Classroom Exercises #8 Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Decide whether the statement is true or false.
1) The greatest common factor of two relatively prime numbers is always 1.
A) True
B) False
1)
2) The greatest common factor of a group of natural numbers is the largest natural number that is
a factor of all the numbers in a group.
A) True
B) False
2)
3) Greatest common factors can not be found by using prime factorization, only by using the
division method.
A) True
B) False
3)
4) Two natural, relatively prime numbers have at most one common factor.
A) True
B) False
4)
5) The set of all common multiples of two given whole numbers is finite.
A) True
B) False
5)
6) Two composite numbers can never be relatively prime.
A) True
B) False
6)
7) The least common multiple of p and q cannot be larger than pq.
A) True
B) False
7)
8) If the least common multiple of p and q is smaller than pq, then p and q have a common factor
other than 1.
A) True
B) False
8)
Find the greatest common factor of the numbers in the group.
9) 44, 63
A) 77
B) 22
C) 6
9)
D) 1
10) 50, 60
A) 2
B) 5
C) 1
D) 10
11) 120, 90
A) 30
B) 6
C) 10
D) 15
12) 240, 2700
A) 60
10)
11)
12)
B) 240
C) 180
1
D) 30
13) 16, 32, 36
A) 8
13)
B) 1
C) 16
D) 4
14) 30, 40, 70
A) 2
14)
B) 5
C) 10
D) 20
15) 120, 2000, 11,250
A) 30
B) 50
C) 10
D) 20
15)
16) 1562, 450, 6750
A) 5
16)
B) 2
C) 12
D) 4
17) 8, 20, 24, 32
A) 1
B) 8
C) 4
D) 2
17)
Find the least common multiple of the numbers in the group.
18) 60, 30
A) 60
B) 30
C) 180
18)
D) 120
19) 8, 44
A) 88
19)
B) 352
C) 44
D) 22
20) 48, 162, 9
A) 648
B) 432
C) 1296
D) 324
20)
21) 112, 96
A) 224
B) 336
C) 1344
D) 672
22) 30, 80, 50
A) 3
B) 600
C) 1200
D) 240
23) 45, 56, 150
A) 1260
24) 43,378, 4715
A) 216,890
21)
22)
23)
B) 12,600
C) 1,050
D) 2520
24)
B) 9430
C) 10
D) 943
Answer the question.
25) Planets A, B, and C orbit a certain star once every 3, 7, and 18 months, respectively. If the three
planets are now in the same straight line, what is the smallest number of months that must
pass before they line up again?
A) 28 months
B) 378 months
C) 54 months
D) 126 months
2
25)
26) Bobʹs frog travels 5 inches per jump, Kimʹs frog travels 8 inches and Jackʹs frog travels 13
inches. If the three frogs start off side-by-side, what is the smallest distance they must all
travel before they are side-by-side again?
A) 26 inches
B) 520 inches
C) 40 inches
D) 104 inches
26)
27) A brick layer is hired to build three walls of equal length. He has three lengths of brick, 4
inches, 12 inches, and 10 inches. He plans to build one wall out of each type. What is the
shortest length of wall possible?
A) 26 inches
B) 60 inches
C) 120 inches
D) 480 inches
27)
28) Three taxi cabs make a complete trip from downtown to the airport and back in 14, 26 and 91
minutes, respectively. If all three cabs leave at the same time, what is the shortest time that
must pass before they are all together again?
A) 2366 minutes
B) 364 minutes
C) 182 minutes
D) 131 minutes
28)
29) Three clocks chime every 14 minutes, 22 minutes, and 77 minutes, respectively. If the three
clocks chime together, how much time must pass before they will chime together again?
A) 113 minutes
B) 1694 minutes
C) 154 minutes
D) 308 minutes
29)
30) Jack has 92 hot dogs and 76 hot dog buns. He wants to put the same number of hot dogs and
hot dog buns on each tray. What is the greatest number of trays Jack can use to accomplish
this?
A) 4
B) 46
C) 2
D) 437
30)
31) Two runners run around a circular track. The first runner completes each lap in 6 minutes. The
second runner completes each lap in 16 minutes. If they both start at the same place and the
same time and go in the same direction, after how many minutes will they meet again at the
starting place?
A) 97
B) 192
C) 96
D) 22
31)
32) Several different bus routes stop at the corner of Second St. and Lincoln Ave. A Wilkenson bus
arrives every 21 minutes and a Harris Road bus arrives every 15 minutes. If both buses arrive
at the stop at 5:07 AM, when will they again arrive at the same time?
A) 10:22 AM
B) 8:22 AM
C) 6:12 AM
D) 6:52 AM
32)
33) At Northwest High School, there are 459 students in the Junior Class and 663 students in the
Senior Class. To let the juniors work with more experienced students, the teachers want to
assign the students to committees with the same number of juniors in each committee and the
same number of seniors in each committee. (For example, there might be 2 juniors and 3
seniors in every committee). What is the largest number of committees that can be formed?
A) 51 committees
B) 153 committees
C) 17 committees
D) 3 committees
33)
3
Answer Key
Testname: SPRING 2011 EXTRA CREDIT #8 MATH 2008 CHAPTER 11
1) A
2) A
3) B
4) A
5) B
6) B
7) A
8) A
9) D
10) D
11) A
12) A
13) D
14) C
15) C
16) B
17) C
18) A
19) A
20) C
21) D
22) C
23) B
24) A
25) D
26) B
27) B
28) C
29) C
30) A
31) C
32) D
33) A
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