money is worth 3 per cent, what is the premium on government 3 per cent bonds? 94. How many liters in 6 gallons of water? 95. How many cords of stone will it take to build a wall 2 ft. thick and 6 ft. high about a rectangular cellar whose interior dimensions, when the wall is completed, shall be 20 ft. long and 16 ft. wide? 96. How long must a note of $243, at 34%, run that its interest may equal the int. on a note of $125, for 7 mo., at 5%? 97. Multiply √2 by √.123, and carry the result to 3 decimals. 98. Reduce 5 mi. 3 fur. 10 rd. to kilometers. 99. If 5 horses will consume 8 bu. 1 pk. 6 qt. of oats in 6 da., what quantity of oats will 7 horses consume in 11 da.? 860. The Roman Notation is the method of expressing numbers by seven capital letters, viz. : D, M. 1000. I, V, X, L, C, 861. To express other numbers, these letters are combined 862. The Roman Notation is based upon the following general principles: 1st. Repeating a letter repeats its value. Thus, I denotes one; II, two; III, three; X, ten; XX, twenty, etc. 2d. Placing a letter of less value before one of greater value, diminishes the value of the greater by that of the less; placing - the less after the greater, increases the value of the greater by |