MTH-2215 APPLIED DISCRETE MATHEMATICS QUIZ
WITH ANSWERS #12
Suppose a "for" loop in algorithm takes 2,300 passes for a particular set of input.
Subsequent to these passes, it terminates, and then another "for" loop takes 4,500
passes. Then there are 6,800 passes total. - correct answer True
Let's say that Sue wants the password on her computer to NOT begin with "Sue." Let's
also say that a password must be of length 20. Each character in the password can be
any digit 0,1,2,...,9, an uppercase letter, a lowercase letter, and the passwords are case
sensitive. Then the number of passwords that meet Sue's requirements can be
determined by computing 62^17. - correct answer False
The 2-permutations of the set {a,r,t} are ar, ra, at, ta, rt, and tr. - correct answer True
Determine the value of C(5,3). - correct answer 10
The number of ternary strings of length 5 can be determined by computing 5^3. - correct
answer False
The list of all the 2-combinations of the set {m,a,t,h} is ma, mt, mh, and ah. - correct
answer False
To determine the number of ways a President, Vice-President, Secretary, Treasurer,
and Song Leader for a club can be chosen for a club that has 50 members, one could
compute the value of P(50,5). - correct answer True
Suppose there are 100 cans of green beans in a grocery store, and 25 of these are
"Best Deal" brand green beans. How many ways are there to choose a can of green
beans at this grocery store that are not the "Best Deal" brand? - correct answer 75
Suppose a set S1 has 50 elements and that S2 has 40 elements. There are also 10
elements common to S1 and S2. How many elements are in the union of the sets S1
and S2? - correct answer 80
Suppose a password must contain 2 characters, where a character can be any of the
digits 1,2,3,4,5 or any lowercase letter. Then to compute the number of possible
passwords, one would compute 31^2. - correct answer True
Suppose that, at a university, the Mathematics Department has two clubs, a Theoretical
Math Club, and an Applied Math Club. Let's say that there are 30 Theoretical Math Club
members, 20 Applied Math Club members, and 5 members of both clubs. Then there
are 50 people that are members of the Theoretical Math Club, Applied Math Club, or
both clubs. - correct answer False
, Suppose a password for an online banking system must have 10 characters, and the
characters be any digit 0,1,2,...,9, an uppercase letter, or lowercase letter, and the
passwords are case sensitive (meaning that, for example, the password A123456789 is
different than the password a123456789). Then, to determine the number of possible
passwords, one could compute 62^10. - correct answer True
Determine the value of P(3,2). - correct answer 6
Suppose we have the following scheme for passwords: Each password must be of
length 4, 5, or 6. The first character of each password must be a digit 0,1,2,...,9. The
remaining characters can be any digits 0,1,2,...,9, an uppercase letter, or a lowercase
letter; the passwords are case sensitive. Then, to determine the number of possible
passwords, one could compute 62^4 + 62^5 + 62^6. - correct answer False
Suppose that a store sells two types of golf balls, namely, brand "Hit it far" and brand
"Lots of Spin." There are 15 boxes of "Hit it far" golf balls and 7 boxes of "Lots of Spin"
golf balls. How many ways are there to select a box of golf balls? - correct answer 22
Suppose we were to perform a trace of the algorithm presented in the textbook to
convert 110002 to base 10. Then, we would name the input a4=1, a3=1, a2=0, a1=0,
and a0=0; also n = 4. - correct answer true
Suppose we were to perform a trace of the algorithm presented in the textbook to
convert 110002 to base 10. What is the value of the variable "sum" after passing
through the i = 2 stage of the "for" loop? - correct answer 0
Convert 150base10 to base 2. - correct answer 10010110
The base 16 integer CAB16 converted to base 10 is 4423. - correct answer false
Convert 1111101base2 to base 16. - correct answer 7D
More than one of the following are true. Choose the ones that are true. - correct answer
5!=120 5!=5x4x3x2x1x0! 5!=5x4!
In tracing the Recursive Fibonacci Sequence Algorithm, the value of the term F6 would
work out to be 13. - correct answer false
In performing a trace of the Recursive Euclidean Algorithm to compute the gcd of a = 12
and d = 8 (using the naming conventions presented in the pseudocode), which of the
following best represents what the output of the algorithm would be? - correct answer 4
Suppose that, in performing a trace of the Recursive Euclidean Algorithm on 20 and 12,
if we set a = 20 and d = 12, per the naming conventions in the pseudocode. When we
first go into the "If" condition where it states "If a mod d = 0," then the statement "20
mod 12 = 0" has what truth value? - correct answer false
WITH ANSWERS #12
Suppose a "for" loop in algorithm takes 2,300 passes for a particular set of input.
Subsequent to these passes, it terminates, and then another "for" loop takes 4,500
passes. Then there are 6,800 passes total. - correct answer True
Let's say that Sue wants the password on her computer to NOT begin with "Sue." Let's
also say that a password must be of length 20. Each character in the password can be
any digit 0,1,2,...,9, an uppercase letter, a lowercase letter, and the passwords are case
sensitive. Then the number of passwords that meet Sue's requirements can be
determined by computing 62^17. - correct answer False
The 2-permutations of the set {a,r,t} are ar, ra, at, ta, rt, and tr. - correct answer True
Determine the value of C(5,3). - correct answer 10
The number of ternary strings of length 5 can be determined by computing 5^3. - correct
answer False
The list of all the 2-combinations of the set {m,a,t,h} is ma, mt, mh, and ah. - correct
answer False
To determine the number of ways a President, Vice-President, Secretary, Treasurer,
and Song Leader for a club can be chosen for a club that has 50 members, one could
compute the value of P(50,5). - correct answer True
Suppose there are 100 cans of green beans in a grocery store, and 25 of these are
"Best Deal" brand green beans. How many ways are there to choose a can of green
beans at this grocery store that are not the "Best Deal" brand? - correct answer 75
Suppose a set S1 has 50 elements and that S2 has 40 elements. There are also 10
elements common to S1 and S2. How many elements are in the union of the sets S1
and S2? - correct answer 80
Suppose a password must contain 2 characters, where a character can be any of the
digits 1,2,3,4,5 or any lowercase letter. Then to compute the number of possible
passwords, one would compute 31^2. - correct answer True
Suppose that, at a university, the Mathematics Department has two clubs, a Theoretical
Math Club, and an Applied Math Club. Let's say that there are 30 Theoretical Math Club
members, 20 Applied Math Club members, and 5 members of both clubs. Then there
are 50 people that are members of the Theoretical Math Club, Applied Math Club, or
both clubs. - correct answer False
, Suppose a password for an online banking system must have 10 characters, and the
characters be any digit 0,1,2,...,9, an uppercase letter, or lowercase letter, and the
passwords are case sensitive (meaning that, for example, the password A123456789 is
different than the password a123456789). Then, to determine the number of possible
passwords, one could compute 62^10. - correct answer True
Determine the value of P(3,2). - correct answer 6
Suppose we have the following scheme for passwords: Each password must be of
length 4, 5, or 6. The first character of each password must be a digit 0,1,2,...,9. The
remaining characters can be any digits 0,1,2,...,9, an uppercase letter, or a lowercase
letter; the passwords are case sensitive. Then, to determine the number of possible
passwords, one could compute 62^4 + 62^5 + 62^6. - correct answer False
Suppose that a store sells two types of golf balls, namely, brand "Hit it far" and brand
"Lots of Spin." There are 15 boxes of "Hit it far" golf balls and 7 boxes of "Lots of Spin"
golf balls. How many ways are there to select a box of golf balls? - correct answer 22
Suppose we were to perform a trace of the algorithm presented in the textbook to
convert 110002 to base 10. Then, we would name the input a4=1, a3=1, a2=0, a1=0,
and a0=0; also n = 4. - correct answer true
Suppose we were to perform a trace of the algorithm presented in the textbook to
convert 110002 to base 10. What is the value of the variable "sum" after passing
through the i = 2 stage of the "for" loop? - correct answer 0
Convert 150base10 to base 2. - correct answer 10010110
The base 16 integer CAB16 converted to base 10 is 4423. - correct answer false
Convert 1111101base2 to base 16. - correct answer 7D
More than one of the following are true. Choose the ones that are true. - correct answer
5!=120 5!=5x4x3x2x1x0! 5!=5x4!
In tracing the Recursive Fibonacci Sequence Algorithm, the value of the term F6 would
work out to be 13. - correct answer false
In performing a trace of the Recursive Euclidean Algorithm to compute the gcd of a = 12
and d = 8 (using the naming conventions presented in the pseudocode), which of the
following best represents what the output of the algorithm would be? - correct answer 4
Suppose that, in performing a trace of the Recursive Euclidean Algorithm on 20 and 12,
if we set a = 20 and d = 12, per the naming conventions in the pseudocode. When we
first go into the "If" condition where it states "If a mod d = 0," then the statement "20
mod 12 = 0" has what truth value? - correct answer false
