GRADE 7 MATHEMATICS

Practice Test I

Direction: Solve each item and write the answer on the provided answer sheet.

1. Let A= { a,b ,c,d ,e } , B={ a ,e ,i ,o ,u } , and C={ e, f , g , h , i } . Find

( A∩B ) ∪( B∩C ) .

2. Let universal set U be { 1,2,3,...,20 } . If S= {2,4,6,8 ,10 ,12 } , E= { 3,6,9,12,15,18 }

, and T={ 15,16 ,17,18,20 } , find ( S∪E∪T ) . ' .

3. Let the universal set U be the set of all prime numbers less than 20, A= { x|x is a
prime factor of 210 } , B={ x|x is a prime greater than 10 } , and C={ 3,19 } .
Find A '∩ ( B∩C ) .' .

4. Given Set A= { x|x is a perfect square . } ; B={ y|y is a factor of 63 . } ;

C={ z|z is a positive odd integer . } . Find A∩B∩C .
5. In Math Department of a school, 10 teachers have Yahoo! Accounts, 13 have Gmail
accounts, and 6 have both accounts. How many teachers in the department have
Yahoo! Or Gmail accounts?
6. In a class of 40 students, 27 like Math and 25 like Filipino. At most how many
students do not like at least one of these subjects?
7. A class of 47 students took examinations in Algebra and in Geometry. If 29 passed
Algebra, 26 passed Geometry, and 4 failed both subjects, how many passed both
subjects?
1. If we begin adding the positive integers consecutively, 1 + 2 + 3 + …, and we stop
when our sum is greater than or equal to 2004, what was the last integer we added?
2. If it is 10 a.m. now, what time will it be in 2004 hours?
3. If the number 150 is increased by 40%, and if that result is then decreased by 40%,
what is the final result?
4. When a certain positive number is added to its square, the result is 56. What is that
number?
5. How many days, hours, minutes, and seconds is 1,000,000 seconds? Your number of
hours must be less than 24, and your number of minutes and seconds must be less
than 60.
6. The speed of light is approximately 3 X 10 8 meters per second. The distance from
Earth to Mars today is 3 x 108 meters. How long, in minutes and seconds, would it
take a signal traveling at the speed of light to go from Earth to Mars?
7. If one pint of paint is needed to paint a statue that is 6 feet high, how many pints of
paint are needed to paint (to the same thickness) 540 statues similar to the original
statue but only 1 foot high?
8. How many counting numbers less than 200 are divisible by all of the numbers 2, 3, 4,
and 5?
9. A store prices an item in dollars and cents so that when 4% sales tax is added, the
total price is n dollars, where n is an integer. What is the smallest value of n possible?
10. A reduction of 10%, followed by a reduction of 20%, is equivalent to a single
reduction of how much?
11. The perfect squares are the elements of the set {1, 4, 9, 16, …}. If x is a perfect
square, what is the next perfect square?
12. What is the number of circular pipes with an inside diameter of 1 inch that will carry
the same amount of water as a single circular pipe with an inside diameter of 6
inches?
13. A bicyclist went up a hill at 10 miles per hour, and down at 20 miles per hour. What
was the average speed for the entire trip?
14. The number 120 has sixteen positive integer divisors. What is the sum of these
divisors?
15. A dog and a wolf, eating together, can devour a deer in four hours. The dog, eating
alone, could have devoured the deer in eight hours. How many hours would it have
taken the wolf, eating alone, to devour the deer?
16. What is the sum of the integers between 50 and 350 which end in 1?
17. What is the largest prime factor of 7425?
18. What is the smallest integer greater than 1 that is both a perfect square and a perfect
cube?
19. If there are 231 cubic inches in a gallon, how many gallons of water are there in a
pool that is 7 feet wide, 22 feet long, and 5 feet deep?
20. Three children divided a box of cookies. One child got half the cookies, another child
got one-third of the cookies, and the third child got eight cookies. How many cookies
were in the box altogether?
21. Pat has 6 shirts, 3 pairs of slacks, and 2 vests. How many different three-piece outfits
can Pat wear?
22. A standard biscuit recipe requires flour and milk in the ratio 5 to 2. How many cups
of milk should be used along with 8 cups of flour?
23. In a group of 40 students, 25 are taking Spanish and 22 are taking History, while 15
are in both of these classes. How many of these 40 students are taking neither Spanish
nor History?
24. I programmed my computer to print out all of the integers from 1 to 1000. How many
times did the digit 7 get printed?
25. A mysterious old house has seven rooms. Each room is connected to every other
room by a secret passageway. If each passageway leads only to the two rooms that it
directly connects, how many such secret passageways must there be?
26. What is the smallest positive number that leaves a remainder of 1 when it is divided
by 2, a remainder of 2 when it is divided by 3, and a remainder of 3 when it is divided
by 4?
27. What positive number is three times as big as its reciprocal?
28. The sum of two numbers is 10. Their product is 15. What is the sum of their
reciprocals?
29. Tom can paint a fence in 3 hours. Becky can paint the same fence in 4 hours. But it
takes Huck 6 hours to do the same job. How many hours will it take all three working
together to paint the fence?
30. Lin and Vin are running on an oval track. They start together, but run in opposite
directions. In the time it takes Lin to run 5 laps, Vin runs 7 laps. Not counting the
beginning and ending of their run, how many times do Lin and Vin pass each other
during the run?
31. The parking lot at the local playground is filled with bicycles and tricycles. If the lot
has 70 wheels and 58 pedals, how many tricycles are there?
32. At a road rally, a car makes an uphill run at a speed of 50 miles per hour. How fast
will it have to come back down the hill in order for its average speed over both
directions to be 60 miles per hour?
33. The sum of the integers from 1 to 25 is 325. What is the sum of the even integers
from 2 to 50?
34. 30% of 55 is 66% of what number?
35. What is the remainder when 789 is divided by 123?
36. What is the largest integer that evenly divides 210, 280, and 336?
37. If the number 40 is increased by 40%, and if that result is then decreased by 40%,
what is the final result?
38. When a certain positive number is subtracted from its square, the result is 420. What
is that number?
39. A department store opened one morning at 6:30 for its annual 1,000 minute sale.
What time did the sale end that evening?
40. Two-thirds of fifty-five is five-sixths of what number?

7
41. What number is of the way from 30 to 84?
9

42. The sum of the integers from 1 to 100 is 5050. What is the sum of the odd integers
from 1 to 99?
43. What is the remainder when 6789 is divided by 1234?
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44. What number is of the way from 300 to 498?
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45. The number 100 has nine distinct positive integer divisors. What is the sum of all
these divisors?
46. A certain number, when subtracted from its own cube, leaves a difference of 13 1/8 .
What is this number?
47. A ship leaves port at noon and sails at a constant speed of 12 knots. A second ship
leaves the same port two hours later and sails on the same course at a speed of 15
knots. At what time will the second ship overtake the first?
48. Tickets for the school play cost $3.50 for students and $5.00 for adults. We sold 120
tickets altogether and took in $501. How many adult tickets were sold?
49. Solve for x in the equation 32x + 3x+1 = 10.
50. There is only one prime number whose square evenly divides 86394. What is this
prime number?
51. How many positive three-digit integers are there that do not contain the digit 7?
52. Two classes took the same test. One class of 20 students had an average grade of
84%; the other class of 30 students had an average grade of 74%. What was the
average grade for all the students in both classes?
53. The integer 8000 is a perfect cube. What is the next largest perfect cube?
54. What two-digit integer yields an increase of 20% when its digits are interchanged?
55. A temperature increase of 9 degrees on the Fahrenheit scale corresponds to an
increase of 5 degrees Celsius. To how many degrees Fahrenheit does an increase of
20 degrees Celsius correspond?
56. Radio signals travel through space at 186,000 miles per second. How many minutes
does it take a radio signal from Earth to reach the Cassini spacecraft at Saturn,
781,200,000 miles away?
57. A certain orchard has 16 rows of trees. There are 20 trees in the first row, 21 trees in
the second row, and so forth. (Each succeeding row has one more tree than the
previous row.) How many trees are in the orchard altogether?
58. A solid wooden cube measuring 3 inches on a side has 1x1 inch square holes bored all
the way through at the centers of each face, as shown. How many cubic inches of
wood remain after the holes are bored?
59. The old professor began school at the age of 6, and spent 30% of his life getting an
education. He then devoted 45% of his life to the teaching of mathematics. If he has
been retired for 12 years now, how old is the professor?
60. The integer 9261 is a perfect cube. What is the next largest perfect cube?
61. On my last trip I drove the first 30 miles in the country at 60 miles per hour. Then I
reached the city and drove another 30 miles but at 40 miles per hour. What was my
average speed, in miles per hour, for this trip?
62. The product of two real numbers is 5, and the sum of their reciprocals is 2. What is
the sum of the two numbers?
63. My lucky number consists of the digit 6 written 500 times. What is the remainder
when my lucky number is divided by 9 ?
64. For a certain set of 12 distinct numbers, which includes the number 47, the average
value
65. will decrease by 3 if 47 is removed from the set. What is the average of all 12 of these
numbers?
66. What is the value of the repeating decimal 0.123123123… written as a fraction in
lowest terms?
67. If it is 10 a.m. now, what time will it be in 2004 hours?
68. If the number 150 is increased by 40%, and if that result is then decreased by 40%, what
is the final result?
69. The speed of light is approximately 3 x 10 8 meters per second. The distance from Earth to
Mars today is 3 x 10 11 meters. How long, in minutes and seconds, would it take a signal
traveling at the speed of light to go from Earth to Mars?
70. If one pint of paint is needed to paint a statue that is 6 feet high, how many pints of paint
are needed to paint (to the same thickness) 540 statues similar to the original statue but
only 1 foot high?
71. A reduction of 10%, followed by a reduction of 20%, is equivalent to a single reduction
of how much? Express your answer as a percentage.
72. A bicyclist went up a hill at 10 miles per hour, and down at 20 miles per hour. What was
the average speed for the entire trip?
73. The number 120 has sixteen positive integer divisors. What is the sum of these divisors?
74. What is the sum of the integers between 50 and 350 which end in 1?
75. A certain circle has its area numerically equal to its circumference. What is the radius of
this circle?
76. What is the largest prime factor of 7425?
77. What is the smallest integer greater than 1 that is both a perfect square and a perfect
cube?
78. If there are 231 cubic inches in a gallon, how many gallons of water are there in a pool
that is 7 feet wide, 22 feet long, and 5 feet deep?
79. Three children divided a box of cookies. One child got half the cookies, another child got
one-third of the cookies, and the third child got eight cookies. How many cookies were in
the box altogether?
80. A standard biscuit recipe requires flour and milk in the ratio 5 to 2. How many cups of
milk should be used along with 8 cups of flour?
81. What positive number is three times as big as its reciprocal?
82. Tom can paint a fence in 3 hours. Becky can paint the same fence in 4 hours. But it takes
Huck 6 hours to do the same job. How many hours will it take all three working together
to paint the fence?
83. The parking lot at the local playground is filled with bicycles and tricycles. If the lot has
70 wheels and 58 pedals, how many tricycles are there?
84. At a road rally, a car makes an uphill run at a speed of 50 miles per hour. How fast will it
have to come back down the hill in order for its average speed over both directions to be
60 miles per hour?
85. The sum of the integers from 1 to 25 is 325. What is the sum of the even integers from 2
to 50?
86. 30% of 55 is 66% of what number?
87. What is the remainder when 789 is divided by 123?
88. What is the cube root of 941,192?
89. What is the largest integer that evenly divides 210, 280, and 336?
90. If the number 40 is increased by 40%, and if that result is then decreased by 40%, what is
the final result?
91. Two-thirds of fifty-five is five-sixths of what number?
9
92. What number is of the way from 30 to 84?
7
93. The sum of the integers from 1 to 100 is 5050. What is the sum of the odd integers from 1
to 99?
94. The number 100 has nine distinct positive integer divisors. What is the sum of all these
divisors?
95. There is only one prime number whose square evenly divides 86394. What is this prime
number?
96. A travel agency wants to take 65 people on a tour of the redwoods. Their tour vans carry
14 passengers apiece. How many tour vans will they need?
97. Two classes took the same test. One class of 20 students had an average grade of 84%;
the other class of 30 students had an average grade of 74%. What was the average grade
for all the students in both classes?
98. What two-digit integer yields an increase of 20% when its digits are interchanged?
99. A temperature increase of 9 degrees on the Fahrenheit scale corresponds to an increase of
5 degrees Celsius. To how many degrees Fahrenheit does an increase of 20 degrees
Celsius correspond?
100. 45% of 70 is 70% of what number?
101. The sum of two integers is 59. If the larger is divided by the smaller, the
quotient is 2 and the remainder is 8. What is the larger number?
102. A laboratory contains two 8-ounce beakers, labeled A and B. A contains 5
ounces of a 50% alcohol solution; B contains 6 ounces of a 30% alcohol solution. If a
lab worker pours as much liquid as possible from A into B, stirs thoroughly, and then
pours as much as possible from B into A, what will be the percent of the alcohol
solution in A?